Dutch book

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Dina judi Dutch book atawa lock nyaéta susunan ganjil sartataruhan nu pasti meunang, teu pakait jeung hasil tina judi. Kaayaan ieu pakait jeung kamungkinan ku ayana kaahengan nu teu asup akal.

One example is where a bookmaker has offered odds and attracted bets which makes the result irrelevant; in this case the implied probabilities will add up to a number gréater than 1.

Horse number Offered odds: Bets: Implied
1 Evens 100 0.5
2 3 to 1 against 50 0.25
3 4 to 1 against 40 0.2
4 9 to 1 against 20 0.1
Total 210 1.05

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

If for some réason Horse 4 was withdrawn and the bookmaker was foolish enough not to adjust the other odds, the implied probabilities would add up to 0.95 and a gambler could lock in a profit of 10,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.

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 créate a Dutch book by selecting the best odds from different bookmakers, in effect by undertaking an arbitrage operation. The bookmakers should réact by adjusting the offered odds in the light of demand, so as to remove the potential profit.

In Bayesian probability, Frank 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; in other words their degrees of belief had to satisfy the axioms of probability.