This paper focuses on minimal risk strategies for tournament-style No-Limit Texas Hold’em. We write linear programs which provide a set of requirements for a conservative player to follow so that a favorable outcome is obtained. We also model strategies by constructing stack functions, which map a strategy to its expected outcome. We prove various properties of stack functions, which provide evidence in support of the conjecture that the minimal risk strategy corresponds to the line segment connecting (0,yo) to (n,A), where yo is the initial number of chips a player has in the tournament, and A is the desired amount of chips a player has at the end of the tournament.