We present a risk-aware utility model for action selection in 2-player, non-cooperative, repeated games of chance. Our model augments expected utility calculations and adapts to changes in accumulated utility, demonstrating rational game play. Motivated by risk aversion and the utility of wealth, our model is parameterized by an agent's wealth, the payoffs of a game, and the probability associated with gain and loss. Using expected utility combined with our model, we can impose desired behavior onto an agent that mimics more closely the types of behaviors we see in social and economic situations where risk is involved. We define our model theoretically and present empirical results showing the effectiveness of a risk-aware utility model against a Nash equilibrium mixed strategy in a repeated game of chance.