The Construction of a Simple Book

Abstract

A book is made for a horse race, and punters place their bets. The problem considered here is how the bookmaker should construct his book. Before this can be solved, it has to be determined how the punters will react to any proposed book. Much of the detailed discussion is confined to a race with two horses, though some results apply in the general case. The punters' problem is solved using a utility function, special attention being paid to the case of constant risk-aversion. Two solutions are provided for the bookmaker's problem, dependent on whether it is desired to maximize expected gain, or achieve the same gain whatever horse wins.