Bookmaker and Pari-Mutuel Betting: Is a (Reverse) Favourite-Longshot Bias Built-In?

A widely documented empirical regularity in gambling markets is that bets on high probability events (a race won by a “favourite”) have higher expected returns than bets on low probability events (a “longshot” wins). Such favourite-longshot (FL) biases however appear to be more severe and persistent in bookmaker markets than in pari-mutuel markets; the latter sometimes exhibit no bias or a reverse FL bias. Our results help understand these differences: the odds grid in bookmaker markets leads to a built-in FL bias, whereas that used in pari-mutuel betting pushes these markets toward a reverse FL bias.