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Counterfactual Regret Minimization on Kuhn Poker

Implementation of CFR and MCCFR (outcome-sampling) with rust.

Verify Result

  • The expected payoff for the first player shall be -1/18

  • Probability of betting with hand card 3 is 3x of with card 1

  • Always pass with hand card 2

Example Result

Here's the example output for 100000 iterations.

CFR

History Check Probability Bet Probability
1 0.77 0.23
1C 0.67 0.33
1B 1.00 0.00
1CB 1.00 0.00
2 1.00 0.00
2C 1.00 0.00
2B 0.66 0.34
2CB 0.42 0.58
3 0.30 0.70
3C 0.00 1.00
3B 0.00 1.00
3CB 0.00 1.00

MCCFR

Explore with epsilon=0.06. Average payoff = -0.05138

History Check Probability Bet Probability
1 0.805 0.195
1C 0.68 0.32
1B 0.97 0.03
1CB 0.97 0.03
2 0.97 0.03
2C 0.94 0.05
2B 0.56 0.44
2CB 0.47 0.53
3 0.422 0.578
3C 0.03 0.97
3B 0.03 0.97
3CB 0.03 0.97

We get 0.03 here because we choose epsilon = 0.06 and we have 2 actions to choose from.

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CFR and MCCFR on Kuhn Poker

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