Orthodox expected utility theory imposes too stringent restrictions on what attitudes to risk one can rationally hold. Focusing on a life-and-death gamble, I identify as the main culprit the theory's Linearity property, according to which the utility of a particular change in the risk of a bad outcome is independent of the original level of risk. Finally, I argue that a recent non-standard Bayesian decision theory, that does not have this property, handles risky gambles better than the orthodox theory.