Egyptian Ratscrew: Discovering Dominant Strategies with Computational Game Theory

Abstract

"Egyptian Ratscrew" (ERS) is a modern American card game enjoyed by millions of players worldwide. A game of ERS is won by collecting all of the cards in the deck. Typically this game is won by the player with the fastest reflexes, since the most common strategy for collecting cards is being the first to slap the pile in the center whenever legal combinations of cards are placed down. Most players assume that the dominant strategy is to develop a faster reaction time than your opponents, and no academic inquiry has been levied against this assumption. This thesis investigates the hypothesis that a "risk slapping" strategist who relies on practical economic decision making will win an overwhelming majority of games against players who rely on quick reflexes alone. It is theorized that this can be done by exploiting the "burn rule," a penalty that is too low-cost to effectively dissuade players from slapping illegally when it benefits them. Using the Ruby programming language, we construct an Egyptian Ratscrew simulator from scratch. Our model allows us to simulate the behavior of 8 strategically unique players within easily adjustable parameters including simulation type, player count, and burn amount. We simulate 100k iterations of 67 different ERS games, totaling 6.7 million games of ERS, and use win percentage data in order to determine which strategies are dominant under each set of parameters. We then confirm our hypothesis that risk slapping is a dominant strategy, discover that there is no strictly dominant approach to risk slapping, and elucidate a deeper understanding of different ERS mechanics such as the burn rule. Finally, we assess the implications of our findings and suggest potential improvements to the rules of the game. We also touch on the real-world applications of our research and make recommendations for the future of Egyptian Ratscrew modeling.