Money for nothing

Horatio Bottomley was a flamboyant Edwardian journalist, financier and crook. It is fitting that he is now chiefly remembered by a story which ought to be true but, apparently, is not.

According to legend, Bottomley arranged a race at a Belgian seaside course in such a way that he owned all six competing horses and could instruct the jockeys as to the precise order in which they should finish. The bets he laid should have made a fortune but, unfortunately, half way through the race, a thick sea fog swept in and all ended in confusion.

On arriving at a race course, the first question that occurs to a mathematician is ‘Can I make money without risk?’. This suggests the harder question ‘If I bet Y, what is the maximum sum L that I can guarantee to get back?’. If L > Y, then I can guarantee a profit. If Y > L, I cannot.

In the old days, when two gentlemen A and B different in their views on the ability of a certain horse to win a certain race, A would offer to back his judgement by wagering y at odds of a to b. If B accepted the wager, then B would pay A the amount y if the horse won and A would pay B the amount ya/b if the horse lost.