{ "cells": [ { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "from ragas.llms import LangchainLLMWrapper\n", "from ragas.embeddings import LangchainEmbeddingsWrapper\n", "from langchain_openai import ChatOpenAI\n", "from langchain_openai import OpenAIEmbeddings\n", "from langchain.document_loaders import PyMuPDFLoader\n", "from langchain_community.document_loaders import DirectoryLoader\n", "\n", "import os\n", "\n", "# Create data/ragas directory if it doesn't exist\n", "if not os.path.exists(\"data/ragas\"):\n", " os.makedirs(\"data/ragas\", exist_ok=True)\n", "\n", "\n", "\n", "loader = PyMuPDFLoader(\"rag-data/PracticalAdviceOnMatrixGames.pdf\", mode='single')\n", "docs = loader.load()\n", "# loader = PyMuPDFLoader(\"data/John Curry, Tim Price - Matrix Games for Modern Wargaming-History of Wargaming Project (2014).pdf\", mode='single')\n", "# docs.extend(loader.load())\n", "\n", "generator_llm = LangchainLLMWrapper(ChatOpenAI(model=\"gpt-4.1-nano\"))\n", "generator_embeddings = LangchainEmbeddingsWrapper(OpenAIEmbeddings())" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " % Total % Received % Xferd Average Speed Time Time Time Current\n", " Dload Upload Total Spent Left Speed\n", "100 137k 0 137k 0 0 229k 0 --:--:-- --:--:-- --:--:-- 229k\n", " % Total % Received % Xferd Average Speed Time Time Time Current\n", " Dload Upload Total Spent Left Speed\n", "100 82375 0 82375 0 0 419k 0 --:--:-- --:--:-- --:--:-- 418k\n" ] } ], "source": [ "!curl https://paxsims.wordpress.com/2014/09/21/toward-serious-matrix-games/ -o data/toward-serious-matrix-games.html\n", "!curl https://sites.google.com/view/free-engle-matrix-games/how-to-play-matrix-games -o data/how-to-play-matrix-games.html" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "loader = DirectoryLoader(\"rag-data/\", glob=\"*.html\")\n", "docs.extend(loader.load())" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "loader = DirectoryLoader(\"rag-data/\", glob=\"*.txt\")\n", "docs.extend(loader.load())" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[Document(metadata={'producer': 'Microsoft® Word 2016', 'creator': 'Microsoft® Word 2016', 'creationdate': '2023-01-01T15:29:59+00:00', 'source': 'data/PracticalAdviceOnMatrixGames.pdf', 'file_path': 'data/PracticalAdviceOnMatrixGames.pdf', 'total_pages': 52, 'format': 'PDF 1.7', 'title': '', 'author': 'Jim Dawson', 'subject': '', 'keywords': '', 'moddate': '2023-01-01T15:29:59+00:00', 'trapped': '', 'modDate': \"D:20230101152959+00'00'\", 'creationDate': \"D:20230101152959+00'00'\"}, page_content='Version 15 \\nPage 1 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\n \\n \\n \\n \\nPractical Advice \\non \\nMatrix Games \\nby \\nMajor Tom Mouat MBE MSc PGCE \\n \\n \\n \\n \\n \\n \\nVersion 15 \\n© Tom Mouat 2019, 2020, 2022, 2023\\n\\x0cVersion 15 \\nPage 2 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nContents \\nPractical Advice on Matrix Games ..................................................................... 4 \\nTerms ................................................................................................................ 4 \\nWhat are Matrix Games? .................................................................................. 4 \\nAcademic Underpinning .................................................................................... 5 \\nMy Version of How to Play a Matrix Game ....................................................... 6 \\nArgument Assessment ...................................................................................... 7 \\nDiceless Adjudication ...................................................................................... 11 \\nVoting for Yourself .......................................................................................... 13 \\nNotes about arguments .................................................................................. 14 \\nTurn Zero ........................................................................................................ 14 \\nNumber of Things you can do in an Argument ................................................ 14 \\nUse of Dice ...................................................................................................... 15 \\nReasonable Assumptions and Established Facts ............................................. 16 \\nTurn Length (in game) ..................................................................................... 16 \\nGame Length ................................................................................................... 17 \\nEnd of Turn \"Consequence Management\" ...................................................... 17 \\nInter-Turn Negotiations .................................................................................. 18 \\nElections .......................................................................................................... 19 \\nSecret Arguments............................................................................................ 19 \\nMeasures of Success ....................................................................................... 20 \\nKilling Arguments ............................................................................................ 21 \\nSpendable Bonuses and Permanent Bonuses ................................................. 21 \\nLevels of Protection and Hidden Things .......................................................... 22 \\nBig Projects or Long-Term Plans ...................................................................... 22 \\nNumber of Actors ............................................................................................ 23 \\nWriting the Briefs for the Participants ............................................................ 25 \\nRecording the Effects of Arguments................................................................ 26 \\nThe Components (and Characters) Affect the Game ....................................... 27\\n\\x0cVersion 15 \\nPage 3 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nStarting Conditions .......................................................................................... 28 \\nCue Cards ........................................................................................................ 28 \\nLarge-Scale Combat ........................................................................................ 29 \\nA House Divided .............................................................................................. 30 \\nAnnouncements .............................................................................................. 30 \\nTrade Agreements ........................................................................................... 30 \\nThe Order in which Actors make their Arguments .......................................... 30 \\nGaming Possible Futures ................................................................................. 31 \\nRandom Events ............................................................................................... 32 \\nSenior Officers, Dominant People and Contentious Arguments ..................... 34 \\nNit-Picking vs Important Clarification .............................................................. 35 \\nWhy I like Matrix Games ................................................................................. 36 \\nA few Words of Warning ................................................................................. 36 \\nFinal Comments .............................................................................................. 37 \\nMatrix Game Checklist .................................................................................... 38 \\nSample Spendable Bonus Cards ...................................................................... 40 \\nSample Random Events ................................................................................... 41 \\nSample Voting Cards for Diceless Adjudication ............................................... 43 \\nSample Estimative Probability Cards ............................................................... 44 \\nSample Turn Order Cards ................................................................................ 45 \\nSample Markers for Matrix Games for Effects and Conventional Forces ........ 46 \\nSample Map for a real-world political Matrix Game ....................................... 50 \\nSample Map for a fictional natural disaster Matrix Game ............................... 51\\n\\x0cVersion 15 \\nPage 4 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nPractical Advice on Matrix Games \\nby Major Tom Mouat MBE MSc PGCE, Head Defence Modelling and Simulation School \\nI have been running Matrix games since 1988. I felt that I should be prepared to stick my \\nneck out and try to provide some practical advice on how to run the games in order to get \\nthe best results. \\nTerms \\nI will use some specific terms relating to Matrix Games that I need to outline: \\n• \"Actors\" are the primary roles in a Matrix Game, such as \"The USA\", \"The Anonymous \\nHacking Collective\", or even \"The Earthquake\". They can represent individuals, groups, \\nconcepts (such as \"the spirit of Clausewitzian Friction\") or complete nations. \\n• \"Players\" are those carrying out the actions of the Actors. There can be one or several \\nplayers operating as a team, representing an Actor. \\n• \"Arguments\" are the expression of an Actor\\'s actions for the turn in the game. They are \\nmade up of \"something the Actor wants to happen\", \"what measurable effect will that \\nhave\" and \"a number of reasons why or how.\" \\n• \"Serious Games\" are those intended for a serious educational or training purposes as \\ntheir primary aim. A Matrix Game used for instruction on the Cyber Operational \\nAwareness Course at the Defence Academy of the UK, would be classed as a \"serious \\ngame\". \\n• \"Recreational Games\" are those whose primary aims are for recreation (even if \\neducation or training takes place). A game about the protagonists on the X-Files \\ntelevision series hunting down a crashed alien spaceship would be classed as \\n\"recreational\" (unless you were on the scriptwriting team looking for plot inspiration!). \\nWhat are Matrix Games? \\nMatrix games are different to normal Wargames. In a Matrix game, there are few pre-set \\nrules limiting what players can do. Instead, each is free to suggest any plausible action or \\nevent during their turn. The chances of success or failure, as well as the effects of the \\naction/event, are largely determine through structured argument and discussion. This \\nprocess allows for imaginative game dynamics that are lively and open-ended, and yet also \\ngrounded in reality. \\nMatrix games are particularly well-suited for complex conflicts and issues involving multiple \\nactors and stake-holders, varying interests and agendas, and a broad range of \\n(diplomatic/political, military, social, and economic) dimensions. The game system \\ncrowdsources ideas and insight from participants, thereby fostering greater analytical \\nunderstanding.\\n\\x0cVersion 15 \\nPage 5 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nIn a Matrix Game, you use words to describe why something should happen, the Facilitator \\nor the players (or both) decide how likely it is, and you might roll a dice to see if it happens \\n(but equally, in the face of a compelling argument, you might not need to). \\nIf you can say \"This happens, for the following reasons...\" you can play a Matrix Game. \\nThe games themselves are not intended to be fiercely competitive, with obvious winners \\nand losers. Instead, they operate with the players working to generate a credible narrative. \\nIt is from examination of this narrative after the game that the players gain insights and \\nunderstanding of the situation being portrayed. The player roles have objectives that will \\nprobably place them in conflict with other players, but it is perfectly possible for all of the \\nplayers to achieve at least some of their objectives by the end of the game. \\nAcademic Underpinning \\nThe academic research that Matrix Games seek to exploit, is in two main areas: \\n• Crowdsourcing1: Robust evidence from research on intelligence analysis and prediction \\nshows that crowds outperform individuals (Tetlock and Gardner 2015, Brynen 2017), \\nespecially when some framework for opinion aggregation is provided. The evidence \\nshows that groups can be better at estimation than individuals, due to a diversity of \\nopinion, decentralisation of expertise, independence of thought and aggregation of the \\nresult. The best predictions come from conflict or contest, but too much \\ncommunication, too early on in the process, can make the group less intelligent. \\n \\nOf course, there are \"Stupid Crowds\" with a homogeneity of opinion, centralisation of \\ndecisions in a formal hierarchy, internal divisions and compartmentalisation, imitation \\nbased on previous decisions, emotionality and peer pressure, and ultimately \\'Group \\nThink\\'. Ultimately diversity of thought is required, rather than merely ensuring ethnic \\nand gender representation is diverse enough. \\n \\n• Role-Play and Prediction2: There is considerable evidence that role-play can be a more \\neffective basis for the prediction of decisions based on conflict resolution, than expert \\nopinion or game theory (Green and Armstrong 2011, Green 2002, Armstrong 2001). The \\nhypothesis being that experts will predict what should happen but that role play predicts \\nwhat will happen. This is because when predicting outcomes in conflict, it is necessary to \\n \\n1 Tetlock, Philip, and Gardner, Dan. (2015) Superforecasting: The Art and Science of Prediction. Toronto: McClelland & Stewart. \\nBrynen, Rex. (2017) \"Here (Very Likely) Be Dragons: The Challenges of Strategic Forecasting.\" In Thomas Junea, ed.,Strategic \\nAnalysis and International Policy-Making: Case Studies in Achieving Analytical Relevance. Rowman & Littlefield. \\n \\n2 Green K.C., Armstrong, J.S. (2011) Role thinking: Standing in other people’s shoes to forecast decisions in conflicts. \\nInternational Journal of Forecasting, Volume 27, Issue 1. Green K.C. (2002) Forecasting decisions in conflict situations: a \\ncomparison of game theory, role-playing, and unaided judgement. International Journal of Forecasting, Volume 18, Issue 3. \\nArmstrong J.S. (2001) Role Playing: A Method to Forecast Decisions. In: Armstrong J.S. (eds) Principles of Forecasting. \\nInternational Series in Operations Research & Management Science, vol 30. Springer, Boston, MA\\n\\x0cVersion 15 \\nPage 6 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nmake predictions in a chain, and it is the \"action, reaction, counter-action\" cycle that \\ngenerates insight and effective understanding. \\n \\nIn order to get the best out of role-play, it is necessary that you assign the roles before \\nreading the scenario, ensure player roles are typecast (there is no point casting a \\nrepressed introvert to play Vladimir Putin or Donald Trump), players should act as if they \\nwere the subject, and briefings need to be accurate but succinct (1 page). It should also \\nbe noted that environment and materials affect the game, the predictions should be \\nbased on a number of games, smaller numbers of players (less than 20) are better than \\nlarge games, and they are better when considering large changes or unusual events. \\nMy Version of How to Play a Matrix Game \\nIn a Matrix Game, actions are resolved by a structured sequence of logical \"arguments\". \\nEach player takes turns to make an argument, much like making a legal argument offered in \\nCourt, with successful arguments advancing the game, and the player\\'s position. There are \\na number of ways you can do this, depending on the size of the game and the purpose \\n(each has their own strengths and weaknesses), but the one I would recommend is the \\n\"Pros and Cons\" System. \\nIn this system, each argument is broken down into: \\n• The active Players states: Something That Happens and a number of Reasons Why it \\nMight Happen (Pros). \\n• The other Players can then state: A number of Reasons Why it Might NOT Happen (if \\nthey can think of any) (Cons). \\n \\nNote: The \"Something That Happens\" should be phrased as an Action or Event with a \\nmeasurable result – the argument is about actions that move the game forwards. \\nThe reasons are evaluated (both Pro and Con) and a judgement made as to the weight of \\nthe argument. If the argument and reasons are compelling, quite often the argument \\nsucceeds automatically. If there are, however, good reasons both Pro and Con, a decision \\nneeds to be made as to the success or failure of the argument. \\nIn most recreational games two six-sided dice are rolled, needing a seven or more to \\nsucceed; with good Pros adding to the dice score and good Cons deducting from it. In \\nprofessional Matrix Games, the appropriate adjudication method is used (usually estimative \\nprobabilities) as detailed, along with other methods, below. \\nThe intention is to force the game to move on; generating a narrative and avoid getting too \\nbogged down in detailed discussions about the merits of particular elements of the story. \\nThe game needs a Facilitator to help adjudicate on the arguments, but if you have a limited \\nnumber of players, you can take it in turns to be the Facilitator – this works out much better\\n\\x0cVersion 15 \\nPage 7 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nthan you might imagine and helps reinforce the idea that your role in the game might be in \\nconflict with others, but you are all working together to generate a credible narrative. \\nThe advantage of the \"Pros and Cons\" system is that you formalise the advantages and \\ndisadvantages of an argument and the role of the Facilitator becomes that of ensuring that \\nthe Pros and Cons carry equal weight - perhaps making compelling reasons worth two Pros \\nand two or three weaker reasons against only worth one Con. You will need to ensure you \\ndon\\'t end up with a laundry list of trivial reasons, or having the player re-stating a reason \\nalready accepted in a slightly different way in a desperate attempt to gain points (which \\nhappens quite often). \\nOf course, one very useful benefit of the \"Pros and Cons\" system is that it provides reasons \\nfor failure should the dice roll not succeed. You can also more easily run the game with very \\nknowledgeable players. \\nArgument Assessment \\nThe object of the game is to generate a credible narrative in the course of the game and \\nfrom this we hope to gain insights into the situation. From this, it logically flows that \\narguments (sensible arguments!) should succeed automatically unless challenged by the \\nother players. The fact that the player has decided that their argument is the most \\nimportant thing they want to happen that turn, means that unless there is something \\nwrong, it should succeed. It follows on from this that arguments which build on previous \\nsuccessful arguments should be given an automatic bonus because they are contributing to \\nthe unfolding narrative. \\nIf two arguments are in direct opposition (\"This happens\" - \"No it doesn\\'t\") they represent a \\nLogical Inconsistency since they cannot both be true. The earlier argument has already \\nhappened, so it is impossible for it not to have happened. The later player may argue that \\nthe event is reversed, but this tends to make for a poor narrative in the game and should be \\ndiscouraged. Please also take a look at \"The Order in Which Actors Make Their Arguments\", \\nbelow. \\nHowever, if arguments are opposed (have a chance of failure), there are a number of ways \\nof working out if the argument will succeed: \\n1. Umpired. Once PROs and CONs have been identified it might be left up to an umpire (or \\nWhite Cell or Control group) to determine what happens. This has the advantage that \\nthe game outcomes can be aligned with research or doctrine, or nudged along a path \\nthat maximizes their educational value. It can also be useful when the players \\nthemselves have only limited knowledge of the game subject matter. However, having a \\nthird party determine success and failure can make the game seem rather scripted. If \\nplayers attribute the outcome of the game to umpiring rather than to their own \\ndecisions and interaction with their fellow participants much of its value may be lost.\\n\\x0cVersion 15 \\nPage 8 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nThis is the preferred method for using with \\n \\n2. Consensus. Of course, you may prefer to simply have a discussion until there is a \\ngeneral consensus as to whether the argument succeeds or fails. This is a nice idea, but \\neven among professionals this can take a long time and there is no guarantee that \\neveryone will agree. As an alternative, you can try to reach a consensus instead on the \\nprobability of the argument succeeding and afterwards throw the dice. This is often \\neasier and faster. \\n \\n3. Ask the Expert. In some technical fields, like Cyber, it can be advantageous to have an \\nexpert panel to decide on the success of an argument or the success probability, \\nproviding that they can fully articulate the reasons why and generate reasons for failure. \\nPlease note that this should only be used for technical subjects – when considering \\nresponses to conflict between groups of people (as opposed to whether a type of \\nhacking attack is actually possible) there is good evidence that role-play is a more \\naccurate predictor of outcomes than asking an expert. \\n \\n4. Weighted Probabilities. This system of adjudication places a great deal of emphasis on \\nthe arguments put forward by the players, while introducing the element of chance. It is \\nslightly more complicated than the previous systems. There is also risk that some \\nprofessional audiences may recoil at the sight of dice—associating these more with \\nchildren’s games than serious conflict simulation and gaming. In this system 2 six-sided \\ndice are used, with a score of 7 or more being required to succeed, with each strong and \\ncredible PRO argument counting as a +1 dice roll modifier, and each strong and credible \\nCON counting as a -1, with especially high or low results representing more extreme \\noutcomes. This also provides a \"narrative bias\" to the game as a score of 7 is actually a \\n58.3% chance of success and helps contribute to the evolving story. If you don\\'t like that \\nidea, you can still roll two six-sided dice for a \"true\" 50% (on the basis that, without any \\nPros or Cons, an argument is equally likely to succeed as to fail) as noted on the \"Result \\nDetermination Cheat Card\" below. This method tends to be used in recreational games, \\nand in instructor-led educational games with junior students (for ease and speed). \\n \\n5. Estimative Probability. Alternatively, players or teams can each be asked to assess the \\nchances of success, and these can be aggregated. In analytical games, this provides \\npotentially valuable insight into how participants rate the chances of a particular course \\nof action. There is a set of estimative probability cards which can be used for this \\npurpose, below. Following discussion, players or teams simply select the card from their \\nhand that, in their view, best represents the probability of an ACTION’s success. These \\nare then aggregated together (you can use the mathematical MEAN, but it is \\nmathematically better to use the MEDIAN number in small groups (less than 20 or so) in \\norder to reduce the effect of extreme outliers), and percentage dice are used to\\n\\x0cVersion 15 \\nPage 9 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\ndetermine success or failure. Of course, the players are supposed to \"step back\" from \\ntheir roles and try to assess the probability objectively – which can be an issue if the \\nplayers are immersed in the developing narrative or are just fiercely competitive. \\n \\nI used to use the Weighted Probability method all the time. I would normally judge the \\nplayers present and form my own opinion of the Pros and Cons, modified to reflect the \\ngeneral consensus in the room, and then roll the dice (if necessary – later in the game you \\nshould find a greater number of arguments succeeding automatically as people adjust to \\nthe developing narrative). If it is a technical argument and we needed advice, I would then \\nask an expert. \\nThis use of Weighted Probabilities reflects the early widespread use of Matrix Games in the \\nhobby community. As a method, it is inherently understood by anyone with any familiarity \\nwith games and is relatively easy to explain for those without. It is fast and provides the \\nAdjudicator more licence in influencing the pace of the game to ensure it doesn\\'t get \\nbogged down in excessive debate. \\nThe main concern I now have is that this, and all the alternatives above, failed to specifically \\naddress to one of the academic underpinnings of Matrix Games, that of Crowd Sourcing the \\nresults. \\nBased on Surowiecki\\'s popular book3, there are a number of elements required to form a \\n\"wise crowd\": \\nCriteria \\nDescription \\nDiversity of \\nopinion \\nEach person should have private information even if it\\'s just an \\neccentric interpretation of the known facts. \\nIndependence \\nPeople\\'s opinions aren\\'t determined by the opinions of those around \\nthem. \\nDecentralization People are able to specialize and draw on local knowledge. \\nAggregation \\nSome mechanism exists for turning private judgments into a collective \\ndecision. \\n \\n \\n3 https://en.wikipedia.org/wiki/The_Wisdom_of_Crowds\\n\\x0cVersion 15 \\nPage 10 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nA fundamental part of Matrix Games involves crowdsourcing ideas from diverse \\nparticipants, and I believe that the element of aggregation would be best served by the use \\nof Estimative Probability cards (above). It is generally felt that this is a more accurate \\nmethod to leverage the work on Crowd Sourcing, as well as making the resulting probability \\nmore accessible and acceptable to the participants. The terms on the cards also reflect \\nthose commonly used in the intelligence community. It also follows that the participants in \\nthe Estimative Probability method should be from all those present and not just be limited \\nto the specific roles in the Matrix Game. \\nOinas-Kukkonen4 has made a number of conjectures based on Surowiecki\\'s work, asserting \\nthat \"too much communication can make the group as a whole less intelligent\", which we \\ncan address by the encouraging relatively quick moves, and the intention to avoid too much \\ndetailed debate following a player\\'s argument. This means the game can have a reasonable \\nnumber of moves, requiring that the participants to have to live with the consequences of \\ntheir actions made earlier in the game. I would suggest at least 6 moves, to allow for two \\ncycles of Action-Reaction-Counter Action by the players. I would therefore recommend, at \\nleast for high level policy and analytical games, that the Estimative Probability method is \\nused. \\nThe procedure should be, following the arguments, to have all participants with their own \\ndeck of cards, and assess the probability of success independently and without discussion. \\nThey should then all reveal them simultaneously to the facilitator for adjudication. My \\npreference would be to select the MEDIAN of the results, rather than the MEAN as \\nexplained above (and is quicker). \\nExcessive outliers can be discussed quickly. In most cases they are nothing more than that – \\noutliers. But on some occasions, it may indicate specialist knowledge, so care should be \\ntaken not to dismiss them. It is usually best to ask if the individual was surprised that \\neveryone voted the other way – and if they were not, why? 5 There may be a good reason. \\nA word of warning, however! If you use the estimative probability cards, it makes the use of \\n\"spendable bonuses\" (discussed elsewhere) a little more problematic. You would have to \\nsay that having a \"Diplomatic Bonus Card\" will offer something like a 10% bonus to the dice \\nroll – but this is not the same as permitting a +1 to the dice when using 2 six-sided dice as \\nmultiple plusses with 2 six-sided dice have a proportionally greater effect, as you can clearly \\nsee in the chart below. \\nIt should also be noted that, when using percentage dice to determine the final result, it is \\nusually best to be consistent in expressing exactly what the dice roll is for (the success of \\n \\n4 Oinas-Kukkonen, Harri (2008). Network analysis and crowds of people as sources of new organisational knowledge. In: A. \\nKoohang et al. (Eds): Knowledge Management: Theoretical Foundation. Informing Science Press, Santa Rosa, CA, US, pp. 173-\\n189. \\n5 Prelec, D., Seung, H. & McCoy, J (2017). A solution to the single-question crowd wisdom problem. Nature 541, 532–535. \\nhttps://doi.org/10.1038/nature21054\\n\\x0cVersion 15 \\nPage 11 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nthe argument) and what score is needed with participants who are not gamers (E.g. \"A 70% \\nchance of success, which is a score on the percentage dice of 70 or less\"). There is evidence \\nthat participants perceive \"a 70% chance of success\" differently to \"a 30% chance of failure\" \\ndespite their mathematical equivalence, so consistency in expression is advised. \\nPersonally, I prefer to use 2 six-sided dice with the score approximating to the probabilities \\nfrom the \"cheat sheet\" below, so: 90% = 4+, 70% = 6+, 50% = 7+ (using red and green dice \\nas explained in the diagram below), 30% = 9+ and 10% =11 +. It is easier for non-gamers to \\nunderstand. \\n \\nThis chart allows for a \"true 50%\" by splitting the score of \"7\" if you don\\'t want a \"narrative \\nbias\" in the \"weighted probability\" adjudication method of adjudication as explained above. \\nDiceless Adjudication6 \\nIt is worth mentioning a couple of alternative methods of assessment without using dice. \\nWhile I personally believe that dice are important to represent risk, there are some who \\ninstinctively recoil from them. They are incorrect to do so, but attempting to explain why \\ntakes time and involves some complexity, and so it may not be appropriate depending on \\nthe circumstances. \\nFor example, if it is intended to have some form of Matrix Game at an international event, \\nsuch as a NATO regional workshop, you will have a large number of delegates from \\n \\n6 I am indebted to Sue Collins from NATO ACT for her work in this particular area.\\n\\x0cVersion 15 \\nPage 12 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\ndifferent nations, with differing levels of facility with English. It would be inappropriate to \\nambush them with a game system involving dice, if you are unable to ensure they have the \\nnecessary \"buy-in\" to the process beforehand. \\nAlso, if someone sufficiently senior says they simply aren\\'t going to roll dice, you are \\nprobably wasting your time – so it is essential that you have alternative methods up your \\nsleeve. \\nI am making the assumption that you do not wish to use the Umpired, Consensus or Expert \\nmethods discussed above, as they don\\'t leverage the benefits of Crowd Sourcing. Instead, I \\nwould strongly suggest you should use some form of \"voting system\": \\n1. Show of Hands. This is the simplest and most basic method of voting and needs every \\nlittle explanation. You will need to ensure that you are consistent, however, in that the \\nvote is always whether the players support the argument, so you avoid confusion. In \\norder to get the best results everyone should try to vote at the same time, with the most \\nsenior personnel voting last so as not to influence their subordinates. Success or failure \\nis judged as to the level of support for the argument, with a majority needed to succeed \\nat some level. \\n \\n2. Agree, Disagree and I\\'m Not Sure. This is slightly more complex, in that the danger of \\nasking for a simple \"Agree/Disagree\" judgement from the players on sometimes \\ncomplex actions, often leads to them deciding on a whim. It is normally much better to \\nallow an option to allow them to vote for indifference, irrelevance, unimportance, or \\ninsignificance. You will need to explain that you only vote for Agree or Disagree if you \\nare sure, and that you use I\\'m not sure under all other circumstances. \\n \\n \\n \\nThe permits more subtle gradations of results, with the number of I\\'m not sure votes \\nindicating the level of importance, but also the level of divisiveness in political or social\\n\\x0cVersion 15 \\nPage 13 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\narguments. For example, if a result is a marginal Agree majority, but with a lot of I don\\'t \\nknow votes, the result is likely to be only marginally effective and people don\\'t really \\ncare about it. If instead, the result has very few I\\'m not sure votes, but is still very close, \\nit is likely to be divisive and has the possibility of sparking a backlash against the result \\nthat could be exploited in later turns. Examining the reasons for such disagreements can \\nbe very illuminating. \\n \\n \\nAn example of voting cards in action: A clear result of I don\\'t agree with the argument, with \\na small number of I don\\'t know and Agree votes. \\n3. A more complex Scale. Normally used with electronic voting systems, either \\ntechnologies like electronic clicker systems7, or mobile phone applications or browsers8. \\nThese have the potential to offer much better graduation in the adjudication of results, \\nsuch as a 5-point Likert scale, and potentially more options in a single vote where a \\nnumber of possible outcomes can be listed and the players vote for which option they \\nthink is the most likely. The danger with these is that they depend on the technology, \\nand while they should be simple and easy, I have never used one in anger without some \\nform of failure at some stage (fortunately I had a box of cards with me, just in case). \\nVoting for Yourself \\nIf you are using voting systems, either as Diceless Adjudication or as Estimative Probability, \\nyou should take great care to ensure that the players are being as professional as possible, \\nand not merely \"voting for themselves\" in a competitive manner. Many players can be quite \\nvery competitive, so it may be necessary to not allow them to vote on their argument – and \\nequally it may be necessary to keep an eye on players who are in direct competition. The \\nintention is to develop a narrative, generating insights – rather than trying to win at all \\ncosts. \\n \\n7 An example is https://www.turningtechnologies.eu/turningpoint/ \\n8 An example is https://www.polleverywhere.com/\\n\\x0cVersion 15 \\nPage 14 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\n \\nNotes about arguments \\nThe important thing to remember in a Matrix game is that arguments can be made about \\nanything that is relevant to the scenario. You can argue about your own troops or about the \\nenemy, the existence of people, places, things or events, the weather, plague, disease or \\npublic opinion. The actions and consequences of arguments are reflected in the placement \\nof the generic counters on a map (examples are enclosed), forming narrative markers for \\nthe game; or by writing the results on a whiteboard or flipchart so the players can keep \\ntrack of what is going on. \\nSome things can seem a little odd to new players – \"how can he argue about my troops?\" – \\nIt is true, he can\\'t give them orders, but he could argue that their morale and motivation \\nare low because they haven\\'t been paid in months. The only criteria for judgement is the \\nlikelihood of the event taking place. With a bit of imagination, common sense and rational \\nthinking, it is possible to present persuasive arguments as to what should happen in any \\nscenario - from traditional military campaigns to the strange worlds of cyber or defence \\nprocurement. \\nA common error in Matrix games is for a player to argue about another player being \\ninfluenced by something or them agreeing to a course of action. The player is present and \\ncan simply be asked – so providing time between turns to allow the players to negotiate \\nwith each other (in secret if necessary) makes for a better game. It might be that a player \\nwants to argue that all parties come to negotiations – in which case let them state their \\ncase, then simply ask the other players if they want to come along. If they agree then the \\nargument is an automatic success. Arguments are for actions – if the players want to \\nnegotiate with each other, they can do that in between turns. \\nTurn Zero \\nIn most games with inexperienced participants, it is usually best to have a \"Turn Zero\" \\ncouple of arguments before you start the game properly. Rather than have an entire Turn \\nwith all the participants making arguments, I usually select two of the actors who are in \\ndirect opposition and ask them to come up with example arguments which we can then \\ndiscuss in detail so people get the idea about how the game works. \\nNumber of Things you can do in an Argument \\nSometimes players get carried away with their arguments and try to do several different \\nthings at once. You should only get to do one action a turn because part of the insight in \\nthe game comes from deciding what the highest priority is. The action itself could be large \\n(like a general mobilisation of the Militia), but it should be a single action, so mobilising the\\n\\x0cVersion 15 \\nPage 15 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nMilitia and ordering a strategic missile strike, would be two separate actions – which one do \\nyou want to do first? \\nThis doesn\\'t mean that they are doing nothing else – it is just that the other things are part \\nof the \"business as usual\" background noise – and the action is the one that they think will \\nhave the most impact, either immediately or in the future. \\nYou shouldn\\'t slavishly follow this rule with inexperienced players, however. Sometimes it \\nmay be necessary, in order to get the participants to come up with ideas outside their \\nnormal way of thinking, to force them for example to make one argument about \\nconventional military things, and a second argument about Political, Economic, Social, \\nInformation or Infrastructure issues. This should be the exception however! \\nOf course, like Newton\\'s Law of Motion, once an argument has succeeded, the situation \\nremains that way until another argument changes it. \\nIn some cases, the players may wish to take time to come up with a plan in advance of the \\n\"game\" itself. This is perfectly permissible but the planning should be conducted in such a \\nway as to be able to break down the elements of the plan into no more than about 3 \\nArguments, and the appropriate timescales in which they would happen. The Arguments \\nshould be written down in the same way as Secret Arguments (below) and not shown to \\nthe opposing players. The opposition will then have the same number of Arguments that \\nthey can make, in the same time period, openly, as usual. Should one of the opposition \\narguments demand an immediate response from the players, the plan is then delayed. If \\nany resources are then used that were needed by the plan, the plan is lost. If both sides end \\nup planning, resolve the written arguments in the normal way. \"Planned\" arguments have a \\nmuch higher chance of success – but are lost if the situation changes. \\nUse of Dice \\nDice are only used where there is a risk of failure established in the arguments and counter \\narguments. If there are no counter arguments or there is overall support for the argument, \\nit succeeds. If there is a risk of failure, however, this risk is realised through the use of dice. \\nIn some circles, the use of dice is a credibility issue, where players who lack a grasp of the \\nrealities of the nature of \"risk\" are unwilling to roll dice. They see it as trivialising the issue \\nand reducing the wargame to the status of a child\\'s pastime. \\nIf such a case arises it is usually best to confront the issue head-on. Point out that the player \\ndoesn\\'t need to roll dice – all they need to do is to come up with an argument that \\neveryone agrees has no chance of failure. If the player refuses to roll the dice or \\ndemonstrates a dismissive attitude, ask them what other mechanism would they suggest. \\nExcel Random number generator? A set of cards with the appropriate probability \\ndistribution, shuffled and selected? All of these alternatives are essentially identical to\\n\\x0cVersion 15 \\nPage 16 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nrolling dice and, in the end, it is essential that where risk has been identified in the game, \\nthere is some mechanism to realise that risk. \\nIn my experience, personnel such as those in the Special Forces and senior commanders, \\nwho understand the nature of risk, have no problems rolling dice. If possible, select them \\nfirst and the others will follow. \\nPassing dice to the player and inviting them to roll is a powerful tool. It focusses attention \\non the nature of risk and exactly who has the responsibility. Are they content with the level \\nof risk? If not, invite them instead, to make a preparatory argument as an alternative, \\nreducing their chance of failure (but using up a valuable argument and failing to \\nimmediately react to their opponent). \\nDiscussions as to the nature of risk in the environment are nearly always very valuable and \\nare an essential part of wargaming, particularly in the diplomatic/political, military, social, \\nand economic domain of Matrix Games. \\nReasonable Assumptions and Established Facts \\nIt is important that the Facilitator understands the difference between \"reasonable \\nassumptions\" in the game, such as the proposition that well trained and equipped Special \\nForces soldiers are going to be much more effective in combat than untrained protestors; \\nand \"established facts\" which are facts that have been specifically mentioned in the game \\nbriefings or have become established during play as the result of successful arguments. \\nThe latter can be immediately deployed as supporting reasons (Pros and Cons), but the \\nformer need to have been argued successfully in order for them to be specifically included. \\nMany inexperienced players will make vast all-encompassing arguments full of assumptions \\nthat are not reasonable. For example: It is not a reasonable assumption that unarmed \\nProtestors could fight off trained Police. It is reasonable to assume that the Police are \\ntrained, armed, equipped and quite capable of dealing with a group of protestors (after all, \\nthat is their job). It would be necessary to argue for large number of Protestors, argue that \\nthey had weapons of some sort or argue that they were especially devoted or fanatical \\nabout their cause, for them to have a reasonable chance of beating the Police. \\nOf course, you might argue that your Protesters hugely outnumber the Police, undergo \\nspecial training, get access to firearms, or are simply fired up with enthusiasm by the \\npowerful and impassioned speech from their leader, so they get a bonus. In this case, you \\nshould mark the counter used in the game with a +1 or something similar (depending on \\nthe strength of the argument) to show their improved status. \\nTurn Length (in game) \\nAnother important element to the game is working out how long each turn is supposed to \\nrepresent. The time allowed in arguments for a turn needs to be appropriate to the\\n\\x0cVersion 15 \\nPage 17 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nscenario and is, to some extent, not precisely defined. \"About 2 to 4 weeks\" might be \\nappropriate for a Cyber Scenario, allowing for reconnaissance, some code writing or \\nacquisition of applications, before the actual attack taking place in a subsequent turn. \\nCare must be taken to ensure this is kept in mind during the game, as timescales can often \\nget unrealistically compressed. Players sometime argue for financial aid or extra troops \\nfrom Government headquarters, which might take some time to reach a decision and even \\nlonger for the resources to arrive. You just need to be aware of the timescales. \\nPlease note that this does not mean that the players cannot argue for long term projects. \\nThe whole point a Matrix Games is to provide the players with the chance to do things \\nbeyond the limitations of normal games. If they wish to commence a project that will not \\ncome to fruition for a number of years, they should be free to do so. Like all Matrix \\nArguments, if they succeed, the project will go ahead and deliver as argued – unless \\nanother argument is made to stop it. \\nIt can be useful to make the players write down what their Actor would aim to achieve over \\nthe period of a full Government term (4 to 8 years) as this focusses their minds on the \\nlonger term. Of course, grand plans often get derailed by short-term reactions to crises, and \\nif they fail to act for the long term, it is their fault. \\nGame Length \\nIt is essential that the game provides the players with an opportunity to have to live with \\nthe consequences of their decisions made in previous turns. To this end, it is vital that the \\ngame has a reasonable number of turns to allow an action – re-action – counter-action to \\ntake place. In my experience, 6 turns are the recommended minimum. \\nSince Matrix Games are intended to be fast and have low overheads, this normally \\ntranslates into a target time of no more than 30 minutes for a turn, making the average \\ngame to be about 3-4hrs. \\nGames can be longer if you wish, some lasting all day, but you need to be aware that you \\ncan reach the point of diminishing returns quite early, and much of the time can be wasted. \\nIt is also common that the situation the game was originally designed to explore might be \\nreached early on in the game, and continuing will stray into a different game situation. In \\nmost cases, if you have all day, it could be preferable to run the game twice, taking time to \\nreview the choice of Actors and their objectives between the two iterations. It can also be \\nuseful to rotate the players to give them different roles. \\nEnd of Turn \"Consequence Management\" \\nAt the end of each game turn (a cycle of player arguments) the Facilitator should go over \\nthose successful and failed arguments that have generate new \"established facts\" in the \\ngame. They should also review situations that are on-going, such as the generation of\\n\\x0cVersion 15 \\nPage 18 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nrefugees from fighting or the arrival of new recruits to a popular cause. If these have not \\nbeen countered during the turn by another successful argument, the Facilitator should \\nmake them continue until someone does make an argument to stop them. \\nIt might also be that some of the arguments, when considered as a whole, will have \\nadditional or even unintended consequences that are reasonable to expect to arise. It is \\ntherefore worth taking time to consider the consequences of the players’ arguments \\nbeyond their immediate results. Invite the players to consider the events of the turn, \\nsuggest possible consequences and then agree on the most likely that should be taken \\nforward to the next turn. \\nIn some games, it is worthwhile having an individual (if you have one to spare) who is \\nparticularly experienced about the sort of subject that the Matrix Game is focussed on, \\nmake “the law of unintended consequences” arguments at the end of a turn. This can help \\nto formalise the process and provide good examples to widen the players’ understanding of \\nthe consequences of their actions. \\nIn many cases \"unintended consequences\" will have an effect on some or all Actors in an \\narea of the game. It is useful to make a note of this on a piece of card and place it on or \\nnear the map so people have their attention drawn to it. It may also be appropriate that on-\\ngoing penalties will apply, until removed by a successful argument. For example, if fighting \\nis taking place in a city, there may well be a flood of refugees moving away from the \\nfighting. This could mean that any operations in the areas of the refugees suffer a \"-1\" \\npenalty until the refugees have left, or until they take specific measures to remove them. \\nInter-Turn Negotiations \\nAs we have already said, the actual “arguments” of the Matrix Game are about actions that \\ntake place in the course of the game. In most cases, the Actors represented by the players \\nmay well want to engage in face-to-face negotiation with each other in an effort to strike a \\ndeal. Players attempting to make Arguments saying that they want to “influence the Prime \\nMinister” are essentially pointless if the Prime Minister is represented by another player. If \\nthey want to strike a deal, then they had better head off to a quiet corner of the room and \\ntry a little influence in real life. Of course, if a player wants to make an argument about a \\nposition or group not represented by another player, they are welcome to do so in the \\nnormal way. \\nIn analytical and policy games, it is important to record the essential elements of these \\ndiscussions. What was suggested? Was agreement reached and why? If no agreement was \\nreached what were the private and public reasons why the negotiations were unsuccessful? \\nAnalysis of these “off-table” negotiations and the reasons the players felt why they were \\nsuccessful or failures can provide important insights. The usual method is to provide a \\njunior member of staff to follow the Actor around and frantically try to record the essentials \\nof the discussions. This is manpower intensive and difficult to do well.\\n\\x0cVersion 15 \\nPage 19 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nAn alternative method is to simply add a short phase to the beginning of each turn (before \\nany arguments take place), where each Actor summarises themselves, what discussions \\ntook place and what they heard. It can be very instructive, especially when “what they \\nheard” was not “what the other party meant”. They should all do this in turn, and a single \\nscribe can then record the details, but care needs to be taken not to take too long and slow \\nthe game down. \\nElections \\nIn certain games Elections are very likely. In general, they would probably need a successful \\nargument to invoke (unless they are planned in the scenario). My advice is to ensure that \\nthere has to be at least one game turn after the Election is announced in order to permit a \\nround of arguments that affect the voting. \\nIn most cases, Elections will be resolved by one vote per Actor, modified by the results of \\nsuccessful arguments (and inter-turn negotiations!). Any successful arguments generating \\npolitical capital during the game (I normally record this using the \"happy face\" icons) can of \\ncourse be \"cashed-in\" for additional votes (see \"Spendable Bonuses\" below). This assumes \\nthat the scenario is balanced between the number of Actors and the position they take in \\nthe game. \\nSecret Arguments \\nThere will be some cases where you want to hide from the other players the thing you want \\nto argue about. It could be that you have booby trapped a piece of equipment you think \\nyour opponent will use, or that you have swapped the vital blueprints for a set of fake ones \\nin case the safe is broken into. In this case, you simply write down your argument on a \\npiece of paper and present it to the Facilitator announcing to the other players that you are \\nmaking a secret argument. \\nThe argument then remains hidden until events in the game cause it to be revealed. For \\nexample, in the example above, the blueprints may eventually get stolen when the spy \\nbreaks into the base. When they take them back to their base, they may find out that the \\nblueprints are actually fake – wasting time, effort and expense. The time to actually \\nadjudicate the secret argument is a judgment, but I would do it as soon as the blueprints \\nare taken. There is a slight chance that the fakery will be obvious and fail to deceive the spy. \\nIf the failure is really bad, it may provide information as to where the real plans are. \\nIf a piece of equipment is sabotaged, the argument should be adjudicated when the \\nequipment is used. In many cases, opposing arguments will be made that a decision to \\nsabotage another government\\'s equipment would be complex and take a long time in a \\nWestern Democracy, and so wouldn\\'t happen. I would judge that this argument, while true, \\nis offset by the fact that the players elected to make the argument in advance (thus\\n\\x0cVersion 15 \\nPage 20 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nallowing time for the decision-making process). They are taking the risk that the events \\nspecified in the secret argument actually take place, so should be rewarded when they do. \\nAn area of potential danger is when the secret argument is not precisely defined. This can \\nlead to the Actor claiming that the event contained in the secret argument happens, while \\nthe opposing Actor claims that the interpretation was too wide and that it might not have \\nbeen triggered at that time, or the argument catered for too many options that would have \\nrequired a disproportionate amount of resources or decision making. It is the responsibility \\nof the Facilitator to ensure that the secret arguments conditions are sufficiently tight to \\nprevent this. In the event of a mistake being made, I would simply require the Actor making \\nthe secret argument, to have to make an additional argument as to why their secret \\nargument should be triggered in this specific instance. \\nYou should be careful, however, that the players don\\'t make too many secret arguments. \\nThis can ruin the game\\'s atmosphere and reduce the focus, so that the game drags on \\nunnecessarily. They must only be permitted when they refer to quite specific things or \\nevents. An argument about gathering information from a spy, in most games, will be quite a \\ngeneric argument and should be argued openly. Similarly arguing about the placement of \\nan IED to catch forces moving down a route should be made openly as the results will take \\neffect the same turn. \\nSecret Arguments should only be for misdirection – something you conceal when you are \\nsure that an opposing Actor will try to take or attack later in the game. A good example \\nwould be to create a \"honeypot\" email server filled with fake documents, as the French \\nPresident Emmanuel Macron did in April/May 2017 during the lead up to the French \\nPresidential Elections. The argument is judged as to its effectiveness when the \"campaign \\nemail server\" honeypot is hacked, and in President Macron\\'s case was very effective. \\nMeasures of Success \\nIn many arguments, success or failure may not be a simple \"Yes\" or \"No\" proposition. There \\nmight well be a sliding scale of success or failure in terms of numbers or the quality of the \\noutcome, which is usually represented by the score on the dice. If you needed a 7+ to \\nsucceed and rolled a double-six (12), this can indicate an especially notable success. \\nConversely, a roll of a double-one (2), it could represent a disastrous failure. The \"Result \\nDetermination Cheat Card\" (above) also shows a normal distribution and standard \\ndeviations in the results, which can help with explanations (or simply blind them with \\nscience). \\nWhen an argument is made players sometimes provide counter-arguments (Cons) that are \\nabout the consequences of the action rather than the action itself. In my mind this means \\nthat they have already accepted that the argument is a good one and should automatically \\nsucceed, so they should switch the discussion to the quality of the results. This can be a\\n\\x0cVersion 15 \\nPage 21 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nsubtle switch in the point of view and as a facilitator you should watch out for it because it \\nis important. \\nKilling Arguments \\nDepending on the context, murder and assassination are perfectly acceptable arguments \\nwhich should be judged like any normal argument – that is, on the likelihood that the \\nreasons given are sound. \\nHowever, just because an individual in the game dies, doesn\\'t mean that the player has to \\nstop making arguments. \\nIt can be interesting to see, after a successful or botched assassination attempt happening, \\nthat the attacked player often responds in an emotional way that is often contrary to their \\nstated objective in the game. Quite often they bear a grudge and act in revenge, rather \\nthan focussing on achieving their aims. It can be very enlightening when this happens so, if \\nyou manage to notice it, be sure to make a note for the after-game review. \\nSpendable Bonuses and Permanent Bonuses \\nIn many cases during Matrix Games, the Actors will argue for policy objectives, for example: \\nanti-corruption measures if the previous Government was accused of being corrupt. If \\nsuccessful, I usually place a \"smiley face\" counter in front of the Actor representing the \\nincrease in popular support for the action (as mentioned above). Unlike the generic \\nrepresentation mentioned in the previous section, in this case it can be used as a \"dice \\nmodifier\" improving the probability of a successful adjudication in a later argument, \\nindicating they are \"calling in favours owed\" or \"spending their political capital\" to ensure \\nthe success of the proposed measures. Of course, in this case the counters are \"used up\" in \\ndoing this and handed over to the Facilitator. \\nYou can differentiate \\'spendable bonuses\\' from the generic effects by using small cards as \\nshown below, relevant to the area in which the bonus can be \\'spent\\': \\n \\nPersonally, I\\'m not sure that all of the cards are relevant for all scenarios. For example, in a \\nhacking scenario the \\'Information Bonus\\' is relevant, but in most other cases it isn\\'t.\\n\\x0cVersion 15 \\nPage 22 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nArguments can also be made for things like permanent increases to unit effectiveness, \\naffecting all units of that type. This sort of wide-ranging argument would normally have a \\nlower chance of success due to its scope (and bearing in mind the \"Reasonable \\nAssumptions\" discussion elsewhere). I would normally have the players roll the dice for the \\nquality of the outcome (see \"Measures of Success\" elsewhere) and if they were only \\npartially successful, I would instead provide a suitable number of \\'spendable bonus\\' \\ncounters that could be used instead of a full-scale permanent bonus. \\nIn some cases, it may be useful to specify exactly what the \\'spendable bonuses\\' can be used \\nfor, such as a single card may be used as a +1 or -1 on a relevant dice roll, two card could be \\nused to generate an additional argument in the relevant area during the players turn; and \\nthree cards could be used to generate an additional argument at any point during the game \\n(but again, only in the relevant area)9. \\nLevels of Protection and Hidden Things \\nAt the start of a game there are certain things that are not readily accessible to some of the \\nplayer characters. For example, in a Cyber-Security Game the secret plans for a new \\nsubmarine would be heavily protected. \\nThings that are hidden or secret require a successful argument merely to find them. Things \\nthat are protected will require successful arguments to overcome the different levels of \\nprotection. A secret government base may be declared by the Facilitator to have 3 levels of \\nprotection: Its hidden location, its boundary fence, and the security guards, all of which \\nmust be overcome by successful arguments before the base can be penetrated. \\nAs a rule of thumb, nothing should have more than 3 levels of protection as it will simply \\ntake too long and dominate the game to the exclusion of everything else. \\nBig Projects or Long-Term Plans \\nDepending on the level of the game, some actions and events represent such a large \\ninvestment in time and effort that they require multiple arguments in order to bring them \\nto fruition. As a rule of thumb, a Big Project should also take no more than 3 successful \\narguments (like protected and hidden things above); otherwise, the game is focussed too \\nmuch on this single thing. \\nThis does not mean that arguments have to only be about things that can happen within \\nthe turn length of the game. It is possible to make \"long term\" arguments like anything else. \\nIf, in a Baltic game with week-long turns, you want to argue that an electricity cable \\nbetween Sweden and Lithuania is to be built with the aim of reducing Lithuania\\'s \\ndependence on Russian energy, this would be judged as normal. It just would not come to \\n \\n9 I am indebted to Prof Rex Brynen for this suggestion.\\n\\x0cVersion 15 \\nPage 23 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nfruition in the length of the game – but, assuming the argument was successful, it would \\nsucceed eventually unless another Actor argued that it lost funding or was delayed. \\nNumber of Actors \\nMatrix Games are best played with an even number of Actors as it is the action and \\ncounter-action running through the game that generates the insights; but occasionally \\nhaving an \"outsider\" role with an interest in events can also be useful. The game works best \\nwith 6-8 Actors and a facilitator. \\nIt quite often happens that the sponsor for a Matrix Game wants the Actors involved in the \\nscenario to be quite one-sided, so that there are several Actors on one side and only one \\nopposing them. Apart from not generating a very interesting game, it may be necessary to \\npoint out that there wouldn\\'t be a crisis if one side outnumbered the other by such a \\nmargin. It might then be necessary to dig down into exactly who the Actors really represent \\nand their capacity for independent action, in order to make the game more balanced and \\ngenerate the insights required. \\nFor example, in high level political/military games it is common for the sponsor to suggest \\nthat the Actors involved are a \"laundry list\" of the States present. This is a fundamental \\nerror because the Actors in a Matrix Game only get to make one argument each so, in a \\nBaltic States game for example, having the USA, Estonia, Latvia, Lithuania, Poland, Sweden, \\nFinland and Russia as Actors would mean that most of the time Russia would only get a \\nsingle action against seven opposing ones each turn. A better way of representing things \\nwould be to have Russia, Russian Dissidents, the Baltic States as a single block, NATO, \\nPoland (with its own agenda) and perhaps the Nordic States as a block. \\nIf this proves too conceptually difficult, you can balance the game by \"points\" where \\nperhaps Russia is allowed a number of points of arguments (so they can argue twice or have \\na single argument with double effect), against everyone else\\'s single point argument. The \\ndifficulty with this approach is that it can introduce too many arguments per turn and slow \\nthe game down excessively. \\nPersonally, I would rather frame the Actors in such a way as to balance the game, rather \\nthan using a chit system with the more powerful players having more chits. I think that \\ngetting people to model people is usually a better way. My standard model is to select \\nActors that break down into 6 rough groupings: The two main protagonists, their two main \\nsupporters (but perhaps with their own additional objectives) and then either their \\noppositions, or associated Actors you might suppose were supporting but definitely have \\nadditional objectives that could be in conflict to the main Actors. Then, after all that, \\npossibly an external power with an interest. \\nSo, for a Dutch Election Game, the Actors were: \\n• The Hofstadt Network: an Islamic Terror Group.\\n\\x0cVersion 15 \\nPage 24 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\n• The Saudi backers of the Group. \\n• The Right-Wing Neo-Nazis. \\n• The Left-Wing Dutch Coalition Government (as a coalition they had 2 players, the Right-\\nWing, Left-Wingers and the Left-Wing, Left-Wingers, each with conflicting objectives, \\nand they had to agree in order to make an argument). \\n• The Dutch Emergency Services (Police, Military, Fire, Medical) \\n• Geert Wilders, the Right-Wing Opposition Parliamentary candidate. \\nIn the \"Lasgah Pol\" Game, about a 6-month Tour of Afghanistan, the Actors were: \\n• Coalition Security Force Commander. \\n• District Governor (pro-security force) \\n• Afghan National Army Commander (pro-security force) \\n• Taliban Commander. \\n• Tribal Elder (anti-security force) \\n• Afghan National Police Commander (corrupt). \\nDiscussions as to the Actors involved and balance in the Matrix Game can generate insights \\ninto the geo-political situation in their own right and prove to be almost as valuable as \\nrunning the game. \\nHowever, it is all very well to conceptually make the game design decision that you are not \\ngoing to represent the Baltic States as Actors in a game about the political situation in the \\nBaltic, because the \"Great Powers\" in the region mostly ignore their wishes and do what \\nthey want; and quite another to play a game involving representatives from those \\ncountries. So, for example, at a NATO workshop on regional stability in the Baltic, it would \\nbe quite inappropriate to design such a game and alienate a significant proportion of the \\nparticipants from the outset. \\nIn this case an alternative approach that can work, is to represent all the relevant Actors in \\nthe game, but only call on them when it is appropriate or necessary to do so10. In this case \\nyou should start the game at the point of crisis between only two of the actors. They will \\nmake their arguments in turn, with all the other players participating in voting on the \\nargument assessment, going back and forth, as if it was a two-player game. This continues \\nuntil one of the other Actors decides that the events taking place have reached a point that \\nis more important than their internal national agenda, and they must act. At which point \\nthey make an additional argument and it is resolved in the normal way. This works far \\nbetter than I expected, because it discourages the smaller actors from \"butting -in\" with \\nminor arguments that don\\'t affect the situation in any significant way, and take up too \\nmuch time in the game. \\n \\n10 Again, I am indebted to Sue Collins from NATO ACT for coming up with this idea.\\n\\x0cVersion 15 \\nPage 25 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nIf you have several players representing an Actor in a Matrix Game, you can get them to \\nwork up alternative arguments for each turn and the team (or team leader) can then \\nchoose the best argument to take forward. This is especially useful for analytical games if \\nrecorded and the reasons for acceptance/rejection noted. \\nWriting the Briefs for the Participants \\nSuccess in Matrix Games lies in making them simple and accessible for the players. Long \\ngames with excessive briefing materials, complex structures and IT support are probably \\nbest carried out using a different technique. Matrix Games are about exploring ideas and \\noriginal thought, so briefings that are excessively serious fail to create the right atmosphere \\nand can encourage institutional thinking. They should be short and interesting. \\nIt is often useful to test the suitability of an Actor\\'s objective by simply putting an \\nexclamation point at the end of the phrase or sentence. If it looks odd, rephrase it until it is \\nappropriate. For example: in a game about an election, it is often better to phrase an object \\nas \"Prevent extremism!\" or \"Stay in Power!\" rather than \"Ensure the continuity of the \\nelectoral process and ensure that extremist politicians do not gain undue influence…\". \\nFor more serious analytical games, it is often best to provide the Actors with briefs (no \\nmore than a single side of paper) about their role and then get the players to derive the \\nactual objectives for the game themselves. This serves two purposes – a short list of pithy \\nbullet-point objectives makes for a faster and easier after game review and, by looking at \\nthe objectives the players have chosen for themselves, you can confirm they have actually \\nread the brief and are prepared to role-play the Actor correctly. \\nIt is also useful if you tell them that at least one of their objectives should be long term (at \\nleast the life of a Presidential Term or Government (say 4-5 years)) so that, at the end of the \\ngame, the players have only themselves to blame if the game only consisted of short-term \\narguments. \\nAs a rule of thumb, if you are writing a brief for a serious game (rather than a few bullet \\npoints) you should always try to broadly cover the full range of effects. These elements of \\npower are often abstracted as Diplomatic, Information, Military, and Economic (DIME) \\nactions and their Political, Military, Economic, Social, Information, and Infrastructure \\n(PMESII) effects, particularly in the USA. I would selectively pick and choose from these to \\nget to the following headings: \\n• Political. \\n• Military. \\n• Economic. \\n• Social. \\n• Infrastructure.\\n\\x0cVersion 15 \\nPage 26 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\n• Nature / Geography – only if the visualisation for the game doesn\\'t cover all the relevant \\nelements of geography or if the timescales would include the effects of global warming. \\nPlease don\\'t feel that in every scenario these aspects should have equal weight applied to \\neach of them, but all of them should be reflected somewhere in the brief, so it is sometimes \\nhelpful after you have written a brief to spend a few minutes going back over it to make \\nsure you have the range of topics covered. \\nIt is also essential to ensure that the briefings reflect the situation from the Actors point of \\nview. We are expecting them to role-play that Actor – so they will need to try to imagine \\nthemselves as that Actor, rather than merely think what that Actor would do. It is therefore \\nessential that the brief reflects the situation from their perspective. \\nI find it useful to generate the Actor briefings by cutting and pasting the relevant material \\nfrom information available on the internet. So, for example, the briefings for the North \\nKorean Actor would be taken from the North Korean website in order to properly express \\ntheir point of view. Similarly, Russia Today or Sputnik are a useful source for Russian views \\non important issues, rather than the dry prose of intelligence briefings. \\nThis has the dual purpose of make the briefing more accessible, but also unclassified. \\nHaving a game where the material can be shared openly, on contemporary topics that are \\nof great concern, is especially useful. It means that organisations can play the game \"in \\nhouse\" under whatever security regime is appropriate, but also, they have the opportunity \\nto compare their results with other groups, into order to widen the diversity of opinions in \\nthe game Actors and also the sample range from which the results are assessed – increasing \\noverall confidence in the results. \\nMatrix Games are about actions and results, rather than the minute detail of ways and \\nmeans. They therefore create an arena in which certain topics, like Cyber, can be sensibly \\ndiscussed without the spectre of high levels of security classification restricting the \\naudience and stifling debate. This can be very helpful. \\nRecording the Effects of Arguments \\nIn most cases the Actors will present arguments for intangibles at some stage in the game, \\nsuch as ensuring that the Police are paid on time, having the population more accepting of \\nthe soldiers operating in their town, or improving the morale of their followers so they \\nwork harder. \\nThere is no need for complex record keeping - in the majority of cases, simple generic \\ncounters such as those with a \"Happy face\" or \"Sad face\" are all that is required to keep \\nscore of the effects of the successful arguments. \\nIf the arguments are more wide-ranging (in that they would affect a number of counters in \\nthe game) it can be better to use a \"Marker Track\" alongside the game map, rather than\\n\\x0cVersion 15 \\nPage 27 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nspend the time piling markers on counters. Tracks can be generic (in that they simply record \\nthe number of plusses or minuses applied) or they might have specific \"trigger levels\" (in \\nthat when the morale of the infantry is reduced to -3, the \"raw\" units will desert and return \\nto their homes. \\nIt can also be useful to have a \"Press\" actor whose job it is to record the results of \\narguments (both visible to the public and those not), as well as putting the \"Press spin\" on \\nthe events. This role can be useful in looking after the \"Consequence Management\" \\nelements mentioned earlier. \\nThe Components (and Characters) Affect the Game \\nWhen participants are thinking on their feet, what they can see will affect what they argue \\nabout, more than most of the other elements in the game briefing. If the game only has \\nrepresentative markers for military units, most arguments will be about military or kinetic \\nactions. If the full range of Political, Military, Economic, Social, Information and \\nInfrastructure effects are represented by counters or markers on a map, play will be more \\nwell-rounded and a full-spectrum approach. \\nIt is also worth bearing in mind that the characters will also affect the game. Quiet and \\nintroverted people who shy away from confrontation are probably unsuitable to play \\nruthless dictators, so an element of character selection is important. This can usually be \\ndealt with by asking for volunteers for the various roles if you don\\'t know the individual \\nparticipants well. \\nLastly, you may wish to consider set decoration in the form of posters, political quotes, or \\neven national headgear for the actors (although in most professional games I would make \\nsure this is acceptable to your audience). Reproductions of political cartoons can also be \\nvery effective.\\n\\x0cVersion 15 \\nPage 28 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nStarting Conditions \\nAt the start of a scenario there may be recognised advantages or penalties understood for \\nan Actor. These can be highlighted and exposed to the players so they can be corrected or \\nexploited during the game, or can be hidden from the other players. Hidden starting \\nconditions can be included in the game objectives for the Actor, such as having an objective \\nthat is important, but not related to the main thrust of the game play that needs to be \\naddressed at some stage during the game (representing this that would distract the Actor \\nfrom the scenario goals). Alternatively, the start conditions affecting the Actor could be \\nprinted on cards and laid out for all to see. This presents a dilemma for the Actor – do they \\nspend time addressing a problem that the card represents or do they get on with the main \\ngame objectives and accept the penalty the card might represent? \\nA good example of this is included in the ISIS Crisis game where the institutional \\nincompetence of the Iraqi Government is a starting condition. In game terms this means \\nthat any arguments involving Government decisions are automatically given a -1 penalty \\nagainst success, unless there is a successful argument made about reforming the \\ninstitutions and ending corruption. \\nAnother aspect of starting conditions is the possibility of an event acting as a trigger to the \\ncrisis. These could be pre-defined as part of the scenario or they could be random. For \\nexample, in a game about the South China Sea, the game started in a state of reasonable \\nequilibrium among the Actors. A number of random even cards were generated and \\nrevealed as a new situation that came into effect at the start of each turn, such as: \\nCorruption allegations against a senior figure, typhoon weather and resulting casualties, a \\nwarship running aground being a national embarrassment or perhaps a valuable mineral \\ndiscovery in the region. These helped the players imagine things they could exploit to \\nimprove their position and achieve their objectives. (Please see Random Events, below). \\nCue Cards \\nCue cards in Matrix Games are similar to starting conditions explained above. They \\nrepresent capabilities that are possibly of interest to the Actors in the scenario and are \\nthere to nudge the player\\'s attention and imagination. An example of a cue card could be to \\ndraw attention to a particularly strong opposition group, a noted gap in weapon system \\ncapability that could affect one side in the timescale in the scenario, or perhaps that one \\nforce has popular support from a section of the population so operations in that area would \\ngain an advantage. These should be printed and visible to all the players. \\nGaining the effect form a cue card requires an argument in the normal way, but they can be \\ngiven weighting scores + or – to represent their ease or difficulty in acquiring.\\n\\x0cVersion 15 \\nPage 29 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nLarge-Scale Combat \\nMost Matrix Games are not about the large-scale engagement of purely military units. \\nThere are other techniques that are usually far more appropriate for those kinds of games, \\nbut there will be games in which numbers of units will engage with each other in the game, \\nin among all of the other Political, Military, Economic, Social, Information and Infrastructure \\neffects in the scenario. For example, in a civil war or coup type scenario. \\nSmall numbers or rare combats are best resolved by having additional separate arguments \\nin the normal way. The Actors should be invited to offer arguments as to why they think \\ntheir forces might win in the conflict, and the opposition why they might fail. If dice are to \\nbe rolled, it is usually best to make the rolls opposed as it heightens the tension and \\nincreases player involvement. So, if the chance of success for Actor \"A\" is 6+ on 2D6 against \\nActor \"B\", both should roll. \"A\" needs to get 6 or more and \"B\" needs to get 5 or less – with \\none succeeding and the other failing to win. If both succeed or both fail, the dice are rolled \\nagain, with the number of repeats reflecting the intensity of the fighting. \\nIf combat is to be more frequent, an easy way of adjudicating combat for a number of units \\nis by using the Simple Combat Resolution Using Dice (SCRUD) technique. In this each unit is \\nrepresented by a single six-sided dice with positive or negative modifiers applied to them. \\nA number of different colours of dice are used, with the different colours representing \\ndifferences in troop quality and equipment capabilities, and their associated modifiers in a \\ntable. The effectiveness for the different units can be assigned in the scenario, but are all \\nabout to be modified by successful arguments.\\n\\x0cVersion 15 \\nPage 30 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nA House Divided \\nIn many cases the Actors represented in a game do not represent a unified and efficient \\ncommand structure – for example the Government may be a coalition of different political \\nparties with differing aims and objectives. This could be represented by allocating a \\nseparate Actor for each faction, each making arguments, but this can unbalance the focus \\nof the game and create too many Actors, slowing down play and losing momentum. \\nIn these cases, it can be better to give the Actor a team of players with conflicting briefs, \\nand require consensual or voting decisions in order for them to make arguments. Without \\nthe consensus, the Actor simple does nothing that turn due to internal bickering. \\nOf course, for an analytical game the intra-team discussion leading to making a successful \\nargument will need to be captured to understand what sorts of concessions led to \\ncooperation in the competing factions. \\nAnnouncements \\nActors quite often make policy announcements or Press statements as part of their turn, to \\ninform the other players of their stated intentions. In many cases these are not really \\n\"arguments\" as part of the game, so shouldn\\'t count as their action for the turn, unless they \\nwish to specify a measurable effect (such as increasing their approval ratings). \\nTrade Agreements \\nIn some games, trade forms a very important part of the game narrative. In most cases this \\ncan be treated simply as part of the normal ebb and flow of the argument process. \\nHowever, in some circumstances, particularly when timescales are long, trade can require \\ngreater attention as to the nuances of the economic benefits and impacts. In these cases, it \\nmay be necessary to get the two sides to make additional arguments as to what they expect \\nto achieve over the agreement (noting that these may be different to what was actually \\nnegotiated!) and adjudicated in the usual way. This may, of course, result in one side \\ngetting more out of the deal than the other. \\nThis can draw particular attention to the deal in itself, leading to further economic \\narguments as to the unintended consequences of the deal on other Actors or stakeholders \\nin the game. \\nThe Order in which Actors make their Arguments \\nAs a designer, you should try to have arguments from opposing points of view alternating in \\nthe turn order, so you get oppositional arguments. \\nIn most cases the order in which the Actors make their arguments doesn\\'t cause any \\nconcern but, occasionally when Actors have been involved in \"inter-turn plotting\", they \\nmight want to change the sequence in order to maximise the effect they wish to have.\\n\\x0cVersion 15 \\nPage 31 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nI normally simply say to the players that the Actors concerned wish to temporarily swap \\ntheir positions in the turn order and carry on. It is very rare for there to be objections and \\nthe very fact that they wish to do so is a good indicator that the Actors are now working \\nclosely together. \\nVery occasionally the turn order can cause problems when an Actor earlier in the sequence \\ncarries out a successful action that prevents, or renders irrelevant, the action an Actor later \\nin the turn order of the same turn was going to do. I normally explain that they were merely \\nunlucky and the other Actor managed to complete their action early – however, it is \\nimperative that you find a way to balance that circumstance to prevent it being repeated. \\nOne way is to randomise the turn order – personally I will always start with a fixed turn \\norder and only change if I need to, because most of the time this situation doesn\\'t arise – \\nbut once it does, you may need to \"rebalance things\" or lose the confidence of the players. \\nThe simplest way of randomising the order is to use a set of numbered cards equal to the \\nnumber of Actors and deal them out at random each subsequent turn. \\nGaming Possible Futures \\nWhen running game events, it is often necessary to consider scenarios taking place at some \\ntime in the future. If the events are in the near future, the implications may be minimal, but \\nif the events take place over some years, political terms, or even decades into the future, \\nthe implications may be considerable. \\nFor example, the Trump administration changed the nature and character of US \\ninternational relations during his tenure, and many policy responses could be characterised \\nby uncertainty compared to previous administrations. It was therefore necessary to \\ndetermine if this is likely to continue in the timescale envisaged by the game, or if there \\nwould be a return to the status quo. This is not limited to US politics, as major elections \\noffer the possibility of similarly significant shifts in the political mood among other Actors. \\nIf the event is singular, such as an important election, with the potential for a significant \\nchange in policy priorities, it is usually best to simply get the participants to vote (using \\ndiceless adjudication or estimative probability). \\nOther examples relate to on-going events such as responses to climate change, advances in \\ntechnology, or things like long-term infrastructure projects that will impact on the Actors in \\nany scenario. \\nIf such a situation exists in the game, one simple method of dealing with it is as follows: \\nEach Player in the game is required to note down the \"the most important things to happen \\nin the specified time period\" from the point of view of the Actor they represent. \\nThe number of things the player should specify is dependent on the number of participants \\nand the time available. As a rule of thumb, a list with perhaps 10 to 15 different items can\\n\\x0cVersion 15 \\nPage 32 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nbe dealt with in a reasonable time. Since it is perfectly possible that several people may \\nchoose the same, or very similar, things, small groups of about 6 participants should \\nconsider coming up with 3 things each. Larger groups, proportionally less, and much larger \\nparties be invited to collaborate in pairs or small groups on the \"single most important \\nthing\" for each group. \\nIn their deliberations, they should be invited to think across the full range of types of things, \\nfollowing the PMESII-N model (expanded to include elements of Nature, such as Climate \\nChange): \\n• Political \\n• Military \\n• Economic \\n• Social \\n• Information \\n• Infrastructure \\n• Nature \\nCare should be taken not to discuss the exact definition of \"things to happen\" in too much \\ndetail, as the most senior or loudest voices in the room may dominate, and this acts to limit \\nthe participant\\'s imagination as to the full range of effects and events. \\nThese things should be noted down in some way, such as bullet points on a PowerPoint \\nslide, or written on separate sheets of paper, and displayed where everyone can see them. \\nThis process is using crowd-sourcing to determine the possible futures. \\nFinally, each Player should be invited to vote as to whether the thing happens, using the \\n\"Yes, I think it will happen\", \"I\\'m not sure…\" or \"No, I don\\'t think it will happen\" voting \\nsystem. The respective scores should be noted against each possible future, and the list re-\\narranged to place the things in order, with the most voted for item at the top. This process \\nis using crowd-sourcing to determine the likely futures. \\nThis will end up with a list of things, for the purposes of this game, that will happen over the \\ntime period, with increasing impact and likelihood higher up the list the item is. \\nRandom Events \\nIn some events the scope of the game may involve a scenario where there is an equilibrium \\nat the start of the game. There is no obvious crisis that has triggered the game to take \\nplace, such as a nerve agent attack in London against a Russian dissident. The game may \\nalso be set to take place over a long timescale, where the players tend to consistently think \\nlong term, so they don\\'t get distracted by a sudden crisis upsetting their plans. In these \\ncases, including random events may be useful to provide a focus for disruption and \\npromote a more engaging game.\\n\\x0cVersion 15 \\nPage 33 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nMy advice is to create a set of cards with generic crises on them, such as: Eco Terrorism, \\nRadiation Leak, Economic Downturn, Mineral Discovery, Extreme Weather, Corruption \\nScandal, etc. \\n \\nThere are two schools of thought with regard to “random events”: \\nThe events should be chosen at random, with random degrees of severity, and applied to \\nthe participants at random during the game. \\nThe events should be chosen at random, but given to a different player, in turn, throughout \\nthe game. They introduce the event as an “additional argument” that they can apply as \\nthey wish in order to contribute to the game narrative. \\nMy view that because a Matrix Game is deliberately short, with a limited number of actions \\npossible throughout the game, having “random events” happen completely at random is \\nproblematic. An Actor may be disadvantaged purely by chance, more than once during the \\ngame, which can reduce their immersion and engagement. The narrative develops during \\nthe game based on the decisions of the players and their reactions to the decisions of other \\nplayers. Having random events imposed on them by chance breaks this “cause and effect” \\ncycle and degrades the game flow. \\nThe alternative is to give the random event to the participants. They will then make a \\ndecision as to how this can contribute to the narrative being developed by the players. They \\nwill still need to make a suitable Matrix Argument as to who it affects and the severity, but \\nit becomes part of the player decision process and so preserves the “cause and effect” cycle \\nof game play. They also know that everyone will have an opportunity to exploit a random \\nevent, so this is a fairer method in a game with limited numbers of Actors and game turns. \\nAn example: During a \"Belt and Road\" game about global infrastructure development, the \\nChinese and Russian players have worked together to exploit the melting ice pack and \\nestablish a trans-Arctic “Road” from China to Europe. This will disadvantage the ASEAN and\\n\\x0cVersion 15 \\nPage 34 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nIndian Actors by reducing trade in their areas. The Indian player has an “Extreme Weather” \\ncard and elects to argue that, despite the ice pack receding in the Arctic, global warming \\nleads to more extreme weather events, and there is a shipping disaster where two huge \\nChinese container ships are lost in a storm in the Arctic, highlighting risk for this route, \\nreducing investment and profitability. \\nThis is perfectly reasonable and it is likely to succeed – but of course opens up the \\npossibility that another Actor may argue later that extreme weather and rising water levels \\ncould affect low lying areas of Bangladesh, causing loss of life, famine, migration and \\nexacerbate regional tensions with India. \\nSenior Officers, Dominant People and Contentious Arguments \\nIt is not uncommon in a Matrix Game that the participants want to \"debate\" the arguments. \\nTo a limited extent this is ok, but as stated elsewhere, the game needs to move at a pace, \\ncreating an immersive narrative and forcing the players to have to live with the \\nconsequences of their earlier decisions. \\nIt can happen that a Senior Officer, used to \"seminar wargames\", will interrupt when you \\nwant to move on and say \"wait a minute - this is a really valuable debate - let\\'s just dig \\ndown...\" You should try to point out that this is not that sort of game - Matrix Games are to \\ngain an insight and understanding in a specific way. Short notice, minimal preparation and \\nmaterials, a short game, and small numbers of participants. If they want to conduct a \"deep \\ndive\", this isn\\'t the appropriate game - the purpose is to identify the insights – so make a \\nnote and move on. The \"deep dive\" should follow later or in a different type of game. You \\nshould, therefore, make sure you include this point in your introductory briefing so that the \\nplayers are clear from the outset. \\nWhen dealing with dominant people, who continually interrupt and dominate the \\nArguments, you need to take a harder line. You should interrupt them when they interrupt \\nanother player making a point. Point out to them that they had their chance. This isn\\'t a \\ndebate. This is a turn based adversarial wargame and the procedure for arguments is \\nsimilar to a Court of Law – you have a chance to have your say, but then you have to remain \\nsilent while the others respond. \\nOne Actor goes, the others respond, then adjudication takes place. There should be strictly \\nlimited back and forth. Just because these are oral arguments doesn\\'t give anyone the right \\nto interrupt after every point. Again, like in a Court of Law - interruptions should only be on \\npoints of provable fact or procedure. \\nYou cannot be too dictatorial, however. It usually happens at least one point in the game, \\nthat the argument is contentious – in that the participants continue to argue after making \\ntheir initial points and are reluctant to stop. This needs to be handled carefully as imposing \\nan adjudication can dramatically reduce buy-in to the result and the game overall. In these\\n\\x0cVersion 15 \\nPage 35 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\ncases, it is usually best to appeal to the professionalism of the participants and a switch to \\nthe estimative voting probability adjudication system is usually the best way of moving on \\nwith the rest of the game. \\nIt also happens that someone may raise an objection late, often during voting – usually \\nbecause they didn’t raise the point at the appropriate time (possibly because the facilitator \\nwas trying to push the game along at pace). It is worth pausing, explaining the right time to \\nmake those points in the turn, apologising for pushing the game forward too fast – and \\nthen re-running the adjudication procedure. \\nNit-Picking vs Important Clarification \\nIt is important to remember that the theory of crowd-sourcing the adjudication requires \\nthat you present the Pros and Cons of an argument, as if you were in a Court of Law, and \\nyou do not discuss the argument too much. Excessive discussion allows the loudest voices \\nand dominant personalities in the room to shape the argument and induce an element of \\n\"group-think\" which we are trying to avoid. \\nThe argument should be simply put with an Action/Event that happens, with a measurable \\nresult, supported by reasons why or how. This is then offset by opposing reasons, if they \\nexist and the appropriate adjudication method is used to gain a result. \\nYou may find that certain players want to have an excessive degree of clarification as to \\nexactly what the argument is, what it really means, and how it will affect the other Actors, \\nin detail. This is dangerous and can lead to \"excessive discussion\" as mentioned earlier, but \\nunder a different guise. A useful measure is to look around the room and if nobody else is \\ndesperately in need of this clarification, then it is usually that individual\\'s problem and play \\nshould proceed – I usually bring to their attention that in the initial briefing about how a \\nMatrix Game works, I explained that too much discussion makes the room less intelligent, \\nso I am happy to proceed unless someone else in the room thinks we need to dig into the \\ndetail. \\nCare should be taken, however, as some points of clarification are important. How elections \\nand voting is carried out is always important to be clear about. Understanding the \\nmeasurable effect should be clear as well – and it is the role of the Adjudicator to ensure \\nthat they understand this and can explain it to the other Actors if necessary. \\nThis is an area where experience counts, so being aware of the issue can help in spotting \\nthis when it occurs, and taking time to reflect on the circumstances may assist in future \\ngames.\\n\\x0cVersion 15 \\nPage 36 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nWhy I like Matrix Games \\n• Designing a Matrix Game can be done quickly with the minimum of fuss. \\n• Participating in a Matrix Game does not require an understanding of complex and \\nunfamiliar rules. \\n• Matrix games can cover a wide variety of possible scenarios, including conceptual \\nconflicts like Cyber. \\n• They are especially good in the non-kinetic, effects based, domain. \\n• Matrix games deal with qualitative outputs so are especially useful for non-analysts. \\n• The games work best with small groups, increasing immersion and buy-in to the game. \\n• Matrix games are extremely inexpensive (and they work best with short sessions lasting \\nhalf a day). \\n• They are perceived to be new and innovative (despite being around since 1987). \\n• They are easy to transport, requiring only pen and paper – with perhaps a few maps and \\ncounters. \\n• They work well in multi-domain, multi-agency contexts allowing all Actors to participate \\nequally. \\nA few Words of Warning \\n• The fact that a Matrix Game requires little infrastructure can be a problem – it just \\ndoesn\\'t look sexy and the strengths that it can be done quickly with the minimum of \\nfuss, can be reduced by efforts to make it look cool/expensive. \\n• The non-quantitative nature of the game can frustrate analysts. \\n• Matrix Games require an experience facilitator to run them. \\n• Components and player selection can affect play: so, if all the counters are military, \\ninexperienced players tend to make the majority of their arguments about military \\nactions; and equally, it is no good getting a quiet introvert to try to play a dynamic \\nleader like Vladimir Putin. \\n• A facility with language is important, which might prejudice play with multi-national \\nparticipants. \\n• Matrix Games don\\'t scale well and, while there are mitigating techniques for large \\ngroups (50+), they lose some of their impact. \\n• There is a paucity of academic research in this area (but this is improving). \\n• The games are vulnerable to a \"Senior Figure\" accusing the game structure as \"just \\nmaking things up!\" \\n• Some players have great difficulty with the concept of \"only 1 action per turn\". \\n• Some players (fortunately very few) appear fundamentally unable to grasp the concept, \\nwhich in a small game has a disproportionate effect.\\n\\x0cVersion 15 \\nPage 37 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nFinal Comments \\nSome of the most insightful and well-run games happen when the players all end up with a \\nmutually shared understanding of the situation. The game has created in the participants a \\nshared story-living experience of the situation of the game, with the Actors role-playing \\ntheir parts. There is good evidence that role-play can more accurately predict outcomes in \\nconflict than other methods, and Matrix Games use this as a fundamental part of the \\nmethodology11. This happens best with small groups (less than 20 participants) and having \\nthe game flow naturally. An experienced Facilitator can be invaluable in helping the story \\nmove along, linking the arguments made and weaving them into the narrative so they make \\nsense. \\nAs a result, Matrix games are probably best served in the early “understand” phase of \\nconsidering a problem. They have demonstrated countless times their efficiency in getting \\nall the participants to a shared level of understanding about a problem situation, far better \\nthan any number of briefing notes. DSTL have used them on numerous occasions in order \\nto confirm if the Sponsor for a piece of research is asking an “intelligent question” before \\nexpensive and time-consuming analytical research is carried out. \\nIt is tempting to add extra rules and complexity to the simple base technique of the Matrix \\nGame. This should be avoided if at all possible – the strength of Matrix Games come from \\ntheir speed and simplicity. Additional rules can slow down production, complicate the \\ngame, hinder play and distract the players. \\nTry not to be clever – just keep it simple. \\nHaving time at the end of the session to discuss the game and understand the objectives of \\nthe different Actors involved is vital. Going around the participants and asking them to read \\nout their objectives and explain why they though they succeeded or failed can be most \\ninstructive. Also, if you then ask the assembled group \"who won?\" and they all agree, then \\nthis can be a very powerful indicator of things that might need to be looked at more closely \\nas a result of the game. \\nFinally, the insights from the game can take a little time to come out. They might not be \\nimmediately obvious, so taking time to consider what happened in the game and whether \\nindividual events are noteworthy, is very useful. I am continually surprised at the predictive \\npower of such a simple game. \\n \\n \\n \\n11 See: Game theory, simulated interaction, and unaided judgement for forecasting decisions in conflicts. Kesten C. Green. \\nInternational Journal of Forecasting 21 (2005) 463-472.\\n\\x0cVersion 15 \\nPage 38 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nMatrix Game Checklist \\nPre-Game \\n• Assemble Map (if appropriate) – if not appropriate, work out how success and failure is \\nto be recorded (Flip chart? PowerPoint?) \\no Wikipedia has very good vector country maps for free download. \\no Avoid making the map too detailed – players get bogged down. \\n• Assemble Briefings \\no Short Briefings with objectives, for recreational games. \\no Full briefings for educational or more analytical games. \\n• Assemble counters to represent forces, effects and influence. \\no Print counters onto A4 labels, stick to foamboard and cut out with a sharp knife. \\no Or print on plain paper, apply to self-adhesive plastic floor tiles and cut out with \\nheavy duty scissors. \\n• Ensure you have the necessary cards for the players if you are using Estimative \\nProbabilities, or Diceless Voting to adjudicate arguments. Also have a pack of numbered \\ncards in case you need to randomise the turn order. \\n• Timings: You want about 6 turns in the game to make the players live with the \\nconsequences of their decisions, so with 30 min turns, allow at least 3 hrs. \\nGame Start \\n• Explain the game type and how arguments work, as well as any special rules for the \\nscenario. \\n• Allocate roles, then get the players to read their briefs and generate objectives (for \\nanalytical games), including long term goals. \\n• Explain turn order (and think about changing the order during the game). \\n• Tell the players how long a \"turn\" is (game time) and how long you expect a turn to take \\n(real time). \\n• For games with inexperienced players it can be a good idea (if you have time) to have a \\n\"rehearsal\" pair of aguments to ensure they understand how \"arguments\" work. \\nIn Game \\n• Ensure that the game is pushed along and there is the minimum of unnecessary chat \\nwhen making an argument. \\no The arguing player give an Action and a measurable Result along with reasons \\nWhy or How (Pros). \\no The other players give reasons Why Not (Cons): \"Can anyone think that argument \\nwon\\'t work?\" \\no The Facilitator works out the chance of success (weighted probability method) or \\nthe player use the estimative probability voting card method.\\n\\x0cVersion 15 \\nPage 39 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\no If unopposed or a really good argument – no need to roll the dice, it just happens. \\no Remember – this isn\\'t a debate – so make sure it doesn\\'t degenerate into one. \\n \\n• Roll the Dice. \\no Roll a 7+ on 2D6 for games with a \"narrative bias\", adding or subtracting \\ndepending on arguments, or, \\no Roll a 7+ on 2D6 for games with no \"narrative bias\", adding or subtracting \\ndepending on arguments, but using Red and Green dice (if the score is 7 and the \\nRed dice is the higher, the argument fails), or, \\no Roll against a percentage if using the estimative probability voting card method, \\nwith success being a roll lower than the stated probability. \\no The scale of success or failure can have an additional effect and the Facilitator \\nshouldn\\'t be afraid of modifying the result to ensure it is consistent with the \\ntimescale of turns in the game – so where the turns are short and someone \\nargues for something that would take a long time, you can say on a success that it \\nhas started and will continue (unless someone stops it). \\n• Alternatively, use a Diceless Adjudication method with voting. \\n• Note successes and failures down (It can help if you use a flip chart where everyone can \\nsee it). \\n• Summarise the successes and failure at the end of the turn. \\n• As the Facilitator, carry out \"consequence management\" based on the arguments of the \\nplayers. Add refugees, note media reactions, etc., and raise issues that if unresolved will \\nhave consequences in later turns. \\n• Between Turns: Take a pause at the end of the turn for players to take a comfort break \\nand talk to each other, conducting diplomacy, plotting or perhaps making deals for the \\nnext turn. Make sure this time is limited because the game should not be allowed to \\ndrag on. Any discussions should be noted down in higher level policy games. \\nPost-Game \\n• Sometimes it is useful to have a final round of long-term arguments – especially for \\ncharacter driven games. \\n• Have the players read out and discuss their objectives. \\n• Always allow time for a discussion about what went well, less well and ideas for better \\nways of working. \\n• Make immediate notes to help you later. There will be a great many observations \\ncoming out, so try not to miss anything. \\n• Take time to reflect on the game. Many insights only become useful after some time to \\nappreciate what they are.\\n\\x0cVersion 15 \\nPage 40 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nSample Spendable Bonus Cards\\n\\x0cVersion 15 \\nPage 41 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nSample Random Events\\n\\x0cVersion 15 \\nPage 42 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023\\n\\x0cVersion 15 \\nPage 43 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nSample Voting Cards for Diceless Adjudication\\n\\x0cVersion 15 \\nPage 44 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nSample Estimative Probability Cards\\n\\x0cVersion 15 \\nPage 45 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nSample Turn Order Cards\\n\\x0cVersion 15 \\nPage 46 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nSample Markers for Matrix Games for Effects and Conventional Forces\\n\\x0cVersion 15 \\nPage 47 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023\\n\\x0cVersion 15 \\nPage 48 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023\\n\\x0cVersion 15 \\nPage 49 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023\\n\\x0cVersion 15 \\nPage 50 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nSample Map for a real-world political Matrix Game\\n\\x0cVersion 15 \\nPage 51 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nSample Map for a fictional natural disaster Matrix Game\\n\\x0cVersion 15 \\nPage 52 of 52 \\n© Tom Mouat 2019, 2020, 2022, 2023 \\nWhat are Matrix Games? \\nMatrix games are different. In a Matrix game, there are few pre-set rules limiting what \\nplayers can do. Instead, each is free to undertake any plausible action during their turn. The \\nchances of success or failure, as well as the effects of the action, are largely determine \\nthrough structured argument and discussion. This process allows for imaginative game \\ndynamics that are lively and open-ended, and yet also grounded in reality. In a Matrix \\nGame, you use words to describe why something should happen, the Facilitator or the \\nplayers (or both) decide how likely it is, and you might roll a dice to see if it happens (but \\nequally, in the face of a compelling argument, you might not need to). If you can say \"This \\nhappens, for the following reasons...\" you can play a Matrix Game. \\nMatrix games are particularly well-suited for complex conflicts and issues involving multiple \\nactors and stake-holders, varying interests and agendas, and a broad range of \\n(diplomatic/political, military, social, and economic) dimensions. The game system \\ncrowdsources ideas and insight from participants, thereby fostering greater analytical \\ninsight. The games themselves are not intended to be fiercely competitive, with obvious \\nwinners and losers. Instead, they operate with the players working to generate a credible \\nnarrative. The player roles may have objectives that will place them in conflict with other \\nplayers, but it is perfectly possible for all of the players to achieve at least some of their \\nobjectives by the end of the game. \\nAbout Tom Mouat \\nTom Mouat MBE is a Graduate of the Army Staff College and has served worldwide since \\n1979. He is an expert in both manual and computer-based simulation systems, running \\nlarge scale military training exercises and designing wargames. \\nHe worked in Headquarters ARRC for 2 years prior to their first deployment to Bosnia, \\nwhere he was awarded the MBE. Following this he ran the British Army\\'s principal land-\\nbased computer simulation system for 3 years. He was also a Requirements Manager for \\nsimulation in the UK MOD\\'s procurement organization for nearly 5 years where he was \\nawarded the Chief of Defence Material Commendation for innovation and costs saving. \\nHe has a Master\\'s Degree in Simulation and Modelling, has published articles and delivered \\nlectures about simulations, military history and wargames for professional development, \\neducation and recreation since 1983. He a contributing author to the \"Handbook of \\nResearch on Serious Games as Educational, Business and Research Tools\", \"The Sandhurst \\nKriegsspiel\", \"Dark Guest: Training Games for Cyberwarfare\", as well as several others, and \\nhas delivered numerous wargames across the MOD. \\nHe is currently the Directing Staff officer responsible for Modelling and Simulation at the \\nDefence Academy of the UK and has recently been awarded the Chief Scientific Officer\\'s \\nCommendation for his contribution to science and technology.'),\n", " Document(metadata={'source': 'data/toward-serious-matrix-games.html'}, page_content=\"About PAXsims\\n\\nBibliography\\n\\nReviews\\n\\nDerby House Principles\\n\\nGames\\n\\nAFTERSHOCK\\n\\nAFTERSHOCK FAQs\\n\\nMaGCK\\n\\nMcGill megagame\\n\\nConnections North\\n\\nOpportunities\\n\\nPAXsims\\n\\nConflict simulation, peacebuilding, and development\\n\\nHome\\n\\nToward serious matrix games\\n\\n1 Comment Posted by Rex Brynen on 21/09/2014\\n\\nIn recent weeks PAXsims has reviewed a new book on Matrix Games for Modern Wargaming, and also offered an after action review of a recent matrix game in the UK that examined the current political and military situation in northern Iraq. Today we’re pleased to feature a guest blog post by Ben Taylor in which he further explores the value of such games for policy analysis and decision support.\\n\\nBen Taylor is Team Leader for Strategic Planning Operations Research at the Centre for Operational Research and Analysis, Defence Research and Development Canada. The views expressed below are those of the author and not necessarily those of DRDC.\\n\\n* *\\n\\nMatrix games exist in a space between conventional rules-based wargames and role-playing games. Rather than have complex rules to cover all the possible actions players can undertake matrix games tend to be very light on rules and instead allow players to make structured arguments as to what actions are undertaken and what results occur. The players, guided by an umpire as to what is plausible or probable, collectively built a narrative. Since players can make arguments as to why another player’s proposed course of action will, or will not, succeed the game has elements of both cooperation and competition.\\n\\nMatrix games can be liberating in that they avoid the need for lots of charts and tables and complex calculations to resolve actions. If the players and umpire agree that something is plausible and likely to work, then it is likely that it will work and the umpire can rule on whether it turns out as planned by a single roll of the dice. This construct allows players who understand the context of a game very well to explore the situation very quickly without cumbersome game mechanics. On the other hand, as Hollywood action movies teach us, historical accuracy and the laws of physics can be set aside in favour of a good story line. If too much violence is done to reality then a matrix game, however much fun to play, will provide the players with few useful insights into the subject of the game. How then do we design a matrix game that is useful as a serious tool?\\n\\nGames for experts\\n\\nReal experts in a subject may not need the artificial construct of a matrix game to have a meaningful and useful discussion on the subject. They may find however that the competitive structure of the game does force them to think through strategies and their strengths and weaknesses. For such a group the role of the umpire is simply to translate the interaction between the players into the matrix argument format and to let the players drive the game.\\n\\nGames without experts\\n\\nWhen setting up a game with a group of players who are not experts in the subject of the game, or who have a mix of levels of expertise, then the designer has other issues to consider. Do non-expert players need more or less discussion around the game? On the one hand they are less familiar with the scenario and the actors and so would benefit from building more shared understanding. On the other hand non-experts talking to one another could just lead to groupthink and building a consensus around false assumptions.\\n\\nIt is likely that more thought need be given to keeping the players grounded in the subject without them feeling overly constrained.\\n\\nProviding players with a rich ‘primer’ of background information will make it easier to role-play. Time spent creating the ‘back story’ for even actors in fictitious conflicts will likely be time well spent. The primer should provide a rich context from which to role-play rather than just the key elements of the current situation and objectives.\\n\\nNon-player roles\\n\\nThree distinct non-player roles can be identified in matrix games. Each of which is critical in ensuring a useful outcome from a serious game:\\n\\nGame owner – the individual for whom the game is being run. This could be the boss if it is being used for a training application or a study director if the game forms part of an analysis exercise.\\n\\nGame controller (or umpire) – the individual charged with making the game work, to administer the rules and to make assessments on the resolution of actions.\\n\\nWhite Cell – one or more individual subject matter experts (SMEs) who provide injects into the game to maintain realism.\\n\\nThe game controller is critical to the success of any matrix game. The skills required include those of a facilitator – to ensure that everyone gets to speak at the appropriate time and nobody dominates –as well as the arbiter of all of the arguments proposed by players. It is essential that the game controller is even-handed and consistent in his or her rulings and application of the rules so that they do not skew the flow of the game. A good game controller can coach less experienced players without guiding their play, which will help the game achieve its intended purpose. The controller may allow a practice round of arguments to help players settle in before starting the game proper. This would help avoid any poor first turn choices by inexperienced players.\\n\\nThe game owner should resist the temptation to inject new events into the game (e.g. “the bridge being used by the aid convoys has collapsed”)? This may be useful in forcing players to investigate specific problems, but on the other hand the owner can be accused of forcing a preferred result or conclusion. The former issue may be a positive in a training or education context, but the latter is troublesome in an analytical game.\\n\\nThe white cell (which could be one or more people depending upon the scale of the game) should be able to inject events, or even introduce new arguments and/or reasons into the game. This would be less problematic than allowing the owner to intervene as the white cell’s role is to make sure the game has the right ‘look and feel’, not that it achieves a preconceived result. Nudging the game toward realistic course of events may be necessary from time to time.\\n\\nThe game controller should not be able to inject events or argument as his/her role is to run the game mechanics. The only exceptions would be:\\n\\nIf it is made clear that the umpire is also the white cell and is so permitted to add reasons for or against player actions.\\n\\nThe scenario has scripted actions (e.g. if the capital falls then new rebel units immediately appear, or on turn 4 a flood washes away the bridge to the northern province).\\n\\nPregame actions\\n\\nIn some cases players could be allowed one or more pregame actions. These would be limited to setting precedents for later and could not be used to change the physical start state of the scenario or to counter any special bonuses or penalties described in the scenario briefing materials. In many cases these could be interpreted as clarifying the start state where the scenario briefing materials are silent. For example the following arguments could be made:\\n\\nAction: NATO has deployed a naval task group to the area. Result: +1 on future actions supported by air strikes or amphibious forces\\n\\nAction: Insurgency has infiltrated Army command. Result: -1 on future army actions to target insurgency units.\\n\\nThe reason for doing this would be to allow players to refine the starting situation before anyone starts making actions to move or attack anywhere. Once this happens other players may feel forced to respond with their own moves. Some players may be in a position where they could gain advantage by forcing the game to quickly escalate on turn one.\\n\\nThere should be limits on the number of such actions and a number of them may be secret actions (i.e. known only to the player and the controller). The umpire, white cell and game owner might need to have the ability to veto pre-game arguments.\\n\\nScenario Design\\n\\nThe design of the scenario, that is the description of the starting situation and any maps and playing pieces used to depict the situation, is clearly critical in providing the context through which the players interact. Very careful thought needs to be given to what information is provided as it may shape player perceptions and lead them to certain courses of action. For example, if one described a failed state intervention scenario and put lots of refugee markers on the map that may guide players into treating it as primarily a humanitarian mission. But if the same scenario was described but players shown no refugee markers but lots of hidden weapon cache markers then that may cause players to treat it as a counter-insurgency mission?\\n\\nIs there a type of scenario that a matrix game is particularly well-suited (or poorly suited) to? Strictly one-sided (government vs. nature in a domestic disaster relief operation), two-sided, multi sided, straight forward shooting war, complex hybrid failed state environment? The opportunity for direct interactions between players to cut deals would suggest that this game type is well suited to multi-sided complex operating environments. Conversely using them for two-sided combat scenarios may be a weaker application (although examples of these have been played in the recreational gaming community). Note that it is always possible to convert a one-sided or two-sided scenario into a multi-sided scenario by splitting sides up into factions that are competing at some level and which may have slightly different objectives (e.g. different allied nations of a coalition, different services, different government agencies or political leaders within the same nation).\\n\\nConclusion\\n\\nA matrix game may be a powerful tool in exploring the dynamics of a scenario through forcing them to articulate arguments as to what would happen and thus build a narrative. If the intention is to draw observations for serious purposes or to use the game to teach an understanding of the scenario then there are steps that can be taken to make the game more robust. Game designers must always keep in mind why the game is being run in the first place.\\n\\nBen Taylor\\n\\nShare this:\\n\\nClick to print (Opens in new window) Print\\n\\nClick to email a link to a friend (Opens in new window) Email\\n\\nClick to share on X (Opens in new window) X\\n\\nClick to share on Facebook (Opens in new window) Facebook\\n\\nClick to share on LinkedIn (Opens in new window) LinkedIn\\n\\nMore\\n\\nClick to share on Reddit (Opens in new window) Reddit\\n\\nClick to share on Tumblr (Opens in new window) Tumblr\\n\\nLike Loading...\\n\\nsimulation and gaming ideas matrix games\\n\\n← Review: Matrix Games for Modern Wargaming Tropico 3 free today via Humble Bundle →\\n\\nOne response to “Toward serious matrix games”\\n\\nTom Mouat 10/10/2014 at 10:30 am\\n\\nI have to say, as one of the co-authors of Matrix Games for Modern Wargaming, that I found this one of the most helpful articles on Matrix Games I have seen – the articulation of insights that have been tugging away at the dim corners of my brain is simply excellent and I’m very grateful!\\n\\nLeave a comment\\n\\nRSS feed\\n\\n\\n\\nPAXsims is devoted to peace, conflict, humanitarian, and development simulations and serious games for education, training, and policy analysis.\\n\\nIf you wish to be notified when new material is posted here, use the “subscribe by email” option below.\\n\\nRelevant comments are welcomed.\\n\\nPAXsims operates on a non-profit basis. 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Log in now.\\n\\n\\n\\nPAXsims\\n\\nSubscribe Subscribed\\n\\nSign up\\n\\nLog in\\n\\nCopy shortlink\\n\\nReport this content\\n\\nView post in Reader\\n\\nManage subscriptions\\n\\nCollapse this bar\\n\\n%d\"),\n", " Document(metadata={'source': 'data/how-to-play-matrix-games.html'}, page_content='Search this site\\n\\nEmbedded Files\\n\\nFree Engle Matrix Games\\n\\nHow to play Matrix Games\\n\\nHow do I play a Matrix Game? Such a simple question. Deceptively simple. On one hand, they are VERY easy to play, but as I\\'ve found from years of experience, people seem to find them hard. In some cases it seems like the game becomes invisible to large parts of the population. They can\\'t imagine a game working like Matrix Games do. That seems to be changing now (2018) but the question remains, how to play them?\\n\\nFirst the simple answer.\\n\\nIf you follow the rules as written, you are playing a Matrix Game. For instance, the rules I use in my convention games: There is no order of play, Someone says something. Others can add to that or alter it. Any and everyone may ask a player to roll for their action. All very straight forward statements. You simply MAKE UP a story, build on other people\\'s stories and only roll dice when the players can\\'t agree. In the professional game players make arguments, a referee decides how likely they are and the players roll. Events build up to tell a story. Simple. The player just MAKES UP an argument.\\n\\nYou will notice my highlights. MAKE UP is the important common ground of all Matrix Games and this, I think, is where they run into trouble.\\n\\nAll games give players choices to make. A game without meaningful choices would be boring. But most games use a limited range of choices. With a little thought players can find optimal strategies. The randomness of games comes from the human factor. People make unpredictable, irrational, or even stupid moves that make outcomes different. Players who min max the best, or who are lucky, come out on top. They \"win\" the game. If this assumption about games is violated, it doesn\\'t deliver a game, or at least not a game everyone wants to play.\\n\\nIf making stuff up is a central feature of all Matrix Games then it means there are no built in rules that limit the range of choices. Think about that for a minute. There are no limits on what you can do. You can try to do anything and work toward any outcome.\\n\\nMy experience is that when people think about it this way they quickly develop a headache. It is too big to wrap our brains around because it is the entire universe. It is like life. We can chose to go in any direction and are only hemmed in by the series of choices we make. There is no automatic \"right\" way to live but there are paths that are likely to be short and miserable. Personally I don\\'t want to pick one of those but to each his own. Given a universe size blank slate, what do you do? Answering this question can feel like re-inventing the wheel each turn. This is much more work than most people are willing to do.\\n\\nSo teaching Matrix Games means not going down the rabbit hole of the literal meaning of the rules. Instead each game focuses in on the scenario being played. Say the game is a military campaign. The players are given two or more different countries, with lists of forces, histories that may help or hurt their actions, maps, political agendas and goals to work on. The player suddenly knows a lot about the world. The blank slate is filled in. In fact the blank slate is more filled than the information given because people\\'s brains gestalt the holes with reasonable guesses about what was not said. This is the matrix of Matrix Games.\\n\\nKnowing the game world allows players to pick what story they want to tell more easily. They have a number of obvious tropes and stereotypes to pick from. In theory they can do anything but they will likely do fairly predictable things. For example, consider two scenarios.\\n\\nHistorical Scenario: Operation Barbarossa: The Invasion of Russia in 1941. Is there any way the Germans could have carried that attack out in a way that would lead to victory? The number of \"what if\" questions is endless which is why people have been gaming this scenario since it happened (and even before). You might already be thinking of possibilities. If so, you are playing a Matrix Game in your mind right now. This is a game with a clear winner and loser and we know exactly what winning and losing means.\\n\\nPresent Day Scenario: The Syrian Civil War. As of writing this (2018) the Syrian civil war is ongoing. No side has yet won, and even when a side does \"win\" all the sides will be losers. It is a mess that has bad outcomes and worse outcomes. There are many players with many different definitions of story. There is no one dominant narrative. The USA player may think of it as a continuation of the War on Terror, the Russian player may see it as a continuation of the Cold War or even a 19th Century war to contain Russia from the Mediterranean Sea. The Iranian player may see it as part of a regional conflict that dates back to the Sunni Shia split or even to the Persian Empire. Forces inside Syria have even more contexts that flavor their moves. What does one do? I don\\'t claim to have an answer. There is not one answer. It is a minefield with many paths. You might be feeling the headache about now because the range of options are so great and so uncertain. It is as much politics as it is cultural, military, and economic. But even with the large range of possibilities it still gives players obvious ideas to work on.\\n\\nA well written scenario is vital to Matrix Games. Without one they just don\\'t work. Maps, casts of characters, story starters, plot tracks (or other goal measures) art work, and even toy soldiers help. Scenarios don\\'t have to be long and certainly don\\'t have to be complete but they do need to be compelling. Like an advertisement, the scenario has to convince the player to give their attention (which means their time - which by extension means a part of their limited lives) to the game.\\n\\nOnce players are hooked there are some nuts and bolts of play that get games going quickly.\\n\\n1. Briefly explain the scenario. People form a mental matrix as they listen to this even when they are not aware they are doing so.\\n\\n2. Briefly explain the rules. Usually this means saying that the players will take turns making up what happens. Don\\'t expect ANY of the players to understand how to play due to this explanation. That is why to keep this very brief.\\n\\n3. Immediately start playing. For the first turn, go around the table and ask each player to make up something. Some will have an easy job of it. Others will struggle. If they struggle, skip them in a low key manner. If people feel shamed for not making stuff up they shut down and are unable to play. It sometimes helps to give encouragement. I\\'ve found saying \"If this were any other game, you where your character, and this was the situation, what would you want to do first?\" helpful. They can then pull on the rules of other games to help them overcome the brain lock that Matrix Games can cause.\\n\\n4. Many if not all players will know how to play after this one turn. The people who had an easy time making up actions will dive in. Other players will engage more slowly, as the game unfolds. The game host needs to be patient with shy players. Don\\'t rush them. They will come out when they are ready and not before.\\n\\n5. Some people will hate this game. It grates on their nerves like finger nails on a chalk board. Often they will walk away. Let them go. Accept that Matrix Games are not everyone\\'s cup of tea. Respect the difference of opinion.\\n\\n6. After that just play the game. People learn fastest by playing. By the end of the first game the players will know all the rules and, though they might not believe it, they could run their own Matrix Game with no more knowledge. All they might lack is confidence.\\n\\nThe old medical teaching adage: See one. Do one. Teach one. Is a good thing to keep in mind. For Matrix Games it might be: Play one. Run one. Write one.\\n\\nBeyond this people will always have questions about the minutia of movement, combat, economic and political rules of each scenario. I have no answers for those questions except to say that if you can\\'t find an answer quickly, it is always okay to fall back on a Matrix Game trope and Just make it up!\\n\\nChris Engle\\n\\nGoogle Sites\\n\\nReport abuse\\n\\nGoogle Sites\\n\\nReport abuse'),\n", " Document(metadata={'source': 'data/MatrixRules.txt'}, page_content='MATRIX GAMES\\n\\nContents\\n\\nWhat are Matrix Games? Where did they come from? Game Arguments Notes about Arguments Resolving Conflicts Comments on Resolving Conflicts\\n\\nPlaying Tips Secret Arguments Big Projects Killing Arguments Player Roles and the Level of the Game Levels of Protection and Hidden Things Having Battles and Fighting Unifying Purpose Ending the Game\\n\\nWhat are Matrix Games?\\n\\nMatrix games are different to normal Wargames and Role-Playing games. In a these games you compare lists of statistics and peer at complicated books of rules containing someone else\\'s idea about what things are important, before rolling a dice. It takes a long time and can be very difficult to explain to a newcomer. Instead, in a Matrix Game you simply use words to describe why something should happen, the Umpire decides how likely it is, and you roll a dice. If you can say \"This happens, for the following reasons...\" you can play a Matrix Game.\\n\\nWhere did the come from?\\n\\nThe Matrix Game was created in the USA by Chris Engle, and published in 1992. Chris wanted to create a system by which it was possible for a player to \"role-play\" anything from a single person to an entire country. Chris felt that previous numbers-ridden game designs essentially missed the point (and anyway were too complicated and boring). What he wanted was a system that could take into account anything the players though was relevant, including intangible elements such as culture, beliefs, and perceptions of themselves. Taking as his starting point the work of the philosopher Emmanuel Kant, Chris began to develop a \"matrix\" of cue words that would form the framework for his \"model\". To this he added George Hegel\\'s idea that argument and counter-argument (thesis and antithesis) lead to a synthesis or consensus of ideas. Thus the basic idea of the Matrix Game was formulated. Over the years the actual \"matrix\" of cue words have been dropped, but the name has stuck. Like all good ideas, the Matrix Game is very simple in concept, but has huge potential in that it can be adapted to fit any game setting.\\n\\nGame Arguments\\n\\nIn a Matrix Game, actions are resolved by a structured sequence of logical \"arguments\". Each player takes turns to make an argument, with successful arguments advancing the game, and the player\\'s position. The arguments themselves are judged by the Umpire based on inherent likelyhood, historical precedence, personal experience, and his own judgement (and quite often the other player\\'s judgement), and a chance of success arrived at (a 6-sided dice normally being thrown to see if the result was achieved).\\n\\nEach argument is broken down into:\\n\\nSomething That Happens. Three Reasons Why or How.\\n\\nFor Example:\\n\\nIn a Peninsular War campaign, Wellington might argue: \"I shall fortify the town, and I am able to do this because:\\n\\nI have a ready source of trained manpower, I have an experienced Engineer in command, and the British Government has recently sent me the money with which to pay for the work\".\\n\\nIn an X-Files Game, Scully might argue: \"I shall spend some time down on the range, so that my shooting improves, because:\\n\\nPractice makes perfect! FBI HQ has very good facilities so it is easy to arrange. The range has well trained instructors who will help me improve\".\\n\\nNotes about Arguments\\n\\nThe important thing to remember in a Matrix game is that Arguments can be made about anything that is relevant to the scenario. You can argue about your own personnel or about the enemy, the existence of people, places, things or events, the political leadership back home, the weather, plague, disease, public opinion, and you can even argue for changes in whatever rules you are using. With a bit of imagination, common sense and rational thinking, it is possible to present persuasive arguments as to what should happen in any scenario - from traditional military campaigns to the bizarre world of the X-Files.\\n\\nWhen an Argument succeeds it remains in effect until another Argument stops it. This means that if you are Napoleon and succeed in Arguing that you march on Moscow, you will continue to move forward, every turn, until you get there - unless of course someone argues that you don\\'t...\\n\\nIf two Arguments are in direct opposition (\"This happens\" - \"No it doesn\\'t\") they represent a Logical Inconsistency since they cannot both be true. If this happens, they must both succeed first as Arguments, then the two sides must roll-off to see who wins between them - so following up a successful argument with one that is merely contradictory puts you at a disadvantage.\\n\\nResolving Conflicts\\n\\nIf two sides are placed in direct Conflict, they resolve the outcome by making additional arguments. The players both make Arguments as to the outcome of the Conflict situation they are in, and the strength of the Arguments is decided upon by the Umpire. I usually allow the player with an advantage to choose who shoud go first (no Conflict situations are every really equal - but if you felt they were, you could make the players write their Arguments down in secret).\\n\\nThey then both roll the dice, together, to see who succeeds. In a Conflict situation, one side must succeed and one side must fail. If both succeed, or both fail, they must both roll again, and again, until one succeeds and the other fails.\\n\\nFor Example:\\n\\nSo if one player makes an argument that he is attacking the town with his troops, and the other player makes and argument that he is improving the defences, the arguments are judged normally. If the attack Argument fails, the attack does not take place at that time, and there is no conflict.\\n\\nIf the attack Argument succeeds, a Conflict situation will be inevitable, but if the defender\\'s Argument about improving the defences succeeds, he might have an advantage in the ensuing battle. Let\\'s say that his Argument does not succeed because the Umpire judged that he really didn\\'t have sufficient time to get the work done, made the Argument Weak, and it failed.\\n\\nThe attacking player elects to go first and argues that he captures the town. The other player argues that he is repulsed with heavy losses. They then both dice to see who wins, with the likelyhood that the defender will have to roll higher, because the towns defences were not what they could have been.\\n\\nComments on Resolving Conflicts\\n\\nThis may seem a little arbitrary and all dependent on a good Umpire (what games doesn\\'t?) but, in practice, it works very well. When a player makes a particularly good argument it is obvious, normally from the rueful grins and grudging nods of the opposition, that he will have a good chance of succeeding.\\n\\n-----------------------------------------------------------\\n\\nPlaying Tips\\n\\nSome players get caught in the Logical Inconsistancy trap by arguing directly against another player who has already had a successful argument. This puts them at a disadvantage because, not only has their argument got to succeed, but they then have to roll off against the other player. It is far better (and much more fun) to be a little more subtle. If he succeeds in arguing that he attacks you, you might argue that the attack does indeed take place, but was ill-timed and badly co-ordinated - which might place you in an advantage in the resulting battle.\\n\\nIt helps the players to insist on an argument failing if you roll a 1 on a D6. Nothing is ever certain, and the player can look on it as not necessarily a total failure, but simply that it didn\\'t happen AT THAT TIME. It might happen later, if they argue again.\\n\\nConversely, you will need to veto stupid arguments. I simply say that I don\\'t believe the argument is realistic - even having to roll a 6 on a D6 - and give them a chance to come up with something else.\\n\\nSecret Arguments.\\n\\nThere will be some cases where you want to hide from the other players the thing you want to argue about. It could be that you have boobytrapped a piece of equipment you think your opponent will use, or that you have swapped the vital blueprints for a set of fake ones in case the safe is broken into. In this case you simply write down your argument on a piece of paper, and present it to the Umpire announcing to the other players that you are making a secret argument. The Umpire will make a judgment and you will roll the dice normally, but the other players have no idea what it is about.\\n\\nYou should be careful, however, that the players don\\'t make too many secret arguments. This can ruin the game\\'s atmosphere and reduce the focus, so that the game drags on unnecessarily. They must only be permitted when they refer to quite specific things or events. An argument about gathering information from a spy, in most games, will be quite a generic argument and should be argued openly.\\n\\nYou may want to limit the players to only a single secret argument per game.\\n\\nBig Projects.\\n\\nDepending on the level of the game, some actions and events represent such a large investment in time and effort that they require multiple arguments in order to bring them to fruition. In a Spy Game, recruiting a spy would take a number of arguments in order to make the spy do everything you want them to. You must make the initial contact, followed by persuasion to carry out a minor act (like stealing a copy of the Pentagon telephone directory), followed by more important spying actions (like photographing secret plans). It would be unreasonable to argue in a Spy Game that you recruit a girl from the typing pool to assassinate the head of the CIA in a single argument!\\n\\nThe level of the game will determine what sort of arguments are Big Projects, so in a game about Wellington\\'s action in the Peninsular War a single argument about fortifying a town would be perfectly reasonable. In a game about individual Refugees in Bosnia, building a house might take several successful arguments. A Matrix Game can easily be at the Strategic level involving the actions of Governments and Countries; or equally at the Individual level involving the actions of you and your close friends.\\n\\nAs a rule of thumb, a Big Project should take no more than 3 successful arguments, otherwise the game is dominated too much by a single event. You should also remember the principal that once an argument has started an ongoing action, it will continue until another argument stops it.\\n\\nThis means that the 3 stages in, for example, building a house could logically be:\\n\\nAcquiring the funds (Can I get a mortgage?). Starting to build the house (When will the right builder be available?). Completing the building of the house (Are they ever going to finish it?).\\n\\nKilling Arguments.\\n\\nIt often arises in Matrix Games where one of the players argues that something happens to kill off one of the other player characters. This is, of course, permitted as you can argue about anything in a Matrix Game, and it will be assessed like any other argument. It may well be less likely to succeed as the player characters in the game are usually chosen from the survivors of a particular historical event, but it is not impossible - nor should it be.\\n\\nIf a character is killed off in a game, however, it does not prevent the player from continuing to make arguments.\\n\\nPlayer Roles and the Level of the Game.\\n\\nWhen you are designing a Matrix Game it is worth thinking about the level at which the players roles will be operating in the game. In is usually better, and produces a more balanced game, when the level on which the player roles are operating are broadly similar. It would be difficult to get a balanced game if 3 of the players are playing Generals in command of vast Armies, and another player is playing a simple individual soldier.\\n\\nLevels of Protection and Hidden Things.\\n\\nAt the start of a game there are certain things that are not readily accessible to some of the player characters. For example, in a Spy Game the secret plans for a new submarine would be heavily protected. Equally, in an X-Files game, the location of the secret government base would be carefully concealed.\\n\\nThings that are hidden or secret require a successful argument merely to find them. Things that are protected will require successful arguments to overcome the different levels of protection. In an X-Files game, the secret government base may declared by the Umpire to have 3 levels of protection: Its hidden location, its boundary fence, and the security guards, all of which must be overcome by successful arguments before the base can be penetrated.\\n\\nHaving Battles and Fighting.\\n\\nMany players feel uneasy about the concept of the result of a single argument (and dice roll) deciding the outcome of a battle or a fight. This is natural, but they should remember that the Matrix Game is about the entire campaign and it is the results of many battles or fights, rather than a single one, that is important.\\n\\nIt is up to the umpire to decide exactly what the outcome of the battle or fight was. He will make a judgement, depending on the strength of the arguments and the difference in the score on the two dice rolls, as to how heavy was the defeat or just how narrow was the margin of victory. If the outcome was very close, the loser may have an opportunity to withdraw in his next turn with most of his forces intact.\\n\\nUnifying Purpose.\\n\\nIt is absolutely essential in a Matrix Game, as in any game, that there is a unifying purpose to the game, and that the players understand it. What is the game all about?\\n\\nIt could be expressed as \"a Spy Game, set in pre-war London, about the efforts of Secret Agents to steal the Secret Plans for a new war-winning weapon\". Alternatively, it could be \"a Napoleonic Game, about Wellington\\'s Campaign in the Spanish Peninsular\"; or \"an X-Files Game, set in modern America, about a crashed Alien Spacecraft\". The unifying purpose lets the players get an immediate handle on the game and what it is going to be about. It also gives them some guidance so that they don\\'t get too far \"off subject\".\\n\\nEnding the Game.\\n\\nSometimes you run out of time and have to finish the game with matters still unresolved. One good way of finishing the game is to have the players each make an argument as to how they think the game turns out.\\n\\nThe \"What happens\" bit can be as long as you like, but it is still supported by only 3 reasons why or how. The Umpire then assigns the chance of success in the normal way - but nobody rolls the dice until everyone has made their argument. Each player now has a chance of succeeding and they all roll together. Each failure is \"knocked out\" and another round of dice rolling takes place until only one player is left. At each stage if everyone fails, the dice are rolled again, but only those left in at that stage get to roll, not those \"knocked out\" in a previous round.'),\n", " Document(metadata={'source': 'data/scrud.txt'}, page_content='S.C.R.U.D. Simple Combat Resolution Using Dice by Timothy McCoy Price\\n\\nThese rules are intended to be used as a simple method of resolving the combats that take place within the larger framework of a game. They are meant for those battles that take place in the boarding actions of Naval Games, the Open Battles that are encountered while playing Matrix Games, and the confrontations that appear during back-to-back Map Games. In short, those small, but vital, elements that are part of the whole that makes up a Wargame, that have to be resolved quickly or the Game itself grinds to a halt.\\n\\nThe Basic Rule. The basic rule is as follows: 1 x 6-Sided Dice = 1 x Combat Unit The size of that Combat Unit will, of course, vary from game to game. In the boarding action it may be as little as 5-10 men; in a Map Game, it could be as much as an entire Brigade, or even a Corps.\\n\\nThe Method. The dice on the opposing sides are rolled as follows: Roll the Dice. Line them up, Highest vs Highest If one side has more dice than the other, any dice that are extra, and score less than the lowest dice of the side with the fewer dice, are ignored.\\n\\nThe Result. Each dice represents a Combat Unit, and the scores on the dice represent how well they did in that particular engagement. Compare the two dice that are paired off: The higher dice beats the lower dice Equal scores are ignored. Each dice defeated represents a push-back in large combats, or a death in smaller combats. For every three defeats, eliminate one of the opponents Combat Units (the lowest value one or, if they have the same value, the lowest scoring one).\\n\\nVariations. The strength in this system is in the number of variations you can build into a very simple mechanism. Each defeat could be translated into a -1 on the next time the dice is thrown. When you exceed -2, the unit is eliminated. Matrix Arguments could be used to add +1 or -1 to the value of a specific dice used. The usual modifiers for: Troop Quality, Fortified Positions, State of Supply, etc; can all be factored in with simple + or - modifiers.\\n\\nYou could even take supply and fatigue into account by saying that each \"6\" scored indicates particularly heavy fighting. The Combat Unit involved fights with a -1 on the dice until resupplied or rested.\\n\\nYou may decide that, despite any + or - factors, a \"6\" is the maximum any unit can score. This will allow you to keep score more easily, as you can turn the dice over after throwing them, to reflect the modifiers used, without having to use a piece of paper. It also means that two Elite units, perhaps with +3 modifiers, are likely to have inconclusive combats (the same dice score) when fighting each other, at least 50% of the time.\\n\\nReserves could be taken into account by adding one \"pip\" from the value of dice thrown \"in reserve\" to the value of the first few dice thrown \"in the front line\". The results can also be easily be translated into battle reports to pass back to the players, as each dice represents a specific unit. Thus, its fortunes can be plotted from battle to battle.\\n\\nS.C.R.U.D.\\n\\nExamples of Combat\\n\\nAs an example we will take part of the battle of Tannenburg during the First World War. The German 20th Corps, under Scholtz, is attacked by elements of the Russian 2nd Army, under Samsonov. The Germans have 4 brigades, the Russians 8. The Russians are poorly trained and equipped and exhausted after advancing for days over sandy soil. Each Russian Unit = -1. The Germans are very well trained, but are not in a defensive position. Each German Unit +1. The battle is as follows:\\n\\nInitial Dice Throw:\\t\\tRUSSIAN:\\t2 5 5 3 3 1 3 3 GERMAN:\\t\\t3 5 3 3 Lined Up and Modified:\\tRUSSIAN:\\t4 4 2 2 2 2 1 1 GERMAN:\\t\\t6 4 4 4 Result of First Day:\\tlose:\\t\\t4 2 2 RUSSIAN:\\t 4 GERMAN:\\t\\t6 4 4 4 lose:\\n\\nThe Russians are pushed back with one Brigade Destroyed, and 2 Brigades are now fighting with a -2. One of the German units has expended a lot of ammunition, so loses its +1 advantage. (These units are represented by bold numbers). The Russians order an attack the very next day.\\n\\nInitial Dice Throw:\\t\\tRUSSIAN:\\t6 1 1 2 6 4 5 GERMAN:\\t\\t6 2 3 2 Lined Up and Modified:\\tRUSSIAN:\\t5 4 4 3 1 1 1 GERMAN:\\t\\t6 4 3 3 Result of Second Day:\\tlose:\\t\\t5 RUSSIAN:\\t 4 4 3 GERMAN:\\t\\t6 4 3 lose:\\t\\t 3\\n\\nThe Russians succeed in pushing back one of the German units and forcing and already depleted unit to use up ammunition, (but are pushed back themselves and 2 units use a lot of ammo (one of which becomes combat ineffective on -3)). Overall, as the success is matched by failure, the line itself holds. The Russians attack again, the next day:\\n\\nInitial Dice Throw:\\t\\tRUSSIAN:\\t6 5 5 4 2 4 GERMAN:\\t\\t1 2 4 4 Lined Up and Modified:\\tRUSSIAN:\\t5 4 3 3 2 1\\t\\t(two of the Russians = -2) GERMAN:\\t\\t4 3 3 2\\t\\t\\t(one of the Germans = -1) Result of Third Day;\\tlose:\\t\\t\\t\\t\\t\\t(one of the Germans = +0) RUSSIAN:\\t5 4 3 3 GERMAN:\\t \\t3 lose:\\t\\t4 3 2\\n\\nThe Russians, throwing their freshest units into the front line, finally overwhelm the German defenders, who lose a Brigade (the depleted one). Had the German time to have fortified their position, the outcome could have been very different. In the game, the combat resolution took less time to work out, than it did for you to read this page...')]" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "docs" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/caleb/projects/matrix-game-rag/.venv/lib/python3.13/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", " from .autonotebook import tqdm as notebook_tqdm\n" ] }, { "data": { "text/plain": [ "KnowledgeGraph(nodes: 0, relationships: 0)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from ragas.testset.graph import KnowledgeGraph\n", "\n", "kg = KnowledgeGraph()\n", "kg" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "KnowledgeGraph(nodes: 5, relationships: 0)" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from ragas.testset.graph import Node, NodeType\n", "\n", "for doc in docs:\n", " kg.nodes.append(\n", " Node(\n", " type=NodeType.DOCUMENT,\n", " properties={\"page_content\": doc.page_content, \"document_metadata\": doc.metadata}\n", " )\n", " )\n", "kg" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Applying [EmbeddingExtractor, ThemesExtractor, NERExtractor]: 74%|███████▎ | 39/53 [00:04<00:00, 18.64it/s]unable to apply transformation: Invalid json output: The main themes and concepts include voting methods and procedures, consistency and fairness in voting, support and opposition assessment, use of multiple voting options, gradations of support and divisiveness, impact of voting results on social and political dynamics, technology in voting systems, risks and limitations of technological voting, self-voting and competitive behavior among players, arguments and negotiation in game scenarios, relevance of arguments to scenario elements, use of narrative markers and tracking in gameplay, role of imagination, rationality, and common sense in argumentation, managing player interactions and negotiations, introduction of \"Turn Zero\" for familiarization, and the complexity and variety of arguments in gameplay.\n", "For troubleshooting, visit: https://python.langchain.com/docs/troubleshooting/errors/OUTPUT_PARSING_FAILURE \n", " \r" ] }, { "data": { "text/plain": [ "KnowledgeGraph(nodes: 29, relationships: 55)" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from ragas.testset.transforms import default_transforms, apply_transforms\n", "\n", "transformer_llm = generator_llm\n", "embedding_model = generator_embeddings\n", "\n", "default_transforms = default_transforms(documents=docs, llm=transformer_llm, embedding_model=embedding_model)\n", "apply_transforms(kg, default_transforms)\n", "kg" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "kg.save(\"matrix_games_kg.json\")" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "KnowledgeGraph(nodes: 29, relationships: 55)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kg = KnowledgeGraph.load(\"data/ragas/matrix_games_kg.json\")\n", "kg" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "from ragas.testset.persona import Persona\n", "\n", "persona_new_wargamer = Persona(\n", " name=\"New Wargamer\",\n", " role_description=\"Is new to matrix wargames and needs clear explanations of core concepts, rules, and how to design or participate in a simple game. May ask about the benefits of matrix wargaming.\",\n", ")\n", "\n", "persona_experienced_designer = Persona(\n", " name=\"Experienced Wargame Designer\",\n", " role_description=\"Has experience designing and running matrix wargames. Interested in advanced design techniques, specific rule nuances, historical examples, and ways to improve game facilitation or player engagement. Might ask for design inspiration for complex scenarios.\",\n", ")\n", "\n", "persona_academic_researcher = Persona(\n", " name=\"Academic Researcher/Analyst\",\n", " role_description=\"Is using or considering matrix wargames for academic research or professional analysis. Interested in the methodology, validity, limitations, and application of matrix games in specific domains (e.g., political science, military strategy, business). May ask about research papers or case studies.\",\n", ")\n", "\n", "personas = [persona_new_wargamer, persona_experienced_designer, persona_academic_researcher]" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [], "source": [ "generator_llm = LangchainLLMWrapper(ChatOpenAI(model=\"gpt-4.1-mini\"))" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "from ragas.testset import TestsetGenerator\n", "\n", "generator = TestsetGenerator(llm=generator_llm, embedding_model=embedding_model, knowledge_graph=kg, persona_list=personas)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "from ragas.testset.synthesizers import default_query_distribution, SingleHopSpecificQuerySynthesizer, MultiHopAbstractQuerySynthesizer, MultiHopSpecificQuerySynthesizer\n", "\n", "query_distribution = [\n", " (SingleHopSpecificQuerySynthesizer(llm=generator_llm), 0.5),\n", " (MultiHopAbstractQuerySynthesizer(llm=generator_llm), 0.5)\n", "]\n", "\n", "# query_distribution = [\n", "# (SingleHopSpecificQuerySynthesizer(llm=generator_llm), 0.5),\n", "# (MultiHopAbstractQuerySynthesizer(llm=generator_llm), 0.25),\n", "# (MultiHopSpecificQuerySynthesizer(llm=generator_llm), 0.25),\n", "# ]" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Generating Scenarios: 100%|██████████| 2/2 [11:51<00:00, 355.55s/it]\n", "Generating Samples: 100%|██████████| 962/962 [14:14<00:00, 1.13it/s]\n" ] } ], "source": [ "from ragas import RunConfig\n", "\n", "custom_run_config = RunConfig(max_wait=361, max_retries=20)\n", "\n", "testset = generator.generate(testset_size=1000, query_distribution=query_distribution, run_config=custom_run_config, raise_exceptions=False)\n", "pandast_testset = testset.to_pandas()\n", "pandast_testset.to_csv(\"data/ragas/testset.csv\", index=False)" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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