Computing Optimal Strategies in Card Sharks

Card Sharks is a television game show featuring a two-player stochastic game, defined as a repeated game with probabilistic transitions. The game is played in a sequence of stages. At the beginning of each stage, the game is in a certain state. In this stochastic game, two contestants compete for control of a row of playing cards by alternating turns answering toss-up questions then subsequently predicting whether the next card is higher or lower in value than the previous card.

My goal was to develop an optimal strategy of gameplay for Card Sharks. Using back- wards induction and the minimax theorem, I employed dynamic programming with memorization to compute an optimal strategy for any game state, given information on the current cards of the player and opponent. I made the simplifying assumptions that both players have a 50% chance of correctly answering a survey question correctly and that only the current card would be taken into consideration when the player guesses whether the next is higher or lower.

In comparing my optimal strategy solutions to the actions of players on the actual game show, players tended to be more aggressive than the optimal strategy suggested they play. This concept appears in game theory as the Martingale betting system. If one’s base card is a 5 through Jack, for example, the likelihood of winning is greatest if you change the base card, yet most human players kept it and chose to play.

This project lies at the intersection of computer science and economics: the development and deployment of an optimally performing agent draws upon principles in computational intelligence, algorithms, and game theory.

• final report (including deliverables)
• proposal
• code files