A bookmaker strives to accept bets on the
outcome of an event in the right proportions in order to make a profit
regardless of which outcome prevails. See Dutch book and coherence
(philosophical gambling strategy). This is achieved primarily by adjusting what
are determined to be the true odds of the various outcomes of an event in a
downward fashion (i.e. the bookmaker will pay out using his actual odds, an
amount which is less than the true odds would have paid, thus ensuring a
profit).[3]
The odds quoted for a particular event may be fixed but are more likely to
fluctuate in order to take account of the size of wagers placed by the bettors
in the run-up to the actual event (e.g. a horse race). This article explains the
mathematics of making a book in the (simpler) case of the former event. For the
second method, see Parimutuel betting. (資料來源)
In settling winning bets either decimal odds are used or one is added
to the fractional odds: this is to include the stake in the return. The place
part of each-way bets is calculated separately from the win part; the method is
identical but the odds are reduced by whatever the place factor is for the
particular event (see Accumulator below for detailed example). All bets are
taken as ‘win’ bets unless ‘each-way’ is specifically stated. All show use of
fractional odds: replace (fractional odds + 1) by decimal odds if decimal odds
known. Non-runners are treated as winners with fractional odds of zero (decimal
odds of 1).
Fractions of pence in total winnings are invariably rounded down by bookmakers
to the nearest penny below. Calculations below for multiple-bet wagers result in
totals being shown for the separate categories (e.g. doubles, trebles etc.), and
therefore overall returns may not be exactly the same as the amount received
from using the computer software available to bookmakers to calculate total
winnings. (資料來源)
