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

Abstract

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.