Betting Odds Explained
Fractional and decimal odds side by side, how to convert them and what implied probability tells you.
Fractional odds tell you your profit. Decimal odds tell you your total return, stake included.
Two formats, one price
Fractional odds are written as a fraction and remain the common display in the UK and Ireland, per Bleacher Nation's odds-types guide. They show profit relative to stake. Decimal odds do something different. They express the full amount returned on a one-unit stake, so the stake is already inside the number.
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Fractional odds show profit against stake; decimal odds show the total return including the stake.
| Fractional | Decimal | Implied probability | £10 returns |
|---|---|---|---|
| 1/2 | 1.50 | 66.7% | £15 |
| Evens (1/1) | 2.00 | 50.0% | £20 |
| 2/1 | 3.00 | 33.3% | £30 |
| 5/1 | 6.00 | 16.7% | £60 |
| 10/1 | 11.00 | 9.1% | £110 |
In a two-way market where both sides are priced at 10/11, each side implies 52.4 per cent; the two add up to 104.8 per cent, and the 4.8 points above one hundred are the bookmaker’s margin.
The conversion rule is simple arithmetic, set out in the Wikipedia entry on the mathematics of bookmaking: divide the first number of the fraction by the second, then add one. That "add one" step is the stake coming back to you, and it is the single most common place newcomers go wrong, treating a decimal price as if it were pure profit.
What decimal odds say about chance
Implied probability is one divided by the decimal price. That is the whole formula. Evens, in other words, is the pivot point of any market. A price of 1.50 implies roughly 67%. A price of 6.00 implies 16.7%, and 3.00 implies 33.3%.
Note what this does and does not tell you. The figure you get is the probability implied by the price on the board. It is not the bookmaker's private estimate of the true chance, because the quoted price has already had the trading margin built into it. Anyone treating 16.7% as a clean forecast is reading a retail price as if it were a wholesale one.
The worked examples
What the arithmetic does establish is the direction of travel. Short prices, close to or below evens, sit above 50% implied probability. Long prices fall away fast: by 6.00 the market is implying less than one chance in five.
What the margin tells a punter
Add up the implied probabilities for every outcome in a market and the total comes to more than 100%. The excess is the bookmaker's margin, also called the overround, the vig, or the juice, and the calculation is the sum of implied probabilities minus 100%. Take the classic two-way market priced at 1.91 on each side. It is not: the two implied probabilities sum to more than 100%, and that surplus is the margin, as Bet-in-Europe's odds guide notes.
Reading a market without fooling yourself
The practical use of all this is comparison. Convert every price you are offered to implied probability and you can rank bookmakers on the same scale, regardless of whether one screen shows fractions and another shows decimals. Shorter price, higher implied probability. That relationship never breaks, because it is just one divided by the number. And the total will always clear 100%. Every quoted price is simultaneously a payout instruction and a statement of the operator's edge, which is why summing a market is the fastest honest test of how much that edge costs.