One feature of experimental work is the heterogeneity in risk attitudes and probability distortion displayed by agents. We outline a more general non-expected utility model, which nests the models of Markowitz, and Kahneman and Tversky. The model can generate the standard favourite–longshot bias or a reverse favourite–longshot bias as a result of optimal behaviour. We also provide new empirical evidence on the relationship between Tote and bookmaker returns and confirm that the relationship is not as originally conjectured by Gabriel and Marsden. We outline how our new model can provide an explanation of the relationship that is observed.