The utility of gambling and the favourite-longshot bias

The traditional explanation for the usual favourite–longshot bias in gambling is that gamblers are risk-lovers. Conditions are derived under which the bias occurs and it is shown to be consistent with a utility function that has elasticity greater than one in a certain range. With a utility function that displays risk-aversion as well as risk-loving behaviour over its domain, it is demonstrated that the expected return–win probability frontier is not monotonic as has been hitherto tacitly assumed. This provides a consistent explanation for both the usual favourite–longshot bias and also for the few examples where a reverse bias has been observed. Pooled data supports the thesis that the frontier is not completely monotonic but does indeed have a turning point.