Just Bookies X Factor Odds

THE X FACTOR:CELEBRITY isn't even on our screens yet but the bookies are already casting their odds.

Find out here who they reckon is in it to win it...

The X Factor: Celebrity odds - who's favourite to win?

Awarded as 4 equal free bets total first deposit amount. Min odds 1/1, 3+ legs & expire in 7 days. Odds boosts: Odds boost crediting relies on marketing comms opt-in. Unlocked on deposit. Deposit £50-99 to get 2 x 25% boost/£100 to get 2 x 50% boost. Min odds 2/1, 2+ legs, expires 7 days, max stake £20. Winnings credited in cash. THE X FACTOR:CELEBRITY isn't even on our screens yet but the bookies are already casting their odds. Find out here who they reckon is in it to win it. The X Factor: Celebrity odds - who's favourite to win? Megan McKenna - 4/1. The former TOWIE star is hoping the. Bookmakers have started taking bets on the first cliche that will be used on this year's X Factor live shows. Fans of the ITV1 talent show can gamble on the first phrase that the judges use when.

Megan McKenna - 4/1

The former TOWIE star is hoping the programme will give her the big break she has dreamt of.

She released her debut album Story of Me in December 2018 and her debut single ‘High Heeled Shoes’ hit number on the iTunes chart in 2017.

Of starring in The X Factor: Celebrity, she said: 'This is the biggest opportunity I have ever had in my entire life.'

Megan McKenna, 26, launched her own ITVBe show There's Something About Megan, which followed her trip to Nashville in a bid to propel her music career.

Thom Evans, Ben Foden and Levi Davis (Try Star) - 11/2

Sports stars Thom Evans, Ben Foden and Levi Davis have formed a three-piece band for The X Factor: Celebrity.

The hunks have proven they are talentend on the pitch but they will be good enough to impress the judges?

Thom has some experience of being on stage as he was part of the band Twen2y4se7en, who supported Peter Andre and Westlife.

Olivia Olson - 7/1

Olivia Olson is best known for starring in Love Actually as Joanna but will try her hand at singing to impress the judges.

Since appearing in the classic rom-com she has gone on to star in the children's programme Phineas and Ferb, as well as Adventure Time.

But instead of lending her voice to animations, Olivia will take centre stage on the talent contest.

Kevin McHale - 15/2

Kevin McHale, who played Artie Abrams in Glee, has signed up to appear on the show.

However, he is nervous about taking to the stage and admitted: 'The X Factor terrifies me.'

The actor will be a familiar face for judge Nicole Scherzinger, as during his time with boyband NLT he opened for the Pussycat Dolls in 2007.

He released his own solo 12 years later titled Help Me Now.

Max and Harvey - 8/1

Max and Harvey, who shot to fame on the app musical.ly three years ago, will take to The X Factor: Celebrity stage this October.

The influencers have almost six million followers on the channel, and have since launched their own children's show Max and Harvey: Fomo.

But will they be the lucky pair who will land a lucrative record deal?

Jonny Labey - 9/1

The former EastEnders star played Paul Coker in the long-running BBC One show.

Jonny Labey has been tipped as 'one to watch' as he trades the streets of Walford in for The X Factor stage.

However, this will not be his first time on a talent competition as two years ago he took part in Dance Dance Dance.

A source told The Daily Star: 'Everyone working on the show is saying he’ll be one to watch.”

Wes Nelson, Samira Mighty, Eyal Booker and Zara McDermott (The Islanders) - 9/1

Love Island 2018 stars Wes Nelson, Samira Mighty, Eyal Booker and Zara McDermott will perform as a group on The X Factor: Celebrity.

Samira often shows off her vocal skills and incredible dancing ability on her Instagram account.

The foursome hope they change people's perception of them. Eyal said: 'We want to prove we're more than just reality stars.'

Sofia, Alondra, Laura, Natalie and Wendii (V5) - 12/1

Social media influencers Sofia, Alondra, Laura, Natalie and Wendii want to be the next big girl band.

The group have 11 million followers combined and will compete against another band, The Islanders.

The Latin American band said: 'We're dreaming big and we're working hard to get there.'

Ricki Lake -20/1

Ricki Lake is best known for hosting her own Emmy winning show in the US from 1993 to 2004.

However, this time she will not be taking to the stage to talk but to sing.

Speaking ahead of her appearance on the show, she said: 'It's time for me to prove I'm not just all talk.'

Victoria Ekanoye - 20/1

Victoria Ekanoye previously appeared in the ITV soap Coronation Street and portrayed Angie Appleton.

But she will be swapping acting for singing as she gives music a go this October.

Despite her success in the nation's much-loved programme, taking to the mic has always been her main passion.

Speaking about the upcoming venture, Victoria said: 'Singing will always be my first love.'

Brendan Cole and Jeremy Edwards - 22/1

Brendan Cole found fame on Strictly Come Dancing, while Jeremy Edwards has appeared on Hollyoaks and Holby City.

The dancing professional is excited to try a 'new challenge' following his departure from the BBC One dance competition.

A source previously told The Sun Online: 'For Brendan’s part, he’s excited about the prospect of a new challenge.

“It’s also not lost on him that appearing on a rival channel in a big prime time slot is a bit of a two fingers up at his old bosses at the BBC.”

Hayley Hasselhoff - 33/1

Hayley is the daughter of Baywatch actor David Hasselhoff and is hoping her appearance on Celebrity X Factor will be her 'big shot' at cracking the music industry.

Speaking in the trailer for the new series the model and actress said: 'This is my big shot.'

Hayley has forged an impressive career in the acting and modelling business, and has tried her hand at presenting, but now she is giving singing a go.

Jenny Ryan - 33/1

Jenny Ryan, who is best known as one of the quiz masters on the ITV gameshow The Chase.

Her intelligence has earned her the nickname The Vixen but can she be just as success in the talent contest?

She recently proved she was a force in the kitchen when she starred in Celebrity Masterchef.

Now, the mastermind is trying something a little outside of her comfort zone as she will belt out the ballads next month.

She said: 'Am I good enough? This is the ultimate test.'

Vinnie Jones - 33/1

Vinnie Jones, who is notorious for playing the hardman in films and TV shows, will take to the stage in this year's The X Factor: Celebrity.

The former footballer has previous singing experience and appeared on Top of the Pops in 2002.

Almost 20 years after appearing in the talent show he will show off his skills once again in a bid to be crowned champion.

Martin Bashir - 66/1

Martin Bashir is a journalist famed for his interview with the late Princess Diana 24 years ago.

Naturally, he says his involvement in the show is miles different to anything he has done before.

He said: 'This is outside of my comfort zone.'

What's the difference between the regular X Factor, Celebrity and All Stars version?

The regular format of the show would see ordinary contestants audition in front of three (or four) judges, hoping that they will advance to the next round, which was famously known as Bootcamp.

From there, the panel will collectively choose 24 acts - which are divided by six for each category - for the next round where judges find out which category they will mentor for the series.

Currently, it's not clear whether X Factor All Stars and Celebrity X Factor will stick to this particular format, particularly since neither will be auditioning for a place on the show.

Some fans seem to think that the new spin-offs will go straight to the live shows, subsequently leaving out the famous Bootcamp stage, judges' houses, among other things.

As more information develops, we'll be sure to keep you informed.

When does The X Factor: Celebrity start?

The official start date for The X Factor: Celebrity has been revealed to be October 12.

It has a timeslot set for 8.35pm on ITV, so set your reminder now!

The usual X Factor series would have already began by now - but has been replaced by the BGT spin-off show.

Find out more about The X Factor: Celebrity line-up here.

What is the winner’s prize?

Traditionally, the winner receives a £1 million record deal under Syco Music, while their winning single is usually known to land the Christmas Number 1 spot.

In recent years, however - and with the ratings decreasing – previous winners of the show have failed to land the Christmas top spot.

This begs the question of whether X Factor bosses will be looking to switch things up and offer more than just a recording contract in the forthcoming series.

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]

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+a⁄_b. 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 ​^b⁄_a+b=​¹⁄_D, e.g. 6-4 corresponds to ​⁴⁄₆₊₄ = ​⁴⁄₁₀ = 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, ​¹⁄_x - 1 to 1), and decimal odds of D=​¹⁄_x.

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 ​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%)

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):

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%)

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​²⁄₃ % 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 × (​⁶⁄₁₁ + ​⁶⁄₁₁) 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 ​¹⁄₄ 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 ​¹¹⁄₆. So the decimal odds of the double bet is ​¹¹⁄₆×​¹¹⁄₆=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 (O_D), expressed as a percentage, is calculated from the individual books B₁ and B₂, expressed as decimals, by O_D = B₁ × B₂ × 100 − 100.In the example we have O_D = 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, ..., B_i given in terms of decimals, is calculated by B₁ × B₂ × ... × B_i × 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

E.g. £100 each-way single at 11-4 ( ​¹⁄₅ 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 ( ​¹⁄₅ odds a place) and 5-4 ( ​¹⁄₄ odds a place); total staked = £200

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 ( ​¹⁄₄ odds a place), 11-8 ( ​¹⁄₅ odds), 5-4 ( ​¹⁄₄ odds), 1-2 (all up to win) and 3-1 ( ​¹⁄₅ 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

Yankee

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

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

Just Bookies X Factor Odds 2020

Ignoring any bonuses, a 50 pence each-way Lucky 63 (total stake £63) with 4 winners [2-1, 5-2, 7-2 (all ​¹⁄₅ odds a place) and 6-4 (​¹⁄₄ odds a place)] and a further placed horse [9-2 (​¹⁄₅ 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

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.

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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]

• OM (2 winners) = (2a − 1) + (2b − 1) = 2(a + b − 1)
• OM (1 winner) = a − 1

• 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)

• 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)

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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.

Vegas Bookies Odds

External links[edit]

Nfl Bookie Odds