Estimating Card Fitness for Discard in Gin Rummy

Abstract

Due to the computation time and resources required, there is no known optimal strategy for the game of Gin Rummy. Previous work in extensive games, such as Texas Hold ’em Poker, has found that hand fitness and information sets about the state of the game can be used to determine an improved strategy. These information sets, combined with algorithms for Counterfactual Regret Minimization, can arrive at a Nash Equilibrium strategy for smaller abstractions of extensive games. This paper builds on previous research by extending the premise of hand fitness to card fitness in the discard decision point of Gin Rummy. We argue that a card can be ranked based on whether it meets four specific characteristics at that stage in the game. These characteristics include its effect on deadwood points after one more turn, its utility to the opponent, and if it can contribute to a meld. An optimal discard choice can then be picked from the highest-ranked card by using a simplified Counterfactual regret minimization strategy that can be trained in less time due to its limited information set. While this does not look at every potential characteristic of card fitness, it outperformed other bots when evaluated in a large number of games. These bots did not consider card fitness as a whole, but rather considered characteristics separately. We argue that the characteristics defined are a part of the total information set that can determine the discard fitness of a card within a hand in the game of Gin Rummy.