Total stakes received are £120.00 with a maximum payout of £100.00 irrespective of the result. A stake of £40.00 6-4 returns £100.00 (exactly) for a drawn match A stake of £20.00 4-1 returns £100.00 (exactly) for an away win Examining how he potentially achieves this:Ī stake of £60.00 4-6 returns £100.00 (exactly) for a home win. Thus, in an "ideal" situation, if the bookmaker accepts £120 in bets at his own quoted odds in the correct proportion, he will pay out only £100 (including returned stakes) no matter the actual outcome of the football match. The amount by which the actual 'book' exceeds 100% is known as the 'overround', : 96–104 : 126–130 'bookmaker margin' or the ' vigorish' or 'vig' and represents the bookmaker's expected profit. Home: 4-6 Draw: 6-4 Away: 4-1 4-6 corresponds to an implied probability of 3⁄ 5 (60%) 6-4 corresponds to an implied probability of 2⁄ 5 (40%) 4-1 corresponds to an implied probability of 1⁄ 5 (20%)īy adding these percentages together a 'book' of 120% is achieved. For the above example, the following odds are in the same proportion with regard to their implied probabilities (3:2:1): Consider the simplest model of reducing, which uses a proportional decreasing of odds. The bookmaker will reduce these odds to ensure a profit. These odds can be represented as implied probabilities (or percentages by multiplying by 100) as follows:Įvens (or 1-1) corresponds to an implied probability of 1⁄ 2 (50%) 2-1 corresponds to an implied probability of 1⁄ 3 (33 1⁄ 3%) 5-1 corresponds to an implied probability of 1⁄ 6 (16 2⁄ 3%)īy adding the percentages together a total 'book' of 100% is achieved (representing a fair book). In considering a football match (the event) that can be either a 'home win', 'draw' or 'away win' (the outcomes) then the following odds might be encountered to represent the true chance of each of the three outcomes: 6-4 corresponds to 4⁄ (6 + 4) = 4⁄ 10 = 0.4 (40%).Īn implied probability of x is represented by fractional odds of (1 − x)/ x, e.g. It is also important to understand the relationship between odds and implied probabilities:įractional odds of a − b (with corresponding decimal odds D) represent an implied probability of b⁄ ( a + b) = 1⁄ D, e.g. b = 1) can be obtained from decimal odds by a = D − 1. We can convert fractional to decimal odds by the formula D = ( b + a)⁄ b. Decimal odds are a single value, greater than 1, representing the amount to be paid out for each unit bet.įor example, a bet of £40 at 6 − 4 (fractional odds) will pay out £40 + £60 = £100. Fractional odds are written a − b ( a/ b or a to b), meaning a winning bettor will receive their money back plus a units for every b units they bet. It is important to understand the relationship between fractional and decimal odds. For the second method, see Parimutuel betting. This article explains the mathematics of making a book in the (simpler) case of the former event. 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. 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). 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. See Dutch book and coherence (philosophical gambling strategy). : 6 : 13, 36 Making a 'book' (and the notion of overround) Ī 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. The phrase originates from the practice of recording such wagers in a hard-bound ledger (the 'book') and gives the English language the term bookmaker for the person laying the bets and thus 'making the book'. In gambling parlance, making a book is the practice of laying bets on the various possible outcomes of a single event. Please help improve this article by introducing citations to additional sources.įind sources: "Mathematics of bookmaking" – news Relevant discussion may be found on the talk page. This article relies largely or entirely on a single source.
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