A Quick Start Guide To Odds Calculation In The UK

For starters, unlike other countries where you can find moneyline (American) or decimal odds, in the UK, betting odds are fractional (e.g. 3/1, 4/1, 5/2 and so on). It means that, if an event has odds of 4/1, for each pound you place on a winning bet, you will receive your pound back plus an additional 4 pounds. In other words, if you place a £10 stake on a 4/1 bet and you guess correctly, you will receive a total of £50. This represents a 20% chance, as you will break even in the long term if you win your 4/1 bet once every 5 times or 20% of the time. This kind of bet on a single event is also known as a single.

We can calculate our winnings as follows:

\(r = s + (s*n/d)\)

where r = potential returns, s = stake, n = numerator of odds, d = denominator of odds.

which in our example gives:

\(r = 10 + (10*4/1) = 50\)

What if you want to bet on more events at once? You make an accumulator bet. With this kind of bet you must guess correctly all of the included selections to win. If you bet on 2 events only, your bet is known as double, treble if you bet on 3 events, then fourfold (4-fold), fivefold (5-fold) and so on.

How do we calculate our potential returns in this case? First, if we convert the fractional odds for each selection into decimal odds, the maths will be much easier, since the cumulative odds is simply the product of all the decimal odds in the accumulator. In the example above, the 4/1 odds represented a 20% chance of occurrence, that expressed as decimal would be 0.20. The conversion is straightforward:

\(dec = (n + d)/d\)

where dec = decimal odds, n = numerator, d = denominator

which in our example gives:

\(dec =(4 + 1)/1 = 5.0\)

Let’s assume that you have placed a 4-fold bet of £5 where odds of single events are as follow: 13/8, 6/5, 2/7 and 9/2, that expressed in decimal odds would be 2.63, 2.20, 1.29 and 5.50 respectively. Multiplying these values we have a total accumulator decimal price of 41.05. Multiplying by the £5 stake amount we have potential returns of £205.26.

But let’s see the full potential of an accumulator bet with this simple example. For the same stake, each event you add will increase your potential winnings dramatically.

Accumulator Type Selection Odds (fractional) Selection Odds (decimal) Overall Price Stake Potential Return
Double 2/1, 5/1 3, 6 18 5 90
Treble 2/1, 5/1, 11/2 3, 6, 6.5 117 5 585
Fourfold 2/1, 5/1, 11/2, 9/5 3, 6, 6.5, 2.8 327.6 5 1638
Fivefold 2/1, 5/1, 11/2, 9/5, 3/1 3, 6, 6.5, 2.8, 4 1310.4 5 6552

I said that you must guess correctly all of the included selections to win your accumulator and that’s true. But what happens if you lose only one selection? Can you some how insure your bet? Actually you can! You must place a so called full cover bet. Basically in a full cover bet you hedge the risk of the accumulator bet, placing multiple bets on subgroups of your selections. In the case of a treble, with a full cover bet, you are indeed placing four bets – three doubles and one treble, as follows:

Bet Bet Type Selections
1 Double 1 and 2
2 Double 1 and 3
3 Double 2 and 3
4 Treble 1, 2 and 3

If you bet £5 on each of these combinations, it will cost a total of £20. Here you want to make sure that even the bet with the lower return at least covers this amount, so that you will end up with a profit even if you miss a guess.

Even the full cover bets have their own names according to the number of selections involved. A full cover bet of a treble like the one I showed above, is known as a trixie. Popular full cover bets include:

Full Cover Bet Name Number of Selections Number of Bets Bet Breakdown
Trixie 3 4 3 doubles and a treble
Yankee 4 11 6 doubles, 4 trebles and a fourfold
Super Yankee 5 26 10 doubles, 10 trebles, 5 fourfolds and a fivefold
Heinz 6 57 15 doubles, 20 trebles, 15 fourfolds, 6 fivefolds and a sixfold
Super Heinz 7 120 21 doubles, 35 trebles, 35 fourfolds, 21 fivefolds, 7 sixfolds and a sevenfold
Goliath 8 247 28 doubles, 56 trebles, 70 fourfolds, 56 fivefolds, 28 sixfolds, 8 sevenfolds and an eightfold

There is of course the possibility to include singles too in the coverage. In this case you will get a return even if you win only one of your selections. With so many bets it’s hard to say whether this return will also include a profit. In fact with four selections, the cover bet will include 15 bets – four singles, six doubles, four trebles and a fourfold, that is four singles in addition to a Yankee. This is named a lucky 15.

Popular full cover bets with singles include:

Full Cover Bet With Singles Name Number of Selections Number of Bets Bet Breakdown
Patent 3 7 3 singles, 3 doubles and a treble
Lucky 15 4 15 4 singles, 6 doubles, 4 trebles and a fourfold
Lucky 31 5 31 5 singles, 10 doubles, 10 trebles, 5 fourfolds and a fivefold
Lucky 63 6 63 6 singles, 15 doubles, 20 trebles, 15 fourfolds, 6 fivefolds and a sixfold

Another kind of bet you can find at bookmakers is the so called “each way” bet. It consists of two separate bets: a win bet and a place bet. To win your win bet, your selection must win, or finish first, in the event. To win your place bet, your selection must either win or finish in one of the predetermined places for the event, such as first place or second place. The odds paid on the place part of the bet are commonly a fraction of the win bet odds (often ​1⁄2, ​1⁄3, ​1⁄4 or ​1⁄5). In football knockout competitions like the FA Cup the quoted place terms may be ​1⁄2.

Of course the total staked in an each-way bet is twice the unit stake. So a £5 each-way single would cost £10, as it would a £5 each-way treble, which would include a £5 win treble and a £5 place treble. Hence a £5 each-way on a football team ‘to win the cup’ at 17/2 and ‘to place 1 or 2’ at ​1⁄2 would cost £10.
Returns for the win bet would be (£5 × 9.5) = £47.5
Returns for the place bet would be (£5 × 4.75) = £23.75
If the team wins the total returns would be £47.5 + £23.75 = £71.25, while if it lose the final match the returns would be £23.75. No doubt that if the team does not reach the final, your wager would be lost.

That’s it. This is the very basics of odds calculation you should master if you want to be successful in your sports betting endeavours.

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