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Baby Poker

https://fivethirtyeight.com/features/can-you-deal-with-these-card-game-puzzles/

 

In this fivethirtyeight article, the Riddler Classic poses a very interesting game theory exercise in the form of Baby Poker. Rather than playing with cards and chips, in this scenario, poker is boiled down to two players each anteing one (1) dollar into the pot and each player making only one decision. Two players, A and B, each roll a die after the initial ante. Player A is then given the opportunity to either “check” – which leads both players to show their die and the higher number taking the pot – or “raise”. When Player A raises, he bets another dollar. Player B then has the option to “call” and match the bet, after which both dice are shown, or “fold”, in which case Player A wins the pot of his raise and the original two antes.

These elements allow the players to explore the fundamental concepts behind bluffing in poker. Without going too in depth into the strategy of the situation, it is clear that the two players must adopt very different strategies. Player B’s strategy can be reduced to frequency he will call when faced with a raise. Since Player B has no incentive to ever call with a value less than a value he would fold, he must only call with a certain top percentage of his values.

On the other hand, since Player A knows that when he rolls a low value, it has a low to non-existent chance of winning, he could also try to bluff and raise with a low value since the chance that the opponent folds may be more valuable than simply checking. Along with this, Player A will also be raising his highest values which means he will adopt a polarizing strategy.

Overall, this game can be described by the choices made by each player on each dice roll (with the potential inclusions of mixed strategies of both). The Nash equilibrium is expected to look like Player A adopting a polarized strategy and Player B adopting a merged strategy.

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