# Counterfactual Regret Minimization (CFR) on Kuhn Poker

This applies Counterfactual Regret Minimization (CFR) to Kuhn poker.

Kuhn Poker is a two player 3-card betting game. The players are dealt one card each out of Ace, King and Queen (no suits). There are only three cards in the pack so one card is left out. Ace beats King and Queen and King beats Queen - just like in normal ranking of cards.

Both players ante chip (blindly bet chip). After looking at the cards, the first player can either pass or bet chip. If first player passes, the the player with higher card wins the pot. If first player bets, the second play can bet (i.e. call) chip or pass (i.e. fold). If the second player bets and the player with the higher card wins the pot. If the second player passes (i.e. folds) the first player gets the pot. This game is played repeatedly and a good strategy will optimize for the long term utility (or winnings).

Here's some example games:

• KAp - Player 1 gets K. Player 2 gets A. Player 1 passes. Player 2 doesn't get a betting chance and Player 2 wins the pot of chips.
• QKbp - Player 1 gets Q. Player 2 gets K. Player 1 bets a chip. Player 2 passes (folds). Player 1 gets the pot of because Player 2 folded.
• QAbb - Player 1 gets Q. Player 2 gets A. Player 1 bets a chip. Player 2 also bets (calls). Player 2 wins the pot of .

He we extend the InfoSet class and History class defined in __init__.py with Kuhn Poker specifics.

38from typing import List, cast, Dict
39
40import numpy as np
41
42from labml import experiment
43from labml.configs import option
44from labml_nn.cfr import History as _History, InfoSet as _InfoSet, Action, Player, CFRConfigs
45from labml_nn.cfr.infoset_saver import InfoSetSaver

Kuhn poker actions are pass (p ) or bet (b )

48ACTIONS = cast(List[Action], ['p', 'b'])

The three cards in play are Ace, King and Queen

50CHANCES = cast(List[Action], ['A', 'K', 'Q'])

There are two players

52PLAYERS = cast(List[Player], [0, 1])

## Information set

55class InfoSet(_InfoSet):

60    @staticmethod
61    def from_dict(data: Dict[str, any]) -> 'InfoSet':
63        pass

Return the list of actions. Terminal states are handled by History class.

65    def actions(self) -> List[Action]:
69        return ACTIONS

Human readable string representation - it gives the betting probability

71    def __repr__(self):
75        total = sum(self.cumulative_strategy.values())
76        total = max(total, 1e-6)
77        bet = self.cumulative_strategy[cast(Action, 'b')] / total
78        return f'{bet * 100: .1f}%'

## History

This defines when a game ends, calculates the utility and sample chance events (dealing cards).

The history is stored in a string:

• First two characters are the cards dealt to player 1 and player 2
• The third character is the action by the first player
• Fourth character is the action by the second player
81class History(_History):

History

95    history: str

Initialize with a given history string

97    def __init__(self, history: str = ''):
101        self.history = history

Whether the history is terminal (game over).

103    def is_terminal(self):

Players are yet to take actions

108        if len(self.history) <= 2:
109            return False

Last player to play passed (game over)

111        elif self.history[-1] == 'p':
112            return True

Both players called (bet) (game over)

114        elif self.history[-2:] == 'bb':
115            return True

Any other combination

117        else:
118            return False

Calculate the terminal utility for player ,

120    def _terminal_utility_p1(self) -> float:

if Player 1 has a better card and otherwise

125        winner = -1 + 2 * (self.history[0] < self.history[1])

Second player passed

128        if self.history[-2:] == 'bp':
129            return 1

Both players called, the player with better card wins chips

131        elif self.history[-2:] == 'bb':
132            return winner * 2

First player passed, the player with better card wins chip

134        elif self.history[-1] == 'p':
135            return winner

History is non-terminal

137        else:
138            raise RuntimeError()

Get the terminal utility for player

140    def terminal_utility(self, i: Player) -> float:

If is Player 1

145        if i == PLAYERS[0]:
146            return self._terminal_utility_p1()

Otherwise,

148        else:
149            return -1 * self._terminal_utility_p1()

The first two events are card dealing; i.e. chance events

151    def is_chance(self) -> bool:
155        return len(self.history) < 2

Add an action to the history and return a new history

157    def __add__(self, other: Action):
161        return History(self.history + other)

Current player

163    def player(self) -> Player:
167        return cast(Player, len(self.history) % 2)

Sample a chance action

169    def sample_chance(self) -> Action:
173        while True:

Randomly pick a card

175            r = np.random.randint(len(CHANCES))
176            chance = CHANCES[r]

See if the card was dealt before

178            for c in self.history:
179                if c == chance:
180                    chance = None
181                    break

Return the card if it was not dealt before

184            if chance is not None:
185                return cast(Action, chance)

187    def __repr__(self):
191        return repr(self.history)

Information set key for the current history. This is a string of actions only visible to the current player.

193    def info_set_key(self) -> str:

Get current player

199        i = self.player()

Current player sees her card and the betting actions

201        return self.history[i] + self.history[2:]
203    def new_info_set(self) -> InfoSet:

Create a new information set object

205        return InfoSet(self.info_set_key())

A function to create an empty history object

208def create_new_history():
210    return History()

Configurations extends the CFR configurations class

213class Configs(CFRConfigs):
217    pass

Set the create_new_history method for Kuhn Poker

220@option(Configs.create_new_history)
221def _cnh():
225    return create_new_history

### Run the experiment

228def main():

Create an experiment, we only write tracking information to sqlite to speed things up. Since the algorithm iterates fast and we track data on each iteration, writing to other destinations such as Tensorboard can be relatively time consuming. SQLite is enough for our analytics.

237    experiment.create(name='kuhn_poker', writers={'sqlite'})

Initialize configuration

239    conf = Configs()

241    experiment.configs(conf)

Set models for saving

243    experiment.add_model_savers({'info_sets': InfoSetSaver(conf.cfr.info_sets)})

Start the experiment

245    with experiment.start():

Start iterating

247        conf.cfr.iterate()
251if __name__ == '__main__':
252    main()