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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | as it is in perfect information games. | https://karpathy.ai/lexicap/0012-large.html#00:16:26.240 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | And I don't wanna say it's simple there either. | https://karpathy.ai/lexicap/0012-large.html#00:16:29.320 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | It's of course very complicated computationally there too, | https://karpathy.ai/lexicap/0012-large.html#00:16:31.080 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | but at least conceptually, it's very straightforward. | https://karpathy.ai/lexicap/0012-large.html#00:16:34.200 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | There's a state, there's an evaluation function. | https://karpathy.ai/lexicap/0012-large.html#00:16:36.520 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | You can try to learn it. | https://karpathy.ai/lexicap/0012-large.html#00:16:38.760 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Here, you have to do something more. | https://karpathy.ai/lexicap/0012-large.html#00:16:39.800 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | And what we do is in one of these papers, | https://karpathy.ai/lexicap/0012-large.html#00:16:43.280 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | we're looking at where we allow the opponent | https://karpathy.ai/lexicap/0012-large.html#00:16:47.160 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | to actually take different strategies | https://karpathy.ai/lexicap/0012-large.html#00:16:50.800 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | at the leaf of the search tree, if you will. | https://karpathy.ai/lexicap/0012-large.html#00:16:53.000 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | And that is a different way of doing it. | https://karpathy.ai/lexicap/0012-large.html#00:16:56.440 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | And it doesn't assume therefore a particular way | https://karpathy.ai/lexicap/0012-large.html#00:16:59.840 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | that the opponent plays, | https://karpathy.ai/lexicap/0012-large.html#00:17:02.560 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | but it allows the opponent to choose | https://karpathy.ai/lexicap/0012-large.html#00:17:04.040 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | from a set of different continuation strategies. | https://karpathy.ai/lexicap/0012-large.html#00:17:05.840 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | And that forces us to not be too optimistic | https://karpathy.ai/lexicap/0012-large.html#00:17:09.800 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | in a look ahead search. | https://karpathy.ai/lexicap/0012-large.html#00:17:13.400 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | And that's one way you can do sound look ahead search | https://karpathy.ai/lexicap/0012-large.html#00:17:15.520 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | in imperfect information games, | https://karpathy.ai/lexicap/0012-large.html#00:17:19.040 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | which is very difficult. | https://karpathy.ai/lexicap/0012-large.html#00:17:21.480 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | And you were asking about DeepStack. | https://karpathy.ai/lexicap/0012-large.html#00:17:23.360 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | What they did, it was very different than what we do, | https://karpathy.ai/lexicap/0012-large.html#00:17:26.080 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | either in Libratus or in this new work. | https://karpathy.ai/lexicap/0012-large.html#00:17:29.280 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | They were randomly generating various situations | https://karpathy.ai/lexicap/0012-large.html#00:17:32.000 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | in the game. | https://karpathy.ai/lexicap/0012-large.html#00:17:35.440 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Then they were doing the look ahead | https://karpathy.ai/lexicap/0012-large.html#00:17:36.440 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | from there to the end of the game, | https://karpathy.ai/lexicap/0012-large.html#00:17:38.080 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | as if that was the start of a different game. | https://karpathy.ai/lexicap/0012-large.html#00:17:39.840 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | And then they were using deep learning | https://karpathy.ai/lexicap/0012-large.html#00:17:42.960 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | to learn those values of those states, | https://karpathy.ai/lexicap/0012-large.html#00:17:44.920 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | but the states were not just the physical states. | https://karpathy.ai/lexicap/0012-large.html#00:17:47.960 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | They include belief distributions. | https://karpathy.ai/lexicap/0012-large.html#00:17:50.280 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | When you talk about look ahead for DeepStack | https://karpathy.ai/lexicap/0012-large.html#00:17:52.560 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | or with Libratus, does it mean, | https://karpathy.ai/lexicap/0012-large.html#00:17:56.800 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | considering every possibility that the game can evolve, | https://karpathy.ai/lexicap/0012-large.html#00:17:59.480 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | are we talking about extremely, | https://karpathy.ai/lexicap/0012-large.html#00:18:02.680 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | sort of this exponentially growth of a tree? | https://karpathy.ai/lexicap/0012-large.html#00:18:04.280 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Yes, so we're talking about exactly that. | https://karpathy.ai/lexicap/0012-large.html#00:18:06.880 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Much like you do in alpha beta search | https://karpathy.ai/lexicap/0012-large.html#00:18:11.280 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | or Monte Carlo tree search, but with different techniques. | https://karpathy.ai/lexicap/0012-large.html#00:18:14.280 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | So there's a different search algorithm. | https://karpathy.ai/lexicap/0012-large.html#00:18:17.480 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | And then we have to deal with the leaves differently. | https://karpathy.ai/lexicap/0012-large.html#00:18:19.280 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | So if you think about what Libratus did, | https://karpathy.ai/lexicap/0012-large.html#00:18:21.920 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | we didn't have to worry about this | https://karpathy.ai/lexicap/0012-large.html#00:18:24.000 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | because we only did it at the end of the game. | https://karpathy.ai/lexicap/0012-large.html#00:18:25.520 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | So we would always terminate into a real situation | https://karpathy.ai/lexicap/0012-large.html#00:18:28.560 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | and we would know what the payout is. | https://karpathy.ai/lexicap/0012-large.html#00:18:32.280 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | It didn't do these depth limited lookaheads, | https://karpathy.ai/lexicap/0012-large.html#00:18:34.000 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | but now in this new paper, which is called depth limited, | https://karpathy.ai/lexicap/0012-large.html#00:18:36.880 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | I think it's called depth limited search | https://karpathy.ai/lexicap/0012-large.html#00:18:40.680 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | for imperfect information games, | https://karpathy.ai/lexicap/0012-large.html#00:18:42.120 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | we can actually do sound depth limited lookahead. | https://karpathy.ai/lexicap/0012-large.html#00:18:43.880 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | So we can actually start to do the look ahead | https://karpathy.ai/lexicap/0012-large.html#00:18:47.040 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | from the beginning of the game on, | https://karpathy.ai/lexicap/0012-large.html#00:18:49.240 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | because that's too complicated to do | https://karpathy.ai/lexicap/0012-large.html#00:18:51.080 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | for this whole long game. | https://karpathy.ai/lexicap/0012-large.html#00:18:53.400 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | So in Libratus, we were just doing it for the end. | https://karpathy.ai/lexicap/0012-large.html#00:18:54.920 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | So, and then the other side, this belief distribution, | https://karpathy.ai/lexicap/0012-large.html#00:18:57.680 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | so is it explicitly modeled what kind of beliefs | https://karpathy.ai/lexicap/0012-large.html#00:19:00.720 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | that the opponent might have? | https://karpathy.ai/lexicap/0012-large.html#00:19:05.320 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Yeah, it is explicitly modeled, but it's not assumed. | https://karpathy.ai/lexicap/0012-large.html#00:19:07.400 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | The beliefs are actually output, not input. | https://karpathy.ai/lexicap/0012-large.html#00:19:11.840 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Of course, the starting beliefs are input, | https://karpathy.ai/lexicap/0012-large.html#00:19:15.400 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | but they just fall from the rules of the game | https://karpathy.ai/lexicap/0012-large.html#00:19:18.840 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | because we know that the dealer deals uniformly | https://karpathy.ai/lexicap/0012-large.html#00:19:20.640 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | from the deck, so I know that every pair of cards | https://karpathy.ai/lexicap/0012-large.html#00:19:23.520 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | that you might have is equally likely. | https://karpathy.ai/lexicap/0012-large.html#00:19:27.720 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | I know that for a fact, that just follows | https://karpathy.ai/lexicap/0012-large.html#00:19:30.440 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | from the rules of the game. | https://karpathy.ai/lexicap/0012-large.html#00:19:32.200 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Of course, except the two cards that I have, | https://karpathy.ai/lexicap/0012-large.html#00:19:33.160 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | I know you don't have those. | https://karpathy.ai/lexicap/0012-large.html#00:19:35.200 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Yeah. | https://karpathy.ai/lexicap/0012-large.html#00:19:36.560 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | You have to take that into account. | https://karpathy.ai/lexicap/0012-large.html#00:19:37.560 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | That's called card removal and that's very important. | https://karpathy.ai/lexicap/0012-large.html#00:19:38.720 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Is the dealing always coming from a single deck | https://karpathy.ai/lexicap/0012-large.html#00:19:40.920 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | in Heads Up, so you can assume. | https://karpathy.ai/lexicap/0012-large.html#00:19:43.760 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Single deck, so you know that if I have the ace of spades, | https://karpathy.ai/lexicap/0012-large.html#00:19:45.880 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | I know you don't have an ace of spades. | https://karpathy.ai/lexicap/0012-large.html#00:19:50.880 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Great, so in the beginning, your belief is basically | https://karpathy.ai/lexicap/0012-large.html#00:19:53.560 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | the fact that it's a fair dealing of hands, | https://karpathy.ai/lexicap/0012-large.html#00:19:56.880 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | but how do you start to adjust that belief? | https://karpathy.ai/lexicap/0012-large.html#00:19:59.320 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Well, that's where this beauty of game theory comes. | https://karpathy.ai/lexicap/0012-large.html#00:20:02.800 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | So Nash equilibrium, which John Nash introduced in 1950, | https://karpathy.ai/lexicap/0012-large.html#00:20:06.800 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | introduces what rational play is | https://karpathy.ai/lexicap/0012-large.html#00:20:10.920 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | when you have more than one player. | https://karpathy.ai/lexicap/0012-large.html#00:20:13.800 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | And these are pairs of strategies | https://karpathy.ai/lexicap/0012-large.html#00:20:16.040 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | where strategies are contingency plans, | https://karpathy.ai/lexicap/0012-large.html#00:20:18.440 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | one for each player. | https://karpathy.ai/lexicap/0012-large.html#00:20:20.360 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | So that neither player wants to deviate | https://karpathy.ai/lexicap/0012-large.html#00:20:22.880 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | to a different strategy, | https://karpathy.ai/lexicap/0012-large.html#00:20:25.720 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | given that the other doesn't deviate. | https://karpathy.ai/lexicap/0012-large.html#00:20:26.960 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | But as a side effect, you get the beliefs from base roll. | https://karpathy.ai/lexicap/0012-large.html#00:20:29.160 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | So Nash equilibrium really isn't just deriving | https://karpathy.ai/lexicap/0012-large.html#00:20:33.840 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | in these imperfect information games, | https://karpathy.ai/lexicap/0012-large.html#00:20:36.440 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | Nash equilibrium, it doesn't just define strategies. | https://karpathy.ai/lexicap/0012-large.html#00:20:38.360 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | It also defines beliefs for both of us | https://karpathy.ai/lexicap/0012-large.html#00:20:41.920 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | and defines beliefs for each state. | https://karpathy.ai/lexicap/0012-large.html#00:20:44.960 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | So at each state, it's called information sets. | https://karpathy.ai/lexicap/0012-large.html#00:20:48.840 |
Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12 | At each information set in the game, | https://karpathy.ai/lexicap/0012-large.html#00:20:53.280 |
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