Some Notes on Optimal "Across the Board'' Parimutuel Bets

Recently I competed in a club golf competition where there was organized parimutuel betting on the outcome. I made an ``across the board'' (ATB) bet of $20 on our team to win, place, and show. Subsequently I wondered whether this was the best thing to do. Hence, this paper examines the theory of an optimal ATB parimutuel bet. The goal is to develop principles that would guide such wagering when a bettor has only limited information about the sizes of the betting pools and the relative probabilities of finish of the various teams.

Surprised by the Parimutuel Odds?

Empirical analyses of parimutuel betting markets have documented that market probabilities of favorites (longshots) tend to underestimate (overestimate) the corresponding empirical probabilities. We argue that this favorite-longshot bias is consistent with bettors taking simultaneous positions on the basis of private information about the likelihood of different outcomes. The ex post realization of a high market probability indicates favorable information about the occurrence of an outcome—and the opposite is true for longshots. This explanation for the bias relies on the bettors' inability to incorporate the surprise revealed by the final odds. (JEL D81, D82, L83)