THE MINIMAX BOOKIE

A bookmaker makes a book on a horse race: he offers odds against the v arious horses winning the race, and gamblers accept bets at those odds when they find the odds attractive. The book at a particular time con sists, of the bookmaker's winnings according to the different outcomes of the race if the race were run at that time. We consider strategies the bookmaker might adopt when deciding how to alter his quoted odds as bets accumulate. The bookmaker is assumed to behave conservatively in the sense that he tries to minimise his expected maximum loss over all possible outcomes of the race.