Dutch book

In gambling a Dutch book or lock is a set of odds and bets which guarantees a profit, no matter what the outcome of the gamble. It is associated with probabilities implied by the odds not being coherent.

Gambling

In one example, a bookmaker has offered odds and attracted bets that make the result irrelevant; in this case the implied probabilities will add up to a number greater than 1.

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In this case, whichever horse wins, the bookmaker will pay out 200 (including returning the winning stake) and so make a profit of 10.

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If for some reason Horse 4 was withdrawn and the bookmaker was foolish enough not to adjust the other odds, the implied probabilities would add up to 0.95 and a gambler could lock in a profit of 10, by betting 100, 50 and 40 on the remaining three horses respectively.

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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 by 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.

Related Topics:
Fixed-odds gambling - Arbitrage

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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.

Related Topics:
Bayesian probability - Frank P. Ramsey - Bruno de Finetti - Coherent - Necessary and sufficient conditions - Axioms of probability

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