How to Convert Odds Formats and Read Implied Probability

Every betting price is a probability in disguise. Decimal, American, fractional, they are just three ways of writing the same number, and behind that number is the chance the market thinks an outcome has. Learn to turn any price into an implied probability in your head and you can compare any two books instantly, see when a line is generous, and start every value decision from the right place. This is the one piece of math that everything else in betting sits on top of.

What implied probability is

Implied probability is the chance an outcome needs to have for a price to be a break even bet. A decimal price of 2.00 pays you double, so it only makes sense if the outcome happens half the time. That is an implied probability of 50 percent. Flip it around: take the payout, ask what win rate would make it fair, and you have the probability the price is quoting.

The formula for decimal odds is the cleanest in betting:

Implied probability = 1 / decimal odds

A price of 1.50 implies 1 / 1.50, or 66.7 percent. A price of 4.00 implies 1 / 4.00, or 25 percent. That is the whole idea. The higher the odds, the lower the probability, and the exact number falls straight out of one division.

The three formats, the same number

Books show prices in three main formats depending on where you are. They look nothing alike, but each one converts to the same implied probability.

Decimal (Europe, most of the world)

Decimal odds show your total return per unit staked, stake included. 2.50 means you get 2.50 back for every 1 you put down, a profit of 1.50. To get the probability, divide 1 by the number.

American (moneyline)

American odds come in two flavours. A positive number like +150 tells you the profit on a 100 stake. A negative number like -200 tells you the stake needed to profit 100.

• Positive: implied probability = 100 / (odds + 100). So +150 is 100 / 250, or 40 percent.
• Negative: implied probability = odds / (odds + 100), using the number without the sign. So -200 is 200 / 300, or 66.7 percent.

Fractional (UK, traditional)

Fractional odds like 3/1 show profit over stake. 3/1 pays 3 profit for every 1 staked. To convert, add the two numbers and divide the second by the total: for a/b, implied probability = b / (a + b). So 3/1 is 1 / 4, or 25 percent, and 10/11 is 11 / 21, or 52.4 percent.

One price, four ways of writing it

Here is a single set of prices shown in all three formats with the implied probability each one carries. Read across any row and you are looking at the exact same bet.

If you only remember one row, make it 2.00 equals +100 equals evens equals 50 percent. It is the hinge of the whole thing. Anything shorter than 2.00 (a negative American number) is an odds on favourite above 50 percent. Anything longer is an underdog below 50 percent.

Converting decimal to the others

Two quick rules cover almost everything you need.

• Decimal to American: if the decimal is 2.00 or higher, American = (decimal minus 1) times 100. If it is below 2.00, American = -100 / (decimal minus 1). So 2.40 becomes +140, and 1.80 becomes -125.
• Decimal to fractional: subtract 1 and write the result as a fraction. 2.50 becomes 1.50, which is 3/2. 3.00 becomes 2.00, which is 2/1.

Why the probabilities add up to more than 100

Convert both sides of a market and something looks off. Add the implied probabilities together and you get a number bigger than 100 percent.

Together that is 104.8 percent. A fair two way market should sum to exactly 100. The extra 4.8 percent is the margin the book builds into the price, the vig, and it is the reason a raw implied probability is never the true probability. To get the real number you have to strip that margin out, which is a short step from here and the whole subject of how to remove the vig. Once you have the true probability, comparing it to the price you are offered is exactly how you find a value bet.

Doing this without a calculator open all day

Reading implied probability by hand is a great skill, but nobody wants to convert hundreds of prices across every book and every market one at a time. Betamigos does the conversion for you, shows odds in whatever format you prefer (decimal, American, fractional, even cents style), and turns every price into a clean no vig probability so you can see at a glance whether a line is generous. Set your format once and read the real number everywhere, from the odds screen to your own bet log where it feeds your closing line value. See it in your Betamigos dashboard.

Betamigos is an odds-analytics tool, not a sportsbook, and none of this is a promise of profit. Bet responsibly. 18+.