$ ~/aibattle/kuhn
🃏 Kuhn Poker · 12 models · round-robin · 30 seat-swapped hands/pair · deck {J,Q,K}, ~2 decisions/hand
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How Kuhn Poker works
A minimal 2-player poker on a 3-card deck — JQK (ranked J < Q < K). One hand plays out like this:- Both players ante 1 chip (pot starts at 2). Each is dealt one private card; the third is unused.
- Player 0 acts first and may
checkorbet(1 chip). - Facing a
bet, the opponent maycall(match it) orfold(forfeit the pot). - Facing a
check, the opponent maycheckback (go to showdown) orbet. - At showdown the higher card wins the pot; a fold hands the pot to the other player. Zero-sum: the winner gains exactly what the loser put in.
Every hand is one of five lines:
check-check, check-bet-fold,
check-bet-call, bet-fold, or bet-call — so a player makes ~1–2 decisions per hand.What the model sees each turn: its own private card, the betting so far, the
pot, and its legal actions — never the opponent's card.
Kuhn Poker is fully solved, so we judge play against the Nash
equilibrium rather than chips alone. At only 30 hands/pair the chip totals
are high-variance and directional — the fundamentals and betting-style sections
below are the real skill signal. The leaderboard is ranked by fewest blunders, then chips;
the Elo column (opponent-adjusted Bradley-Terry rating over per-hand results, field mean
1500) is shown for reference, with ±1 bootstrap SD — note how wide those error bars are at this
sample size, which is exactly why the ranking leans on blunders instead.
Bet frequency by card (when first to act)
Equilibrium is polarized: bet the King (green) ~100%, bluff the Jack (blue) ~33%,
and almost never bet the Queen (red). The closer a model matches that shape, the more GTO it plays.
GTO fundamentals (unambiguous blunders)
Fold K to a bet = folding the nuts (always wins the showdown).
Call a bet with J = calling with the worst card (can never win the showdown). Both are
pure mistakes independent of mixing. Shown as occurrences / opportunities.
| # | model | fold K vs bet | call J vs bet | total blunders |
|---|---|---|---|---|
| 1 |  Claude Sonnet 4.6 | 0/3 | 0/45 | 0/48 (0%) |
| 2 |  MiniMax-M2.7 | 0/2 | 0/26 | 0/28 (0%) |
| 3 | MiniMax-M3 | 0/10 | 0/50 | 0/60 (0%) |
| 4 |  GLM-5.1 | 0/8 | 0/41 | 0/49 (0%) |
| 5 |  Qwen3.7 Plus | 0/1 | 0/48 | 0/49 (0%) |
| 6 |  DeepSeek V4 Pro | 0/7 | 0/61 | 0/68 (0%) |
| 7 | GLM-5.2 | 0/4 | 0/50 | 0/54 (0%) |
| 8 |  GPT-OSS 120B | 0/5 | 0/35 | 0/40 (0%) |
| 9 | GPT 5.5 | 0/4 | 0/40 | 0/44 (0%) |
| 10 |  Kimi K2.6 | 0/2 | 0/46 | 0/48 (0%) |
| 11 | GPT 5.4 | 0/1 | 0/38 | 0/39 (0%) |
| 12 | Claude Opus 4.8 | 0/4 | 0/43 | 0/47 (0%) |
columns: fold K vs bet folds a King (best card) to a bet — a blunder · call J vs bet calls a Jack (worst card) to a bet — a blunder · total blunders sum of the two
Betting style (bet % by card, first to act · GTO: K 100% / Q 0% / J ~33%)
| model | bet K (value) | bet Q (trap) | bet J (bluff) |
|---|---|---|---|
| Claude Sonnet 4.6 | 100% | 6% | 0% |
| MiniMax-M2.7 | 100% | 27% | 7% |
| MiniMax-M3 | 100% | 30% | 28% |
| GLM-5.1 | 86% | 11% | 21% |
| Qwen3.7 Plus | 99% | 4% | 0% |
| DeepSeek V4 Pro | 100% | 0% | 4% |
| GLM-5.2 | 100% | 1% | 14% |
| GPT-OSS 120B | 97% | 11% | 7% |
| GPT 5.5 | 100% | 0% | 47% |
| Kimi K2.6 | 99% | 0% | 42% |
| GPT 5.4 | 100% | 0% | 43% |
| Claude Opus 4.8 | 100% | 0% | 46% |
Leaderboard
| # | model | Elo | net/hand | win% | hands | decisions | invalid% | trunc% | tokens/dec | $/1K dec |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | Claude Sonnet 4.6 | 1502 ±19 | +0.041 | 50% | 270 | 319 | 0.0% | 0.0% | — | — |
| 2 | MiniMax-M2.7 | 1499 ±27 | +0.040 | 50% | 150 | 181 | 0.0% | 0.0% | 12,668 | $15.20 |
| 3 | MiniMax-M3 | 1502 ±18 | +0.033 | 50% | 330 | 395 | 0.0% | 0.0% | 3,723 | $4.47 |
| 4 | GLM-5.1 | 1508 ±17 | +0.024 | 51% | 330 | 404 | 0.0% | 0.0% | 1,945 | $8.56 |
| 5 | Qwen3.7 Plus | 1483 ±19 | +0.013 | 47% | 300 | 372 | 0.0% | 0.0% | 5,542 | $8.87 |
| 6 | DeepSeek V4 Pro | 1494 ±18 | +0.009 | 49% | 330 | 410 | 0.0% | 0.0% | 1,992 | $6.93 |
| 7 | GLM-5.2 | 1494 ±18 | +0.007 | 49% | 300 | 371 | 0.0% | 0.0% | 1,022 | $4.50 |
| 8 | GPT-OSS 120B | 1482 ±24 | +0.005 | 48% | 210 | 257 | 0.0% | 0.0% | 773 | $0.46 |
| 9 | GPT 5.5 | 1516 ±20 | -0.011 | 52% | 270 | 321 | 0.0% | 0.0% | — | — |
| 10 | Kimi K2.6 | 1510 ±18 | -0.030 | 52% | 330 | 394 | 0.0% | 0.0% | 13,303 | $53.21 |
| 11 | GPT 5.4 | 1500 ±19 | -0.052 | 50% | 270 | 323 | 0.0% | 0.0% | — | — |
| 12 | Claude Opus 4.8 | 1511 ±21 | -0.070 | 52% | 270 | 322 | 0.0% | 0.0% | — | — |
Head-to-head (row's net chips/hand vs column)
| Claude Opus 4.8 | Claude Sonnet 4.6 | DeepSeek V4 Pro | GLM-5.1 | GLM-5.2 | GPT 5.4 | GPT 5.5 | Kimi K2.6 | MiniMax-M3 | Qwen3.7 Plus | GPT-OSS 120B | MiniMax-M2.7 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Claude Opus 4.8 | — | -0.07 | -0.20 | -0.07 | +0.03 | -0.13 | -0.03 | -0.07 | -0.23 | +0.13 | +0.00 | +0.00 |
| Claude Sonnet 4.6 | +0.07 | — | +0.03 | +0.03 | +0.00 | +0.10 | +0.03 | +0.10 | +0.03 | -0.03 | +0.00 | +0.00 |
| DeepSeek V4 Pro | +0.20 | -0.03 | — | -0.10 | +0.07 | +0.13 | -0.07 | +0.07 | -0.10 | +0.00 | -0.03 | -0.03 |
| GLM-5.1 | +0.07 | -0.03 | +0.10 | — | +0.03 | +0.07 | -0.07 | +0.10 | +0.10 | -0.17 | +0.07 | +0.00 |
| GLM-5.2 | -0.03 | +0.00 | -0.07 | -0.03 | — | +0.00 | +0.07 | +0.13 | +0.00 | +0.00 | +0.00 | +0.00 |
| GPT 5.4 | +0.13 | -0.10 | -0.13 | -0.07 | +0.00 | — | +0.13 | -0.07 | -0.20 | -0.17 | +0.00 | +0.00 |
| GPT 5.5 | +0.03 | -0.03 | +0.07 | +0.07 | -0.07 | -0.13 | — | -0.03 | +0.10 | -0.10 | +0.00 | +0.00 |
| Kimi K2.6 | +0.07 | -0.10 | -0.07 | -0.10 | -0.13 | +0.07 | +0.03 | — | -0.03 | +0.03 | +0.10 | -0.20 |
| MiniMax-M3 | +0.23 | -0.03 | +0.10 | -0.10 | +0.00 | +0.20 | -0.10 | +0.03 | — | +0.00 | +0.07 | -0.03 |
| Qwen3.7 Plus | -0.13 | +0.03 | +0.00 | +0.17 | +0.00 | +0.17 | +0.10 | -0.03 | +0.00 | — | -0.17 | +0.00 |
| GPT-OSS 120B | +0.00 | +0.00 | +0.03 | -0.07 | +0.00 | +0.00 | +0.00 | -0.10 | -0.07 | +0.17 | — | +0.07 |
| MiniMax-M2.7 | +0.00 | +0.00 | +0.03 | +0.00 | +0.00 | +0.00 | +0.00 | +0.20 | +0.03 | +0.00 | -0.07 | — |