A sure-win betting scheme. If there are h horses in a race, with the odds quoted for horse j being oj to 1 against that horse winning, then an arbitrage is possible if δ>0, where
If such a set of odds exists, then it is referred to as a Dutch book. In this case a win of N (ignoring betting costs) is guaranteed by backing each horse, with xj, the bet on horse j, being given by![arbitrage](Images/oree/doc/10.1093/acref/9780199679188.001.0001/acref-9780199679188-math-0019-full.gif)
As a simple example, suppose that there are two horses in a race, each with odds of two to one against. A punter placing 1 cent on each (total cost 2 cents) would receive back 2 cents, together with the winning stake—for an assured gain of 1 cent.