How to work out implied probability from decimal odds (with examples)

The implied probability of a price is 1 divided by that price. Odds of 2.00 imply 50%, 4.00 implies 25%, 1.50 implies 66.7%. It is one division, and with a little practice you can do it in your head.

The name already states the limit: it is the probability that price *implies*, not the one the event *has*. They are two different things, and confusing them is the commonest beginner's mistake.

Why it isn't the true probability

Every price already has the bookmaker's margin inside it: the price is shaded slightly below what a fair market would pay, and that margin inflates every implied probability. Which is why, when you add up the three outcomes of a 1X2, you don't get 100% but something more.

On a 1X2 priced 2.00 / 3.40 / 4.00: 50% + 29.4% + 25% = 104.4%. Those 4.4 points of excess are the bookmaker's margin, not a rounding error.

Normalising: how you get back to 100

To compare two bookmakers on the same outcome it pays to strip the margin out, that is, to divide each implied probability by the total. In the example: 50 / 104.4 = 47.9% · 29.4 / 104.4 = 28.2% · 25 / 104.4 = 23.9%. Now they add up to 100 and can be compared across operators that keep different percentages.

This is the step professionals call «removing the vig». It doesn't make a bet good: it makes two prices comparable that otherwise are not, because one of them carries more margin than the other.

Three things it is good for, and one it isn't

• Understanding how likely the market thinks an outcome is, in a language — a percentage — that reads more easily than a price.
• Comparing two bookmakers on the same outcome after normalising, that is, on equal margin terms.
• Measuring what one market costs you against another: Under/Over carries lower margins than a 1X2 because it has one outcome fewer to cover.
• ⚠ What it cannot do: stand in for a prediction. It tells you what the bookmaker put into the price, not what will happen.

The sum in reverse

It also works the other way round: if you think an outcome is worth 40%, the fair price is 1 divided by 0.40, that is 2.50. Below that you are paying more than (in your view) it is worth; above it, less. With that sum in your head a price stops being a number and becomes a price with a yardstick.