2022/01/28 by Tanya Khovanova, Khovanova, Tanya, Atharva Pathak +1
Computer Science · Psychology · Social Sciences · #05A99 #Artificial Intelligence in Games #Combinatorics (math.CO) #Digital Games and Media #FOS: Mathematics #Gambling Behavior and Treatments
paper · pdf · doi:10.48550/arxiv.2202.00473
openalex publication_date 2022/01/28 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
This paper studies a single-suit version of the card game War on a finite deck of cards. There are varying methods of how players put the cards that they win back into their hands, but we primarily consider randomly putting the cards back and deterministically always putting the winning card before the losing card. The concept of a passthrough is defined, which refers to a player playing through all cards in their hand from a particular point in the game. We consider games in which the second player wins during their first passthrough. We introduce several combinatorial objects related to the game: game graphs, win-loss sequences, win-loss binary trees, and game posets. We show how these objects relate to each other. We enumerate states depending on the number of rounds and the number of passthroughs.