Simplified Poker

This is in­tended as a three-part se­quence. Part two will go over my strat­egy. Part three will re­veal the re­sults and dis­cuss some im­pli­ca­tions.

In the same class in which we later played The Dar­win Game, we played a less com­plex game called Sim­plified Poker. As in The Dar­win Game, we were given the rules and asked to sub­mit in­struc­tions for a com­puter pro­gram that would play the game, and the pro­fes­sor would then code our pro­grams for us.

The rules of Sim­plified Poker are as fol­lows:

Game is played with a 3-card deck, with the cards la­beled 1, 2 and 3.

Each hand, the play­ers al­ter­nate who goes first, each player antes one chip and is dealt one card.

The first player can bet one chip, or check.

If the first player bets, the sec­ond player can ei­ther call the one chip bet, or fold.

If the first player checks, the sec­ond player can ei­ther also check, or can bet. If the sec­ond player bets, the first player can ei­ther call the one chip bet, or fold.

There is at most one bet per hand, as nei­ther player is al­lowed to raise.

If ei­ther player folds, the other wins the pot of 2 chips and takes back their 1 chip bet. Nei­ther card is shown. If nei­ther player folds – ei­ther both play­ers check, or there is a bet and a call – then both cards are re­vealed and the player with the higher card takes all 4 chips.

In the class, all pro­grams would play a round robin with all other pro­grams, with 50 hands per match. Your goal is to max­i­mize the av­er­age num­ber of chips won over all rounds – note that how many op­po­nents you beat does not mat­ter, only the num­ber of chips won.

The game is sim­ple. A lot, but far from all, of your de­ci­sions are forced. There’s no weird trick, but op­ti­mal play still isn’t ob­vi­ous. I’ll pause here to al­low and en­courage think­ing about what strat­egy you’d sub­mit.