Game-theoretic analysis of Guts Poker

We carry out a game-theoretic analysis of the recursive game "Guts," a variant of poker featuring repeated play with possibly growing stakes. An interesting aspect of such games is the need to account for funds lost to all players if expected stakes do not go to zero with the number of rounds of play. We provide a sharp, easily applied criterion eliminating this scenario, under which one may compute a value for general games of this type. Using this criterion, we determine an optimal "pure" strategy for the 2-player game consisting of a simple "go/no-go" criterion. For the $n$-player game, $n\geq 3$, we determine an optimal go/no-go strategy against "bloc play" in which players 2-n pursue identical strategies, giving nonnegative return for player 1. Against general collaborative strategies of players 2-n, we show that player 1 cannot force a nonnegative return. It follows that there exists a nonstrict symmetric Nash equilbrium, but this equilibrium is not strong