Stochastic game theory unifies both strategic interactions and random processes into a single analytic framework. Along these lines, we develop a simple risky choice problem, and then extend that decision theoretic problem into a strategic context. We derive the equilibrium for this simple 2-player zero sum game and show that its mixed strategy equilibrium is both complicated and highly sensitive to the stochastic process. Further we show a non-zero sum version of this game, and then outline several experiments along these lines.