ansarzeinulla/bestemshe-tablebase

Bestemshe Table Base — Strong Solution Proof

Authors: Ansar Zeinulla & Murat Manassov
Affiliation: Nazarbayev University, Kazakhstan
Code Repository: github.com/ansarzeinulla/Bestemshe
Live Interactive Explorer: huggingface.co/spaces/ansarzeinulla/Bestemshe-God-Algorithm

Bestemshe is a traditional Kazakh two-player mancala-style game (5 pits per player, 50 total stones). This artifact is a strong solution of the game: for every reachable, legal position the exact game-theoretic value (win / draw for the side to move) has been computed by retrograde analysis and stored, enabling perfect play via direct $O(1)$ memory-mapped lookup without runtime search.

Together with the solver that produced it, this tablebase constitutes a machine-verifiable proof of the game's outcome under optimal play: a forced win for the second player (Follower).

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Game Encoding

A position is described by the two Kazans (captured-stone stores) K1 (side to move) and K2 (opponent), and ten pits of 0..N stones. The 50 stones are conserved: $$\sum _{i=1}^{10}\text{pits}[i]+K_1+K_2=50\backslash sum\_\{i=1\}^\{10\}\; \backslash text\{pits\}[i]\; +\; K\_1\; +\; K\_2\; =\; 50$$

Captures are strictly even, so each Kazan score is an even integer. A Kazan reaching $\ge 26$ decides the game immediately and lies outside the stored range ($0 \le K_1, K_2 \le 24$). Positions are stored canonically from the side-to-move perspective.

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Layer Layout

The tablebase is sharded into layers indexed by the Kazan pair (K1, K2), where each Kazan is even in $0..24$ ($13 \times 13 = 169$ pairs). Every pair consists of two Zstandard-compressed bitset files:

• layer_<K1>_<K2>_win.bin.zst — The WIN/LOSS bitset for that layer.
• layer_<K1>_<K2>_draw.bin.zst — The DRAW bitset for that layer.

Files are Zstandard-compressed bitsets indexed by a combinatorial ranking of the pit configuration (StateIndex).

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Summary Statistics

Metric	Value
Layer pairs (K1, K2)	169
Total files	338 (169 win + 169 draw)
WIN files total size	6.0 GB
DRAW files total size	2.4 GB
Grand Total Size	8.3 GB (8,962,782,421 bytes)

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How to Query (Quickstart)

import zstandard as zstd

# Example: Loading a specific layer in Python
def load_layer(k1, k2, result_type="win"):
    filename = f"data/layer_{k1}_{k2}_{result_type}.bin.zst"
    with open(filename, 'rb') as fh:
        dctx = zstd.ZstdDecompressor()
        decompressed_data = dctx.decompress(fh.read())
    return decompressed_data

# Query bit at index
def is_winning_state(decompressed_bytes, state_index):
    byte_idx = state_index // 8
    bit_idx = state_index % 8
    return bool((decompressed_bytes[byte_idx] >> bit_idx) & 1)

Per-layer file sizes

K1	K2	win.bin	draw.bin
0	0	960.4 MB	394.1 MB
0	2	755.2 MB	287.9 MB
0	4	456.0 MB	164.6 MB
0	6	238.7 MB	87.6 MB
0	8	114.8 MB	44.0 MB
0	10	52.5 MB	20.3 MB
0	12	23.8 MB	8.3 MB
0	14	11.6 MB	3.1 MB
0	16	6.3 MB	978.9 KB
0	18	3.5 MB	252.9 KB
0	20	1.9 MB	64.5 KB
0	22	828.4 KB	11.0 KB
0	24	202.5 KB	455.0 B
2	0	440.9 MB	188.7 MB
2	2	487.8 MB	204.0 MB
2	4	367.9 MB	143.3 MB
2	6	212.7 MB	79.0 MB
2	8	106.5 MB	39.8 MB
2	10	49.4 MB	18.6 MB
2	12	22.4 MB	7.8 MB
2	14	10.8 MB	2.9 MB
2	16	5.7 MB	922.9 KB
2	18	3.1 MB	236.7 KB
2	20	1.6 MB	59.2 KB
2	22	702.7 KB	10.5 KB
2	24	160.6 KB	306.0 B
4	0	149.2 MB	63.0 MB
4	2	220.2 MB	96.1 MB
4	4	233.8 MB	99.9 MB
4	6	168.5 MB	67.0 MB
4	8	93.1 MB	35.0 MB
4	10	44.9 MB	16.5 MB
4	12	20.6 MB	7.0 MB
4	14	9.9 MB	2.7 MB
4	16	5.1 MB	856.7 KB
4	18	2.7 MB	217.5 KB
4	20	1.4 MB	53.2 KB
4	22	561.6 KB	9.3 KB
4	24	123.9 KB	157.0 B
6	0	43.6 MB	17.2 MB
6	2	72.5 MB	31.4 MB
6	4	103.6 MB	45.9 MB
6	6	104.9 MB	45.7 MB
6	8	71.8 MB	28.9 MB
6	10	38.1 MB	14.1 MB
6	12	18.1 MB	6.1 MB
6	14	8.7 MB	2.4 MB
6	16	4.4 MB	756.5 KB
6	18	2.3 MB	195.4 KB
6	20	1.1 MB	46.3 KB
6	22	426.8 KB	7.5 KB
6	24	91.1 KB	157.0 B
8	0	12.7 MB	4.5 MB
8	2	20.5 MB	8.2 MB
8	4	33.4 MB	14.6 MB
8	6	45.6 MB	20.4 MB
8	8	43.5 MB	19.2 MB
8	10	28.2 MB	11.3 MB
8	12	14.5 MB	5.1 MB
8	14	7.1 MB	2.0 MB
8	16	3.6 MB	650.7 KB
8	18	1.8 MB	168.6 KB
8	20	855.6 KB	38.3 KB
8	22	306.1 KB	6.5 KB
8	24	66.4 KB	157.0 B
10	0	4.3 MB	1.3 MB
10	2	6.2 MB	2.1 MB
10	4	9.6 MB	3.8 MB
10	6	14.9 MB	6.3 MB
10	8	18.8 MB	8.2 MB
10	10	16.5 MB	7.3 MB
10	12	10.0 MB	3.9 MB
10	14	5.1 MB	1.5 MB
10	16	2.6 MB	521.9 KB
10	18	1.3 MB	131.7 KB
10	20	571.3 KB	28.1 KB
10	22	199.9 KB	4.9 KB
10	24	42.6 KB	157.0 B
12	0	2.0 MB	371.6 KB
12	2	2.4 MB	596.9 KB
12	4	3.3 MB	990.2 KB
12	6	4.8 MB	1.7 MB
12	8	6.7 MB	2.6 MB
12	10	7.3 MB	2.9 MB
12	12	5.5 MB	2.2 MB
12	14	3.1 MB	1.0 MB
12	16	1.6 MB	334.4 KB
12	18	752.9 KB	79.0 KB
12	20	316.2 KB	13.6 KB
12	22	108.6 KB	3.0 KB
12	24	25.5 KB	157.0 B
14	0	1.3 MB	107.1 KB
14	2	1.3 MB	176.7 KB
14	4	1.5 MB	287.4 KB
14	6	2.0 MB	481.2 KB
14	8	2.6 MB	770.0 KB
14	10	3.0 MB	983.1 KB
14	12	2.6 MB	878.9 KB
14	14	1.5 MB	481.3 KB
14	16	787.7 KB	162.0 KB
14	18	356.4 KB	37.1 KB
14	20	144.9 KB	3.4 KB
14	22	51.7 KB	157.0 B
14	24	12.1 KB	157.0 B
16	0	919.0 KB	30.7 KB
16	2	903.3 KB	47.6 KB
16	4	933.4 KB	77.1 KB
16	6	1.0 MB	127.0 KB
16	8	1.2 MB	211.7 KB
16	10	1.4 MB	286.9 KB
16	12	1.2 MB	258.7 KB
16	14	727.8 KB	149.3 KB
16	16	344.9 KB	58.0 KB
16	18	145.1 KB	12.9 KB
16	20	56.2 KB	157.0 B
16	22	19.6 KB	157.0 B
16	24	5.3 KB	157.0 B
18	0	663.0 KB	6.8 KB
18	2	620.0 KB	11.2 KB
18	4	595.9 KB	18.1 KB
18	6	609.5 KB	32.1 KB
18	8	672.2 KB	53.9 KB
18	10	697.9 KB	76.3 KB
18	12	555.7 KB	64.2 KB
18	14	316.9 KB	32.5 KB
18	16	140.8 KB	12.9 KB
18	18	55.5 KB	157.0 B
18	20	19.3 KB	157.0 B
18	22	6.3 KB	157.0 B
18	24	1.8 KB	157.0 B
20	0	457.5 KB	2.5 KB
20	2	407.7 KB	3.0 KB
20	4	371.0 KB	5.8 KB
20	6	354.0 KB	11.2 KB
20	8	349.6 KB	18.7 KB
20	10	318.2 KB	21.5 KB
20	12	226.6 KB	13.3 KB
20	14	122.3 KB	3.5 KB
20	16	53.4 KB	157.0 B
20	18	19.4 KB	157.0 B
20	20	6.1 KB	157.0 B
20	22	1.8 KB	157.0 B
20	24	609.0 B	157.0 B
22	0	255.1 KB	720.0 B
22	2	217.5 KB	1.0 KB
22	4	186.4 KB	1.7 KB
22	6	163.2 KB	2.1 KB
22	8	142.2 KB	3.4 KB
22	10	113.0 KB	3.6 KB
22	12	73.0 KB	2.7 KB
22	14	39.9 KB	157.0 B
22	16	17.6 KB	157.0 B
22	18	6.3 KB	157.0 B
22	20	1.9 KB	157.0 B
22	22	598.0 B	157.0 B
22	24	240.0 B	157.0 B
24	0	88.0 KB	455.0 B
24	2	67.2 KB	306.0 B
24	4	51.4 KB	157.0 B
24	6	40.3 KB	157.0 B
24	8	30.4 KB	157.0 B
24	10	21.3 KB	157.0 B
24	12	13.6 KB	157.0 B
24	14	7.8 KB	157.0 B
24	16	3.8 KB	157.0 B
24	18	1.6 KB	157.0 B
24	20	587.0 B	157.0 B
24	22	243.0 B	157.0 B
24	24	164.0 B	157.0 B

Citation

If you use this tablebase, solver architecture, or game-theoretic proof in your research, please cite:

@misc{zeinulla2026bestemshe,
  title={Strongly Solving Bestemshe: A 10-Gigabyte Retrograde Tablebase Proof},
  author={Zeinulla, Ansar and Manassov, Murat},
  year={2026},
  publisher={Hugging Face Datasets},
  howpublished={\url{https://huggingface.co/datasets/ansarzeinulla/bestemshe-tablebase}}
}