How To Run A Gambling Book

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In gambling parlance, making a book is the practice of laying bets on the various possible outcomes of a single event. The term 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'.[1][2]

Setting up a Bookmaking Business. If you are debating whether to open your own bookie shop but worry about not making it in such a competitive industry, then keep reading to learn how to run a bookie operation. Insider Tips to Ensure Success. In addition to this record book, you should also have other documentation, such as:. Form W-2G, Certain Gambling Winnings. Form 5754, Statement by Person(s) Receiving Gambling Winnings. Wagering tickets. Canceled checks, substitute checks, credit records, bank statements/withdrawals. Statements of actual winnings or payment slips. 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).

Making a 'book' (and the notion of overround)[edit]

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.

It is important to understand the relationship between fractional and decimal odds. Fractional odds are those written a-b (a/b or a to b) mean a winning bettor will receive their money back plus a units for every b units they bet. Multiplying both a and b by the same number gives odds equivalent to a-b. Decimal odds are a single value, greater than 1, representing the amount to be paid out for each unit bet. For example, a bet of £40 at 6-4 (fractional odds) will pay out £40 + £60 = £100. The equivalent decimal odds are 2.5; £40 x 2.5 = £100. We can convert fractional to decimal odds by the formula D=​b+ab. Hence, fractional odds of a-1 (ie. b=1) can be obtained from decimal odds by a=D-1.

It is also important to understand the relationship between odds and implied probabilities:Fractional odds of a-b (with corresponding decimal odds D) represent an implied probability of ​ba+b=​1D, e.g. 6-4 corresponds to ​46+4 = ​410 = 0.4 (40%).An implied probability of x is represented by fractional odds of (1-x)/x, e.g. 0.2 is (1-0.2)/0.2 = 0.8/0.2 = 4/1 (4-1, 4 to 1) (equivalently, ​1x - 1 to 1), and decimal odds of D=​1x.

Example[edit]

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:

Home: Evens
Draw: 2-1
Away: 5-1

These odds can be represented as implied probabilities (or percentages by multiplying by 100) as follows:

Evens (or 1-1) corresponds to an implied probability of ​12 (50%)
2-1 corresponds to an implied probability of ​13 (33​13%)
5-1 corresponds to an implied probability of ​16 (16​23%)

By adding the percentages together a total 'book' of 100% is achieved (representing a fair book). The bookmaker, in his wish to avail himself of a profit, will invariably reduce these odds. Consider the simplest model of reducing, which uses a proportional decreasing of odds. For the above example, the following odds are in the same proportion with regard to their implied probabilities (3:2:1):

Book
Home: 4-6
Draw: 6-4
Away: 4-1
4-6 corresponds to an implied probability of ​35 (60%)
6-4 corresponds to an implied probability of ​25 (40%)
4-1 corresponds to an implied probability of ​15 (20%)

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',[4][5] 'bookmaker margin' [3] or the 'vigorish' or 'vig':[3] it represents the bookmaker's expected profit.[3] 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 what the actual outcome of the football match.Examining how he potentially achieves this:

A stake of £60.00 @ 4-6 returns £100.00 (exactly) for a home win.
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

Total stakes received — £120.00 and a maximum payout of £100.00 irrespective of the result. This £20.00 profit represents a 16​23 % profit on turnover (20.00/120.00).

In reality, bookmakers use models of reducing that are more complicated than the model of the 'ideal' situation.

Bookmaker margin in English football leagues[edit]

Bookmaker margin in English football leagues decreased in recent years.[6] The study of six large bookmakers between 2005/06 season and 2017/2018 season showed that average margin in Premier League decreased from 9% to 4%, in English Football League Championship, English Football League One, and English Football League Two from 11% to 6%, and in National League from 11% to 8%.

Overround on multiple bets[edit]

When a punter (bettor) combines more than one selection in, for example, a double, treble or accumulator then the effect of the overround in the book of each selection is compounded 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.

To explain the concept in the most basic of situations an example consisting of a double made up of selecting the winner from each of two tennis matches will be looked at:

In Match 1 between players A and B both players are assessed to have an equal chance of winning. The situation is the same in Match 2 between players C and D. In a fair book in each of their matches, i.e. each has a book of 100%, all players would be offered at odds of Evens (1-1). 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). This results in a book for each of the tennis matches of 109.09...%, calculated by 100 × (​611 + ​611) i.e. 9.09% overround.

There are four possible outcomes from combining the results from both matches: the winning pair of players could be AC, AD, BC or BD. As each of the outcomes for this example has been deliberately chosen to ensure that they are equally likely it can be deduced that the probability of each outcome occurring is ​14 or 0.25 and that the fractional odds against each one occurring is 3-1. A bet of 100 units (for simplicity) on any of the four combinations would produce a return of 100 × (3/1 + 1) = 400 units if successful, reflecting decimal odds of 4.0.

The decimal odds of a multiple bet is often calculated by multiplying the decimal odds of the individual bets, the idea being that if the events are independent then the implied probability should be the product of the implied probabilities of the individual bets. In the above case with fractional odds of 5-6, the decimal odds are ​116. So the decimal odds of the double bet is ​116×​116=1.833...×1.833...=3.3611..., or fractional odds of 2.3611-1. 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%. Thus the overround has slightly more than doubled by combining two single bets into a double.

In general, the combined overround on a double (OD), expressed as a percentage, is calculated from the individual books B1 and B2, expressed as decimals, by OD = B1 × B2 × 100 − 100.In the example we have OD = 1.0909 × 1.0909 × 100 − 100 = 19.01%.

This massive increase in potential profit for the bookmaker (19% instead of 9% on an event; in this case the double) is the main reason why bookmakers pay bonuses for the successful selection of winners in multiple bets: compare offering a 25% bonus on the correct choice of four winners from four selections in a Yankee, for example, when the potential overround on a simple fourfold of races with individual books of 120% is over 107% (a book of 207%). This is why bookmakers offer bets such as Lucky 15, Lucky 31 and Lucky 63; offering double the odds for one winner and increasing percentage bonuses for two, three and more winners.

In general, for any accumulator bet from two to i selections, the combined percentage overround of books of B1, B2, ..., Bi given in terms of decimals, is calculated by B1 × B2 × ... × Bi × 100 − 100. E.g. the previously mentioned fourfold consisting of individual books of 120% (1.20) gives an overround of 1.20 × 1.20 × 1.20 × 1.20 × 100 − 100 = 107.36%.

Settling winning bets[edit]

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.[7][8]

Singles[edit]

Win single

E.g. £100 single at 9-2; total staked = £100

Returns = £100 × (9/2 + 1) = £100 × 5.5 = £550

Each-way single

How to run a gambling books

E.g. £100 each-way single at 11-4 ( ​15 odds a place); total staked = £200

Returns (win) = £100 × (11/4 + 1) = £100 × 3.75 = £375
Returns (place) = £100 × (11/20 + 1) = £100 × 1.55 = £155
Total returns if selection wins = £530; if only placed = £155

Multiple bets[edit]

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). However, a more uncommon way of settling these type of bets is 'Each-Way all Each-Way' (known as 'Equally Divided', which must normally be requested as such on the betting slip) in which the returns from one selection in the accumulator are split to form an equal-stake each-way bet on the next selection and so on until all selections have been used.[9][10] The first example below shows the two different approaches to settling these types of bets.

Double[11][12]

E.g. £100 each-way double with winners at 2-1 ( ​15 odds a place) and 5-4 ( ​14 odds a place); total staked = £200

Returns (win double) = £100 × (2/1 + 1) × (5/4 + 1) = £675
Returns (place double) = £100 × (2/5 + 1) × (5/16 + 1) = £183.75
Total returns = £858.75
Returns (first selection) = £100 × (2/1 + 1) + £100 × (2/5 + 1) = £440 which is split equally to give a £220 each-way bet on the second selection)
Returns (second selection) = £220 × (5/4 + 1) + £220 × (5/16 + 1) = £783.75
Total returns = £783.85
How To Run A Gambling Book

Note: 'Win to Win, Place to Place' will always provide a greater return if all selections win, whereas 'Each-Way all Each-Way' provides greater compensation if one selection is a loser as each of the other winners provide a greater amount of place money for subsequent selections.

Treble[11][12]

E.g. £100 treble with winners at 3-1, 4-6 and 11-4; total staked = £100

Returns = £100 × (3/1 + 1) × (4/6 + 1) × (11/4 + 1) = £2500

Accumulator[11][12]

E.g. £100 each-way fivefold accumulator with winners at Evens ( ​14 odds a place), 11-8 ( ​15 odds), 5-4 ( ​14 odds), 1-2 (all up to win) and 3-1 ( ​15 odds); total staked = £200

Note: 'All up to win' means there are insufficient participants in the event for place odds to be given (e.g. 4 or fewer runners in a horse race). The only 'place' therefore is first place, for which the win odds are given.

Returns (win fivefold) = £100 × (1/1 + 1) × (11/8 + 1) × (5/4 + 1) × (1/2 + 1) × (3/1 + 1) = £6412.50
Returns (place fivefold) = £100 × (1/4 + 1) × (11/40 + 1) × (5/16 + 1) × (1/2 + 1) × (3/5 + 1) = £502.03
Total returns = £6914.53

Full-cover bets[edit]

Trixie

E.g. £10 Trixie with winners at 4-7, 2-1 and 11-10; total staked = £40
Returns (3 doubles) = £10 × [(4/7 + 1) × (2/1 + 1) + (4/7 + 1) × (11/10 + 1) + (2/1 + 1) × (11/10 + 1)] = £143.14
Returns (1 treble) = £10 × (4/7 + 1) × (2/1 + 1) × (11/10 + 1) = £99.00
Total returns = £242.14

Yankee

E.g. £10 Yankee with winners at 1-3, 5-2, 6-4 and Evens; total staked = £110
Returns (6 doubles) = £10 × [(1/3 + 1) × (5/2 + 1) + (1/3 + 1) × (6/4 + 1) + (1/3 + 1) × (1/1 + 1) + (5/2 + 1) × (6/4 + 1) + (5/2 + 1) × (1/1 + 1) + (6/4 + 1) × (1/1 + 1)] = £314.16
Returns (4 trebles) = £10 × [(1/3 + 1) × (5/2 + 1) × (6/4 + 1) + (1/3 + 1) × (5/2 + 1) × (1/1 + 1) + (1/3 + 1) × (6/4 + 1) × (1/1 + 1) + (5/2 + 1) × (6/4 + 1) × (1/1 + 1)] = £451.66
Returns (1 fourfold) = £10 × (1/3 + 1) × (5/2 + 1) × (6/4 + 1) × (1/1 + 1) = £233.33
Total returns = £999.15

Trixie, Yankee, Canadian, Heinz, Super Heinz and Goliath form a family of bets known as full cover bets which have all possible multiples present. Examples of winning Trixie and Yankee bets have been shown above. The other named bets are calculated in a similar way by looking at all the possible combinations of selections in their multiples. Note: A Double may be thought of as a full cover bet with only two selections.

Should a selection in one of these bets not win, then the remaining winners are treated as being a wholly successful bet on the next 'family member' down. For example, only two winners out of three in a Trixie means the bet is settled as a double; only four winners out of five in a Canadian means it is settled as a Yankee; only five winners out of eight in a Goliath means it is settled as a Canadian. The place part of each-way bets is calculated separately using reduced place odds. Thus, an each-way Super Heinz on seven horses with three winners and a further two placed horses is settled as a win Trixie and a place Canadian. Virtually all bookmakers use computer software for ease, speed and accuracy of calculation for the settling of multiples bets.

Full cover bets with singles[edit]

Patent

E.g. £2 Patent with winners at 4-6, 2-1 and 11-4; total staked = £14
Returns (3 singles) = £2 × [(4/6 + 1) + (2/1 + 1) + (11/4 + 1)] = £16.83
Returns (3 doubles) = £2 × [(4/6 + 1) × (2/1 + 1) + (4/6 + 1) × (11/4 + 1) + (2/1 + 1) × (11/4 + 1)] = £45.00
Returns (1 treble) = £2 × (4/6 + 1) × (2/1 + 1) × (11/4 + 1) = £37.50
Total returns = £99.33

Patent, Lucky 15, Lucky 31, Lucky 63 and higher Lucky bets form a family of bets known as full cover bets with singles which have all possible multiples present together with single bets on all selections. An examples of a winning Patent bet has been shown above. The other named bets are calculated in a similar way by looking at all the possible combinations of selections in their multiples and singles.

Should a selection in one of these bets not win, then the remaining winners are treated as being a wholly successful bet on the next 'family member' down. For example, only two winners out of three in a Patent means the bet is settled as a double and two singles; only three winners out of four in a Lucky 15 means it is settled as a Patent; only four winners out of six in a Lucky 63 means it is settled as a Lucky 15. The place part of each-way bets is calculated separately using reduced place odds. Thus, an each-way Lucky 63 on six horses with three winners and a further two placed horses is settled as a win Patent and a place Lucky 31.

Algebraic interpretation[edit]

Returns on any bet may be considered to be calculated as 'stake unit' × 'odds multiplier'. The overall 'odds multiplier' is a combined decimal odds value and is the result of all the individual bets that make up a full cover bet, including singles if needed. E.g. if a successful £10 Yankee returned £461.35 then the overall 'odds multiplier' (OM) is 46.135.

If a, b, c, d... represent the decimal odds, i.e. (fractional odds + 1), then an OM can be calculated algebraically by multiplying the expressions (a + 1), (b + 1), (c + 1)... etc. together in the required manner and subtracting 1. If required, (decimal odds + 1) may be replaced by (fractional odds + 2).[13][14]

Examples[edit]

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.Therefore to calculate the returns for a winning Patent it is just a case of multiplying (a + 1), (b + 1) and (c + 1) together and subtracting 1 to get the OM for the winning bet, i.e. OM = (a + 1)(b + 1)(c + 1) − 1. Now multiply by the unit stake to get the total return on the bet.[15][16]

E.g. The winning Patent described earlier can be more quickly and simply evaluated by the following:

Total returns = £2 × [(4/6 + 2) × (2/1 + 2) × (11/4 + 2) − 1] = £99.33

Ignoring any bonuses, a 50 pence each-way Lucky 63 (total stake £63) with 4 winners [2-1, 5-2, 7-2 (all ​15 odds a place) and 6-4 (​14 odds a place)] and a further placed horse [9-2 (​15 odds a place)] can be relatively easily calculated as follows:

Returns (win part) = 0.50 × [(2/1 + 2) × (5/2 + 2) × (7/2 + 2) × (6/4 + 2) − 1] = £172.75
or more simply as 0.50 × (4 × 4.5 × 5.5 × 3.5 − 1)
Returns (place part) = 0.50 × [(2/5 + 2) × (5/10 + 2) × (7/10 + 2) × (6/16 + 2) × (9/10 + 2) − 1] = £11.79
or more simply as 0.50 × (2.4 × 2.5 × 2.7 × 2.375 × 2.9 − 1)
Total returns = £184.54

For the family of full cover bets that do not include singles an adjustment to the calculation is made to leave just the doubles, trebles and accumulators. Thus, a previously described winning £10 Yankee with winners at 1-3, 5-2, 6-4 and Evens has returns calculated by:

£10 × [(1/3 + 2) × (5/2 + 2) × (6/4 + 2) × (1/1 + 2) − 1 − [(1/3 + 1) + (5/2 + 1) + (6/4 + 1) + (1/1 + 1)]] = £999.16

In effect, the bet has been calculated as a Lucky 15 minus the singles. Note that the total returns value of £999.16 is a penny higher than the previously calculated value as this quicker method only involves rounding the final answer, and not rounding at each individual step.

In algebraic terms the OM for the Yankee bet is given by:

OM = (a + 1)(b + 1)(c + 1)(d + 1) − 1 − (a + b + c + d)

In the days before software became available for use by bookmakers and those settling bets in Licensed Betting Offices (LBOs) this method was virtually de rigueur for saving time and avoiding the multiple repetitious calculations necessary in settling bets of the full cover type.

Settling other types of winning bets[edit]

Up and down

E.g. £20 Up and Down with winners at 7-2 and 15-8; total staked = £40
Returns (£20 single at 7-2 ATC £20 single at 15-8) = £20 × 7/2 + £20 × (15/8 + 1) = £127.50
Returns (£20 single at 15-8 ATC £20 single at 7-2) = £20 × 15/8 + £20 × (7/2 + 1) = £127.50
Total returns = £255.00
Note: This is the same as two £20 single bets at twice the odds; i.e. £20 singles at 7-1 and 15-4 and is the preferred manual way of calculating the bet.
E.g. £10 Up and Down with a winner at 5-1 and a loser; total staked = £20
Returns (£10 single at 5-1 ATC £10 single on 'loser') = £10 × 5/1 = £50
Note: This calculation of a bet where the stake is not returned is called 'receiving the odds to the stake' on the winner; in this case receiving the odds to £10 (on the 5-1 winner).

Round Robin

A Round Robin with 3 winners is calculated as a Trixie plus three Up and Down bets with 2 winners in each.

A Round Robin with 2 winners is calculated as a double plus one Up and Down bet with 2 winners plus two Up and Down bets with 1 winner in each.

A Round Robin with 1 winner is calculated as two Up and Down bets with one winner in each.

Flag and Super Flag bets may be calculated in a similar manner as above using the appropriate full cover bet (if sufficient winners) together with the required number of 2 winner- and 1 winner Up and Down bets.

Note: Expert bet settlers before the introduction of bet-settling software would have invariably used an algebraic-type method together with a simple calculator to determine the return on a bet (see below).

Algebraic interpretation[edit]

If a, b, c, d... represent the decimal odds, i.e. (fractional odds + 1), then an 'odds multiplier' OM can be calculated algebraically by multiplying the expressions (a + 1), (b + 1), (c + 1)... etc. together in the required manner and adding or subtracting additional components. If required, (decimal odds + 1) may be replaced by (fractional odds + 2).[13][14]

Examples[edit]

2 selections with decimal odds a and b in an Up and Down bet.
  • OM (2 winners) = (2a − 1) + (2b − 1) = 2(a + b − 1)
  • OM (1 winner) = a − 1
3 selections with decimal odds a, b and c in a Round Robin.
  • OM (3 winners) = (a + 1) × (b + 1) × (c + 1) − 1 − (a + b + c) + 2 × [(a + b − 1) + (a + c − 1) + (b + c − 1)] = (a + 1)(b + 1)(c + 1) + 3(a + b + c) − 7
  • OM (2 winners) = (a + 1) × (b + 1) − 1 − (a + b) + 2 × (a + b − 1) + (a − 1) + (b − 1) = (a + 1)(b + 1) + 2(a + b) − 5
    or more simply as OM = ab + 3(a + b) − 4
  • OM (1 winner) = 2 × (a − 1) = 2(a − 1)
4 selections with decimal odds a, b, c and d in a Flag.
  • OM (4 winners) = (a + 1) × (b + 1) × (c + 1) × (d + 1) − 1 − (a + b + c + d) + 2 × [(a + b − 1) + (a + c − 1) + (a + d − 1) + (b + c − 1) + (b + d − 1) + (c + d − 1)]
    = (a + 1)(b + 1)(c + 1)(d + 1) + 5(a + b + c + d) − 13
  • OM (3 winners) = (a + 1) × (b + 1) × (c + 1) − 1 − (a + b + c) + 2 × [(a + b − 1) + (a + c − 1) + (b + c − 1)] + (a − 1) + (b − 1) + (c − 1) = (a + 1)(b + 1)(c + 1) + 4(a + b + c) − 10
  • OM (2 winners) = (a + 1) × (b + 1) − 1 − (a + b) + 2 × (a + b − 1) + 2 × [(a − 1) + (b − 1)] = (a + 1)(b + 1) + 3(a + b) − 7
    or more simply as OM = ab + 4(a + b) − 6
  • OM (1 winner) = 3 × (a − 1) = 3(a − 1)

See also[edit]

Notes[edit]

  1. ^Sidney 1976, p.6
  2. ^Sidney 2003, p.13,36
  3. ^ abcdCortis, Dominic (2015). Expected Values and variance in bookmaker payouts: A Theoretical Approach towards setting limits on odds. Journal of Prediction Markets. 1. 9.
  4. ^Sidney 1976, p.96-104
  5. ^Sidney 2003, p.126-130
  6. ^Marek, Patrice (September 2018). 'Bookmakers' Efficiency in English Football Leagues'. Mathematical Methods in Economis - Conference Proceedings: 330–335.
  7. ^Sidney 1976, p.138-147
  8. ^Sidney 2003, p.163-177
  9. ^Sidney 1976, p.155-156
  10. ^Sidney 2003, p.170-171
  11. ^ abcSidney 1976, p.153-168
  12. ^ abcSidney 2003, p.169-177
  13. ^ abSidney 1976, p.166
  14. ^ abSidney 2003, p.169,176
  15. ^Sidney 1976, p.161
  16. ^Sidney 2003, p.176

References[edit]

  • Cortis, D. (2015). 'Expected Values and variance in bookmaker payouts: A Theoretical Approach towards setting limits on odds'. Journal of Prediction Markets. 1. 9.
  • Sidney, C (1976). The Art of Legging, Maxline International.
  • Sidney, C (2003). The Art of Legging: The History, Theory, and Practice of Bookmaking on the English Turf, 3rd edition, Rotex Publishing 2003, 224pp. ISBN978-1-872254-06-7. Definitive, and extensively revised and updated 3rd edition on the history, theory, practice and mathematics of bookmaking, plus the mathematics of off-course betting, bets and their computation and liability control.

Further reading[edit]

  • 'Finding an Edge', Ron Loftus, US-SC-North Charleston: Create Space., 2011, 144pp.
  • 'How to make a book', Phil Bull, London: Morrison & Gibb Ltd., 1948, 160pp.
  • 'The book on bookmaking', Ferde Rombola, California: Romford Press, 1984, 147pp. ISBN978-0-935536-37-9.
  • The Art of Bookmaking, Malcolm Boyle, High Stakes Publishing 2006.
  • Secrets of Successful Betting, Michael Adams, Raceform, 2002.
  • The Mathematics of Games and Gambling, Edward W. Packel, Mathematical Association of America, 2006.
  • The Mathematics of Gambling, Edward O. Thorp, L. Stuart, 1984.
  • 'Maximin Hedges', Jean-Claude Derderian, Mathematics Magazine, volume 51, number 3. (May, 1978), pages 188–192.
  • 'Carnap and de Finetti on Bets and the Probability of Singular Events: The Dutch Book Argument Reconsidered' Klaus Heilig, The British Journal for the Philosophy of Science, volume 29, number 4. (December, 1978), pages 325–346.
  • 'Tests of the Efficiency of Racetrack Betting Using Bookmaker Odds', Ron Bird, Michael McCrae, Management Science, volume 33, number 12 (December, 1987), pages 152–156.
  • 'Why is There a Favourite-Longshot Bias in British Racetrack Betting Markets', Leighton Vaughan Williams, David Paton. The Economic Journal, volume 107, number 440 (January, 1997), pages 150–158.
  • Optimal Determination of Bookmakers' Betting Odds: Theory and Tests, by John Fingleton and Patrick Waldron, Trinity Economic Paper Series, Technical Paper No. 96/9, Trinity College, University of Dublin, 1999.
  • 'Odds That Don't Add Up!', Mike Fletcher, Teaching Mathematics and its Applications, 1994, volume 13, number 4, pages 145–147.
  • 'Information, Prices and Efficiency in a Fixed-Odds Betting Market', Peter F. Pope, David A. Peel, Economica, New Series, volume 56, number 223, (August, 1989), pages 323–341.
  • 'A Mathematical Perspective on Gambling', Molly Maxwell, MIT Undergraduate Journal of Mathematics, volume 1, (1999), pages 123–132.
  • 'Probability Guide to Gambling: The Mathematics of dice, slots, roulette, baccarat, blackjack, poker, lottery and sport bets', Catalin Barboianu, Infarom, 2006, 316pp. ISBN973-87520-3-5.

External links[edit]

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The amount of material written about sports betting has grown exponentially since the dawn of eBooks. My local Barnes & Noble has an entire row dedicated to sports betting titles, with a further 99 books available through their online store. If you add the amount of free advice for sports bettors in the form of poorly-written Web content, you've got a deluge of noise that's impossible to wade through.

In some ways, I'm a really lucky guy. I've worked in libraries and bookshops throughout my years of recreational sports betting. I've managed to put together quite a library, including a couple of first-edition gambling tomes. Having collected and read just about every major sports betting book to hit the market in the past few decades, I consider myself an expert on the subject.

Here are the 7 best books for sports bettors. If you aren't into the idea of collecting a library of these titles, you can read just these seven titles and get a solid education in sports betting.

1. Sharp Sports Betting by Stanford Wong

Sharp Sports Betting is a classic, a must-read for anyone even remotely serious about wagering on sports. For some bettors, this book is the Bible. It's long, and you'll need to wade through a few pages of the basics (definitions of various bets, a glossary, etc.), but it's easy to skim to the meatier chapters later on. Sharp Sports Betting focuses almost exclusively on NFL football, though the lessons apply to a variety of different markets.

Stanford Wong is a pen name, by the way – the real author is John Ferguson, famous for writing the book Professional Blackjack. The name Stanford Wong was chosen as a portmanteau of the author's alumni and a random Asian last name to give the whole thing 'mystique.'

The original version of this text appeared in 2001, but don't worry about buying the latest and greatest edition. It's had few revisions. Some information is a little outdated – ironically, most books have changed some of the ways they represent odds to prevent the techniques described in Stanford Wong's book.

2. The Man with the $100,000 Breasts: and Other Gambling Stories by Michael Konik

Most of the books on this list are educational, and (I'll admit it) a little dry. Michael Konik's book is not that. The purpose of this book is to give you a glimpse into the lives of degenerate gamblers, high rollers, and sports betting hustlers. Endless impossible-to-believe true stories fill the pages of this book, including plenty of highly-profitable gamblers and the tactics they used to win.

Yes, this book is a bit of a love story to gambling. It highlights some of the glamorous and exciting aspects of the hobby. But Konik also gives plenty of advice – on how to get more comps, how to identify long-odds casino games, and other ways to increase your edge against the book or the house legally.

Here's a quote from a review that I just read off the flap – 'The people in The Man With the $100,000 Breasts operate in a hairier zone of human behavior, where desire and risk are intertwined and the normal social customs don't apply. Wickedly fascinating.' If that doesn't make you want to read the book, you probably won't like any of the titles in my library...

3. Gambling Wizards: Conversations with the World's Greatest Gamblers by Richard Munchkin

Richard Munchkin is an interesting character. He put himself through college playing backgammon for money. He's worked as a blackjack dealer, Vegas pit boss, and TV and film producer. His greatest contribution is Gambling Wizards.

The interviewees in this book include:

  • the one-time resident backgammon player at the Playboy Mansion
  • a two-time WSOP champion
  • a wildly-successful race bettor

But it's not just interviews – the conversations go into great detail, asking questions like: 'If your son came to you and said he wanted to be a professional gambler, what would you say?' It's a great read for gamblers and non-gamblers alike. The candid conversations in this book are educational and entertaining.

4. The Signal & the Noise by Nate Silver

This book is about much more than betting. Written by the famed numbers-junkie behind the popular blog FiveThirtyEight, The Signal & the Noise is all about making predictions. Sometimes lapsing into complex math, but always quick with a real-world example, Silver's book is a great companion to an education in sports markets.

This works well for Silver, since he's the modern poster-child of predictive ability. You may know him as the pundit who predicted the correct result of every state in the 2012 Presidential Election. You may not know that Nate Silver came to prediction markets through the world of baseball analytics and Sabermetrics.

This text is basically an introduction to the concepts of probability and risk. Silver's constant point is that, despite limitless raw data, most of our predictive abilities are very limited. He begins by analyzing why we're so bad at predicting things like earthquakes, forest fires, and financial markets.

Sure, this is a high-concept book, and it doesn't always relate directly to wagering on sports. Where this book reveals its genius is later, during your extended education on the hobby. Silver's lessons on how weather forecasters achieve their relatively-high rates of predictive success aren't immediately applicable, but you won't find a better education in prediction.

5. Mathletics by Wayne L. Winston

Gambling Books Amazon

Wayne L. Winston is an MIT-educated operations research specialist (and professor of business) who just happened to create one of the most amazing little sports betting texts I've ever come across.

Mathletics is an entertaining AND educational read. Winston uses mathematics that any of us can understand to explain and offer analysis on a number of statistical and probability-related questions that sports bettors may have. Winston looks at professional sports – baseball, basketball, and football – to explain difficult math concepts.

Winston's book goes into great detail on topics like how MLB teams evaluate hitters and predict success, the question of whether teams will pass or run on first down in different situations, and the influence of money on pro sports and sports betting.

My favorite parts of Mathletics have little to do with betting. Winston's book teaches about the frequency and effectiveness of bunts, the effect of overtime on different NFL teams, and general stats and numerical analysis behind several recent pro sport championships. If you're a novice sports bettor or a seasoned veteran, you'll appreciate the statistics and probability details, as well as insight into several long-held beliefs and clichés about sports, and the reality that undermines them.

6. Lay the Favorite by Beth Raymer

The author, who spent years studying the gambling trade in Central America, wrote this book after spending four years as a pay and collect agent for a bookie. In this (maybe a bit too honest) memoir, you get to peek into the sports betting underworld. If you are looking for a good read, a book about the hustlers, idiots, criminals, and crooks that populate the dark side of sports betting, this is your text.

How To Run A Gambling Book

Lay the Favorite also has the distinction of being the only book on this list that was also made into a movie. Raymer's book was released as a film starring Bruce Willis, Catherine Zeta-Jones, and Vince Vaughan in 2012.

No, you won't learn how to improve your ROI or find new trends in MLB starting pitching, but you will have a heck of a time reading about the seedier aspects of the illegal bookmaking trade. It's a great beach book, and hey, we can't study all the time, can we?

7. Fixed-Odds Sports Betting by Joseph Buchdal

How To Run A Betting Book

The sub-title of this book is: 'Statistical Forecasting & Risk Management.' That should give you a sense of the serious tone throughout. Joseph Buchdal has written a textbook for serious sports bettors, not a light read at all. This is another 'must-own' for anyone serious about placing sports wagers.

Why is Fixed-Odds Sports Betting so important?

It was the first text to really explain concepts like the over-round, it includes details on the Asian handicap that (for years) you couldn't find anywhere else, a guide to staking, bankroll-building tips, and a ton of other topics that few writers have covered with as much clarity.

If you're looking to seriously analyze your betting system, increase the power of your bankroll, or learn to find value in just about any sports market, you should own a copy of Buchdal's book and be reading it for a few minutes every day. Along with the Stanford Wong text above, and a couple of other titles on this list, Fixed-Odds Sports Betting is the anchor of my essential sports betting books list.

Conclusion

Thankfully, sports bettors are literate folk. When you want an infusion of strategy, a distraction from your hectic work day, or strategy tip that put more money in your pocket, you can count on any of dozens of top-notch sports betting titles. The list above is by no means complete – but if you were to read these seven books in the next year, you'd be a much smarter (if not necessarily more profitable) bettor.