# Settling Complicated Bets with a Calculator

Created | Updated Jun 1, 2009

Bet-settling is a disappearing art-form, or more accurately, a disappearing science. The majority of high street bookmakers now use computer systems to settle bets, but these are only as reliable as the data fed into them. How do you know when your bet has been incorrectly settled? The answer is to learn to settle bets yourself...

### Settling

To settle a bet means to calculate how much a winning bet is worth. People who work in betting shops or for bookmakers in the UK who do this are called 'Settlers'.

Most bet-settling today is done by automated computer systems, which are far faster, and more accurate than any human settler. However, if incorrect data is fed into a computer system, incorrect results will follow, so it may help if you know how much your bet is worth, so you can spot mistakes when they happen.

The objective of this entry is to teach you the basics of settling common bets placed in UK betting shops in the quickest, most accurate way.

Often speed and accuracy go hand in hand. The fewer calculations you have to do, the less likely it is that an error will creep in. Speed is also of the essence, as a typical settler may have to deal with up to a thousand individual bets on a typical day, sometimes many more^{1}.

### Marking-up

Bet-settlers have a standard notation that they use when writing results onto a betting slip before actually settling it. Most marking-up is done in red ink, as betting shop customers do not write in red (or rather, those that do are moaned at), and therefore it's obvious who has written what.

Where a selection on a betting slip loses, a horizontal line is drawn through the selection.

Where a selection on a betting slip wins, the odds at which it wins are written over, or to the side of the selection. It's worth noting at this stage that bookmakers rarely write the '/1' in odds such as '3/1', instead just writing '3'. Also the notation '0/3' is common shorthand for '100/30'

Where a selection is placed in an each-way bet, for example, coming second, the odds are written over or to the side of the selection, and circled. In this text, circled odds will be represented using square brackets, such as [11/2]

Also, for each-way bets, if the each-way odds are a quarter of the winning odds, an asterisk or cross is written next to the circle. For each-way bets where the place odds are the same as the winning odds, the letter 'A' is written after the odds

It's also common practice to cross out the time of a selection as you mark-up the bet, whether or not the selection is a winner. This makes it easier to spot the remaining selections, and speeds up the whole process

Examples:

11/4 | A selection that has won at odds of 11/4 |

[8]x | A selection that has been placed, at quarter odds, at odds of 8/1 |

5/2A | A selection that has won, in an each-way bet with four or fewer runners |

While marking up, the settler will look out for losing bets, and remove them from the pile of bets to be settled. For instance, a four-horse accumulator can be marked as a losing bet the moment any one of the four selections has lost.

Once all selections in a bet have been marked up, the bet is ready for settling. Check the batteries in your calculator, and follow me...

### Odds and fractions

Betting odds in the UK are usually expressed in terms of fractions, for example, 3/1. This fraction represents the fraction of your stake that you will win if your selection wins. 3/1 is 'three to one', meaning that for every one stake, you will win three stakes. Because you also get your stake back, the total amount returned will be four stakes in this example case.

In another example, 7/4 (seven to four) can be thought of as being seven quarters. If you place a £1 bet at 7/4, you have placed four 25p stakes, and will win seven 25p stakes (£1.75p) plus your stake back, leaving you with a total of £2.75p

Because calculators work in decimal, these odds need to be converted to decimal. (There are some calculators which handle real fractions, but these are generally scientific calculators, the use of which is a really bad idea, as is explained below). These decimal equivalents, known to many settlers as 'basic factors' are often learned by rote, but can be calculated easily enough if you forget them. The basic factor is total winnings from that selection for a one pound win bet, and is calculated as the fraction value plus one. For instance, 7/4, or seven quarters, is 1.75. The basic factor for 7/4 is 1.75 + 1 = 2.75.

Here are some basic factors for common prices:

Odds | Factor | Odds | Factor |

Evens | 2.0000 | 11/10 | 2.1000 |

4/6 | 1.6667 | 6/4 | 2.5000 |

1/2 | 1.5000 | 2/1 | 3.0000 |

2/5 | 1.4000 | 5/2 | 3.5000 |

1/3 | 1.3333 | 3/1 | 4.0000 |

1/4 | 1.2500 | 4/1 | 5.0000 |

Note: In the text below, All basic factors are quoted with four decimal digits even where those digits are redundant. This is mainly so that readers can tell basic factors from amounts of money and other values used in calculations. Professional settlers tend to use five or more decimal places, especially for some of the more irrational numbers, like 2/7, which is 1.285714, plus an infinite number of decimal places.

Another interesting, but irrelevant point, is that settlers based in South Africa do not generally deal with large irrational numbers. South African bookmakers use a set of prices that generate basic factors which generally have no more than two decimal places. Where a UK bookmaker might use 100/30 (or 4.3333) the South African bookmaker might use 33/10 (or 4.3000). Customers watching South African racing in a UK betting shop are sometimes confused by the 'weird' prices seen on betting shop monitors, despite the fact that the maths is much easier. This difference is largely due to the use of 'old money' (pounds, shillings, and pence) prior to decimalisation.

### Betting Each Way

Each-way bets are really two bets. The first bet is a standard win bet, and the second bet is for that selection to be 'placed'. For instance, in an eight-runner race, a runner is placed if it finishes anywhere in the first three.

The rules for determining the odds you get for placed runners are as follows:

Number of runners | Handicap Race | Non-Handicap Race |

Less than 5 | No place betting. All money goes to win only | |

5,6 or 7 | 1/4 of the odds for the first two to finish | |

8 to 11 | 1/5 of the odds for the first three to finish | |

12 to 15 | 1/4 odds, first three | 1/5 odds, first three |

16 or more | 1/4 odds, first four | 1/5 odds, first three |

### Calculators

Calculators come in various shapes and sizes, and at least two common types. The best shape calculator to use for settling bets is whatever shape suits the settler's hand personally. The best size to select is 'as big as possible' so that the operator can hit keys rapidly and accurately without fumbling onto other keys.

The two types of calculators that can be bought from shops are scientific, and non-scientific. For settling bets, you need a non-scientific calculator. The difference is in the way the calculator handles arithmetical precedence. The rules of arithmetic state that in the statement 2 + 3 x 4, the correct method is to multiply first, and add second. Scientific calculators follow this rule, non-scientific calculators do not. All the rules laid out below assume a non-scientific calculator. The vast majority of large desk calculators are non-scientific, and so settlers are trained to use non-scientific calculators. If a calculator that supports proper arithmetic logic rules is used by a settler, the settler will soon be yelled at by their manager for settling bets completely inaccurately.

To find out what type of calculator you have, try the following:

**[2] [+] [3] [X] [4] [=]**

If the answer you reached was 20, you have a non-scientific calculator. If you got 14, you have a scientific calculator and will run into problems.

Another way to spot a scientific calculator is to count the number of keys other than numbers, [+], [-], [X], [/], [=], [C], and memory keys. If you have at least another 15 keys marked with such obscure functions as (r->p), sin, cos, x^{3}, log, and hyp, you have a scientific calculator, and probably have some difficulty hitting only one key at a time due to the small key size.

### Settling Singles

A single bet is a bet that a particular runner will win a race. This is by far the most common bet taken by a bookmaker. To settle a single bet, you simply take the basic factor, and multiply by the stake. For example, £5.00 win at 3/1 is calculated as 5 x 4.0000 = £20.00

### Settling Each-way singles

Each-way singles are only slightly more complicated then win singles. First, the settler calculates the each-way basic factor by multiplying the fractional odds by the 'place factor' from the each-way table above, and adds on either one or two, depending if the selection was placed, or actually won.

For instance, in an eight runner race, the second placed horse was 15/1. The win part of an each-way bet on this horse is a loser, and the place part is calculated as 15/1 multiplied by the place factor (1/5 for 8-runner races), plus one (to include the place part of the bet's stake), and works out as 15 / 1 x 0.2 + 1 = 4.0000

If the same horse won, the each-way factor would be calculated as 15/1 multiplied by the win-and-place factor (the place factor, plus one, in this case 1.2), plus two (to include both stakes) as 15/1 x 1.2 + 2 = 20.00. This new each-way basic factor is then multiplied by the each-way stake to get a settlement figure.

Some examples:

£2 each-way, 14/1 winner in a 12-runner handicap - 14/1 x 1.25 + 2 = 19.5 x £2 = £39.00

£1.40 each-way, 8/1 second place in a 9-runner race - 8/1 x 0.2 + 1 = 2.6 x £1.40 = £3.64

### Settling Win Doubles, Trebles, and Accumulators

A double is a bet that two selections will win their respective races, and the winnings from the first runner are re-invested on the second. A treble is the same thing, but with three selections. An accumulator is a generic term that refers to any number of selections, where the money from each runner is re-invested on the next runner.

Settling simple multiple bets, such as doubles, trebles and accumulators is done by multiplying together the basic factors of each of the selections, and then multiplying by the stake

For example:

£10 double, two winners at 11/8 and 4/1. - 2.3750 x 5.0000 = 11.875 x £10 = £118.75

£2.50 treble, three winners at 2/1, 3/1 and 4/1. - 3.0000 x 4.0000 x 5.0000 = 60. x £2.50 = £150.00

### Settling Each-way Doubles, Trebles, and Accumulators

Each-way accumulators are settled as two bets. A win accumulator, and a place accumulator. The win accumulator is settled in exactly the same way as above, and the place accumulator is similarly settled, but using the place odds instead of the win odds.

Remember, place odds are calculated from the win odds by multiplying by the place factor, typically a quarter or a fifth. So the place odds for 11/2 at a quarter of the odds would be 11/8, which yields a basic factor of 2.375.

Where an each-way accumulator contains one or more selection that is only placed, then the win part of that accumulator is a loser, and you only have to calculate the place part

Example: A £2.50 each-way treble, with one winner at 5/1, and two placed runners at 13/2 and 8/1. In this example, all place odds are 1/5.

The each-way odds are therefore 5/5, 13/10, and 8/5, which yield basic factors of 2.0000, 2.3000, and 2.6000. The calculation is therefore 2.0000 x 2.3000 x 2.6000 = 11.9600 x £2.50 = £29.90

### Settling Full-cover Multiple Bets

Full cover bets involve multiple selections in different events, with all possible combinations of doubles, trebles, four-folds (four selection accumulators), five-folds, and so on, up to and including an accumulator on all of the selections. All of the individual bets are at the same stake.

There are two main groups of full-cover multiples; The difference being whether or not they contain singles. For a list of common multiple bets, see the entry on accumulators and multiple bets. The most common types of these bets are the Lucky 15, and the Yankee. Both of these bets have four selections, the difference being that the Lucky 15 includes singles, and the Yankee does not.

Many people attempt to settle these bets by settling each and every bet included within them. This is a futile move, as a bet with as few as six selections can have as many as 63 possible bet combinations. So, the settler needs a shortcut. Remember all those years ago, during mathematics classes, where the teacher droned on for hours about multiplying out equations like (A + 1)x(B + 1)x(C + 1) ? The solution to this type of bet lies within that method.

If you multiply out (A + 1)x(B + 1)x(C + 1) you get ABC + AB + AC + BC + A + B + C + 1. This just happens to be nearly the combination of bets in a multiple bet, with singles, but with an extra '+1' on the end. So all the settler has to do to settle these bets is take all of the winning entries, calculate the basic factors as above, add one to each of those basic factors, multiply them all together, and subtract the extra one that this process introduces. The result, when multiplied by the stake unit is the correct settlement for the bet.

Example: A £2.00 win Lucky 15 with four winners, at 8/1, 5/1, 13/2, and 7/1. The basic factors are 9.0000, 6.0000, 7.5000, and 8.0000. Add one to each of these (10.0000, 7.0000, 8.5000, and 9.0000), and multiply the results together and you get 5335. Subtract the odd one, and you have 5334. Multiply by the stake unit, and you have a quite impressive £10,668.00, plus whatever bonuses your bookmaker chooses to offer on that type of bet.

Multiple bets which do not include singles are settled in a similar way, differing only in that the settler has to deduct the singles from the figure. If the bet above had been a Yankee, the settler would have deducted the original basic factors (9.000, 6.0000, 7.5000, and 8.0000) before multiplying by the stake.

Each-way bets of either type are settled in a similar way, but in two parts. The win part, and the place part, using the place basic factors (the original fractional price divided by four or five as appropriate, plus one).

### Settling Doubles from Any Number of Selections

Another common bet is doubles from some number of selections. This is common in greyhound racing, where one of the most popular bets placed in UK betting shops is the greyhound forecast double bet.

It should be said at this point that forecast returns, as well as tricast, and all types of tote returns, are always expressed in decimal, and are used as basic factors. You don't add one to forecast returns to make basic factors, the forecast return already includes it.

To settle 'doubles from *N* selections', think of each double as the area of a rectangle, where the two basic factors which are used to calculate that double are the lengths of it's sides. Expanding on that idea, think of what happens when you add all of the basic factors together, and make a square, the size of which is the sum of all of those factors. If you were to draw a grid separating all of the individual doubles, you might notice that the area of this square includes each of our rectangular doubles exactly twice, and it also includes a diagonal line of squares, each of which represent the result of a basic factor being multiplied by itself

What use is this? Simple. All the settlers have to do is work out the total area, subtract each of the squares representing the unwanted result of one factor being multiplied by itself, and divide what is left by two. The net result is the answer that the settler was looking for.

Example:

Ten races generate 45 doubles, which the customer has bet on in units of 5p. Out of these ten races, there are five winning forecasts. The winning forecasts are 14.00, 18.30, 19.45, 72.60, and 9.26. The sum of all of these forecasts is 133.61. Multiply that figure by itself (square it), and you get 17851.6321. Store that figure in the calculators memory by pressing [M+]. Subtract each basic factor squared from that figure, by entering that figure, and pressing [X] [M-] (times, memory subtract). Retrieve the contents of memory, which should be 11585.9320. Divide that figure by two, and multiply the result (5792.966) by the unit stake in pounds, £0.05 to get the total return, which is £289.65p (rounded up a little).

### Settling sequential Multiples

Sequential multiples are bets which involve singles, doubles, trebles, four-folds, and so forth, but only on adjacent selections. These bets are known variously as *fivespot, pontoon* and *magnificent seven*

Settling these bets with a calculator is simple. Ensure that there is nothing in the calculator memory by pressing [MC], and then proceed as follows:

- Enter the basic factor of the first winning selection
- Press [M+]
- If there are no more winning selections after this one, Goto 7.
- If the next selection is a winner, hit [+] [1] [X]
- Enter the basic factor of the next winner
- Goto 2.
- Press [MR] and multiply by the stake unit

Example:

A 50p pontoon bet has four winners, all of which are mysteriously 4/1, so the basic factor is 5.0000 for each of the selection. Selection number 2 is a losing selection. The sequence of button presses on the calculator is therefore:

[MC]

[5] [M+]

[5] [M+] [+] [1] [X]

[5] [M+] [+] [1] [X]

[5] [M+]

[MR] [X] [0] [.] [5] [0] [=]

which gives an answer of 487.50

### Settling Any-to-come Bets

Any-to-come bets, also known as 'if cash' bets are conditional bets. In their simplest form, a bet is written as '£5 win A, any-to-come £5 win B'. This means that if A wins, five pounds of the winnings are taken to fund a win single on B. If A doesn't win, then there is no bet on B.

Any-to-come bets were commonplace prior to the introduction of licensed betting shops in 1968, where customers had to write all of their bets for the day and post them to a bookmaker, and had to make up their mind how to spend their winnings in advance.

Another common variation, and the basis for most of the other common bets involving ATC (any-to-come) bets is the 'Single Stakes About', or 'SSA' bet. The SSA bet is also known by the names 'Up and Down', 'Vice Versa' and 'Twist' depending on the part of the country that you are from. A £1 SSA bet on A and B could be written out longhand as '£1 win A, if cash £1 win B' and '£1 win B, if cash £1 win A'.

To settle an SSA bet with only one winner, take the basic factor for that winner, subtract one, and multiply by the stake. One is subtracted because the second part of the bet is a loser, and that one unit represents the stake that goes over to the other selection. With two winners, take the basic factor of both selections, add them together, multiply by two, and subtract two (to remove the two stakes that cross over to the other selection), and multiply by the stake unit

The most common bet that involves SSA bets is the Round Robin. This bet involves three selections in different races, and is made up of a trixie (doubles and a treble = 4 bets) and three SSA bets (accounting for six stakes, ten bets in total), so a £1 round robin will cost you £10.

To settle a round robin with only one winner, take it's basic factor, multiply by two, subtract two, and multiply by the unit stake. With two winners, there is a winning double settled in the usual manner, and a four win singles, from which four stakes must be deducted. If the basic factors are A and B, the settlement is AxB + A+A + B+B - 4^{2}.

With three winners, there is a winning treble and three winning doubles, settled in the usual way as detailed above, plus twelve win singles, from which six ATC stakes must be deducted.

Variations on the Round Robin are the Flag (which is the same principle, but with four selections, 23 bets in total) and the Super Flag (with five selections, 46 bets). The general rule for settling a bet of this type with N runners with W winners is to take all of the basic factors, add them together, multiply by W, subtract Wx(N-1) stakes, and multiply by the stake. This produces a figure for the ATC part of the bet only, and the settler still needs to handle the doubles, trebles, and accumulators using the previously described 'additional point' method.

It is possible that in an ATC bet, that the first selection does not return sufficient cash to satisfy the stake on the second selection. For example, in the bet '£1 win A, any-to-come £5 win B', if A wins at 9/1, £5 is taken from the £10 returns to place a bet on B. If A wins at 3/1, there is only £4 to take, so the second part of the bet is understaked.

### Any Other Business

There are a few other bets which are not covered above, all of which can be explained to you by your local neighbourhood bookmaker. Most of these bets are merely variations, or combinations of the basic bets above.

### Dead Heats, Rule Four, and Other Complications

Various things can happen in a race result which complicate the settlement of the bet. In the majority of cases these simply adjust the basic factors used to calculate the bet settlement

#### Dead Heats

Where a selection wins the race in a dead heat with another runner, it is deemed to have 'half-won' the race, and the returns are divided accordingly. In essence, the basic factor - and therefore the returns - are halved. Where there is a triple dead heat, the basic factor is divided by three, and so forth. It is worth noting that a dead heat for first place does not usually affect the place part of an each-way bet, because whether the selection came first or second, provided that there are five runners or more, then the selection is still placed.

Dead heat example:

A horse priced at 6/1 finishes in a dead-heat with another horse. A customer had £2 to win on that horse. Instead of the 2 x 7.0000 that he would have received had that horse won by itself, he receives 2 x 3.5000 = £7.00.

A common mistake made by customers is to assume that 6/1 in a dead heat is 3/1. It isn't, it's 5/2. The quick way to calculate the new price is to subtract the bottom half from the top half of the fraction, and double the bottom half. Thus 9/4 becomes 5/8, 7/2 becomes 5/4.

Dead heat rules also apply to unnamed favourite bets where there is more than one favourite in a race^{3}. Where a bet is on the favourite and two runners are joint favourites, the bet is on both. If only one wins, which is quite likely, then you only get half of the money on that runner. It is easily possible, given multiple favourites in a race, to get back less than your stake as a result of this.

#### Rule 4

Rule 4 refers to Tattersalls Rule 4, which states that should a runner be withdrawn from a race at short notice, such that the bookmakers do not have time to create a new book (a set of prices for the now revised field), then the bookmakers can deduct, from winning bets, an amount calculated from the current price of the withdrawn runner.

In practice, rule 4 applies only to bets at fixed odds (not bets placed at starting price, which is what you get if you didn't ask for a price) prior to the withdrawal. However, if the withdrawal occurs just before the start of the race, it can apply to all bets. Rule 4 deductions are declared as some number of pence in the pound, and apply to *winnings only*. The stake is returned intact. To calculate the new basic factor for a selection affected by a rule 4 deduction, take the fractional price, multiply by one less the rule four factor (for example, for a 15p rule 4, use 0.85), and add one to get the new basic factor. This basic factor can then be used in all of the calculations above.

Rule four starts off at 5p in the pound for selections at 14/1 or lower and goes up to a maximum 95p in the pound for selections which are heavily odds on, such as 1/25. ('Odds on' means that the price is less than evens, meaning that if it wins, you get less than double your money back; 'odds against' means the opposite) The rule 4 table should be on your local bookmaker's rules poster. Ask your shop staff for details.

#### Non Runners

Where non-runners are selected, they effectively have a basic factor of 1.0000. This means that any money that goes onto a non-runner is returned unaltered. Rule 4 does not apply to non-runners, nor do dead heats. Where a selection is repeated in a bet, for instance a treble on horses A, B, and A, the second and subsequent times the selection is mentioned, it is treated as a non-runner. One non-runner in a forecast turns that forecast into a non-runner, with returns of 1.0000, but a single non-runner in a tricast turns that bet into a forecast on the remaining two selections.

#### Incorrect Instructions

Customers are humans, and humans make mistakes. For instance, where a customer stakes his bet as a Yankee, but writes only three horses, a non-runner is added to make up the numbers. If a customer pays too much, the excess is refunded. If a customer pays too little, the returns from the bet are adjusted in proportion. If a customer stakes his bet as a Yankee but writes five selections, the bet is treated as a Super-Yankee, but as one where the customer has not paid enough, and so the bet is settled in proportion. Finally, a bet may call for four runners in four different races, but the customer includes two from the same race. In all of the bets where both selections are considered, the stake is divided equally between them. For instance, a £5 win double on A and B becomes two £2.50p singles on A and B if A and B are in the same race.

### Disclaimer

Gambling can be fun, but it can also be dangerous if not properly handled. Bet only with what you can afford to lose.

If you have a problem gambling, ask your local betting shop for information on GamCare, a charitable organisation that exists to help people with gambling problems.

Neither the BBC, nor the author are responsible for any losses you may incur while gambling; nor are they responsible for any winnings you may acquire, but you can certainly buy the Researcher a drink if you like.

^{1}On big race days, such as Grand National day, the volume of bets typically triples.

^{2}Note the use of A+A rather than Ax2 because multiplying at this stage on a non-scientific calculator would yield an incorrect result.

^{3}A favourite is the selection or selections in the field with the lowest price, the second favourite is the selection with the second lowest price, and so forth.