In gambling parlance, making a book is the practice of laying bets on the various possible outcomes of a single event.
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'.
This article explains the mathematics of making a book in the (simpler) case of the former event.
Decimal odds are a single value, greater than 1, representing the amount to be paid out for each unit bet.
For the above example, the following odds are in the same proportion with regard to their implied probabilities (3:2:1): By adding these percentages together a 'book' of 120% is achieved.
The amount by which the actual 'book' exceeds 100% is known as the 'overround',[1]: 96–104 [2]: 126–130 'bookmaker margin'[4] or the 'vigorish' or 'vig'[4] and represents the bookmaker's expected profit.
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.
Examining how he potentially achieves this: Total stakes received are £120.00 with a maximum payout of £100.00 irrespective of the result.
Bookmaker margin in English football leagues decreased in recent years.
This is to the detriment of the punter in terms of the financial return compared to the true odds of all of the selections winning and thus resulting in a successful bet.
However, a bookmaker would probably offer odds of 5-6 (for example) on each of the two possible outcomes in each event (each tennis match).
There are four possible outcomes from combining the results from both matches: the winning pair of players could be AC, AD, BC or BD.
This represents an implied probability of 29.752% (1/3.3611) and multiplying by 4 (for each of the four equally likely combinations of outcomes) gives a total book of 119.01%.
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.
[1]: 138–147 [2]: 163–177 Win single E.g. £100 single at 9 − 2; total staked = £100 Each-way single E.g. £100 each-way single at 11 − 4 ( 1⁄5 odds a place); total staked = £200 Each-way multiple bets are usually settled using a default "Win to Win, Place to Place" method, meaning that the bet consists of a win accumulator and a separate place accumulator (Note: a double or treble is an accumulator with 2 or 3 selections respectively).
Virtually all bookmakers use computer software for ease, speed and accuracy of calculation for the settling of multiples bets.
The other named bets are calculated in a similar way by looking at all the possible combinations of selections in their multiples and singles.
[1]: 166 [2]: 169, 176 3 selections with decimal odds a, b and c. Expanding (a + 1)(b + 1)(c + 1) algebraically gives abc + ab + ac + bc + a + b + c + 1.
This is equivalent to the OM for a Patent (treble: abc; doubles: ab, ac and bc; singles: a, b and c) plus 1.