this example, the bookmaker will pay out $200 (including returning the winning stake)—but the punter has bet $210, hence making a loss of $10 on the race. However, if horse 4 was withdrawn and the bookmaker does not adjust the other odds, the implied probabilities would add up to 0.95. In such a case, a gambler could always reap a profit of $10 by betting $100, $50 and $40 on the remaining three horses, respectively, and not having to stake $20 on the withdrawn horse, which now cannot win. Another possibility is for a crooked gambler to fix a race by sabotaging the favourite. If the favourite horse starts the race at odds-on (less than 1–1 odds), then the remaining horses can be bet in proportion to their odds so as to guarantee a profit, no matter which horse wins. Other forms of Dutch books can exist when incoherent odds are offered on exotic bets such as forecasting the order in which horses will finish. With competitive fixed-odds gambling being offered electronically, gamblers can sometimes create a Dutch book by selecting the best odds from different bookmakers, in effect undertaking an arbitrage operation. The bookmakers should react by adjusting the offered odds in the light of demand, so as to remove the potential profit. In Bayesian probability, Frank P. Ramsey and Bruno de Finetti required personal degrees of belief to be coherent so that a Dutch book could not be made against them, whichever way bets were made. Necessary and sufficient conditions for this are that their degrees of belief satisfy the axioms of probability (with only finite additivity). Economics In economics, the classic example of a situation in which a consumer X can be Dutch-booked is if they have intransitive preferences. Suppose that for this consumer, A is preferred to B, B is preferred to C, and C is preferred to A. Then suppose that someone else in the population, Y, has one of these goods. Without loss of generality, suppose Y has good A. Then Y can first sell A to X for B+ε; then sell B to X for C+ε; then sell C to X for A+ε, where ε is some small amount of the numeraire. After this sequence of trades, X has given 3·ε to Y for nothing in return. This method is a money pump, where Y exploits X using an arbitrage-opportunity by taking advantage