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 chips.
In the class, all programs would play a round robin with all other programs, with 50 hands per match. You know the results of previous hands during the match, but not the results of hands from other matches. 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.
(Edited to explicitly note that you have knowledge of earlier hands in the same match)