An Analysis of Equilibria in Poker Tournaments with Bounties

Abstract

In this thesis, we find and analyze equilibrium strategies for poker tournaments with bounties. We use a recent technique in algorithmic game theory to find an approximate equilibrium for three-player No-Limit Texas Hold’em tournaments with bounties of various sizes. We find that as bounties increase, players become more aggressive and enter the pot more frequently, even those with fewer chips. We also analyze a model for poker, or “toy game,” to attempt to gain intuition for how the presence of bounties might affect equilibria. We solve for how an aggressive player’s probability of bluffing changes as his individual utility changes, and similarly we do the same for a defensive player and his calling probability.