Date on Senior Honors Thesis
5-2025
Document Type
Senior Honors Thesis
Degree Name
B.S.
Department
Mathematics
Committee Chair
Grzegorz Kubicki
Author's Keywords
two-player games; scores and game value; bipartite tournaments; perfect matching
Abstract
We consider a two-person game played on a bipartite tournament with equal size parts. The game is modeled after trick-taking card games like bridge or euchre. The two players, South and North, each receive one of the parts as their hand, and the arcs from a vertex in one hand beat the corresponding vertices in the other hand. The game is played over rounds called tricks where the number of tricks is equal to the number of vertices in each player’s hand. At the beginning of the game, one player is designated as the leader, and they play the first vertex of the first trick after which the other player, the follower, plays one of their vertices. Whichever player’s vertex beats the other vertex wins the trick and becomes the leader for next trick. The goal of the game is to win as many tricks as possible. On account of the changing leads, deducing an optimal strategy is difficult. In this paper we derive some bounds for the scores achieved on different tournaments and compare these to some of the corresponding bounds derived for a game where the tournament has no directed cycles.
Recommended Citation
Bagley, Allan, "Two-player trick-taking games on bipartite tournaments." (2025). College of Arts & Sciences Senior Theses. Paper 330.
Retrieved from https://ir.library.louisville.edu/honors/330
Lay Summary
We are considering a game modeled after trick-taking card games like bridge or euchre. In this game each player receives n cards that make up their hand. Instead of how normal playing cards have a hierarchy in their ranks, we are not necessarily able to order these cards from strongest to weakest. Each card in one player’s hand wins or loses to each card in their opponent’s hand, but while one card might beat card A and lose to card B, a different card might lose to card A and beat card B. In a game, there are n rounds called tricks. After an initial leader is determined, the person who wins the preceding trick is the leader in the next trick. The way each trick is played is that the leader plays one of their cards and then their opponent chooses one of their cards to play. The goal of the game is to win as many of the n tricks as possible. In this paper we derive a couple ways to have some degree of comparison between the strength of different hands.
