  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
