How to convert betting odds into implied probability
Change the price to decimal odds, then divide 1 by it. Decimal 2.50 gives 1 / 2.50 = 0.40, or 40%. Fractional a/b becomes a / b + 1; American +X becomes X / 100 + 1; American -X becomes 100 / X + 1. The result includes the bookmaker's margin, so it is not the true chance.
What a price is really saying
Betting odds are two things at once: a statement of what a winning bet pays, and, read the other way, a statement of probability. The second reading is the useful one, because it lets you compare any price with your own sense of how likely something is.
The conversion is short arithmetic. You can do it by hand with the steps below or let the odds converter do the same sums. Either way the output describes the price only. It does not forecast the event.
Step 1: get the price into decimal form
Decimal odds, written here as D, are the total amount returned for each shilling staked when the bet wins, with the stake included. The other two formats describe profit only, so each needs one small adjustment.
Fractional odds such as 5/2 say "five of profit for every two staked". Divide and add the stake back: 5 ÷ 2 + 1 = 3.50.
American odds come in two kinds. A plus price is the profit on a stake of 100, so +250 is 250 ÷ 100 + 1 = 3.50. A minus price is the stake needed to make a profit of 100, so −150 is 100 ÷ 150 + 1 = 1.67 (rounded).
Step 2: divide 1 by the decimal odds
The logic is a break-even one. If a bet at odds D wins a share p of the time, the average return per shilling is p × D. That average equals the one shilling staked exactly when p = 1 ÷ D. So the implied probability is the win rate at which the price would neither cost nor pay anything over the long run.
Illustrative example
Three prices, three formats. Fractional 5/2: D = 3.50, so p = 1 ÷ 3.50 = 28.57%. American −150: D = 1.6667, so p = 60.00%. Decimal 1.40: p = 1 ÷ 1.40 = 71.43%.
In shillings: KES 100 at 3.50 returns KES 350 if it wins (KES 250 profit). KES 100 at 1.40 returns KES 140 (KES 40 profit). In both cases a losing bet returns nothing.
Step 3: read the table instead, if you prefer
The same price in every format, with its implied probability. Fractions are the exact equivalents of the decimal figure.
| Decimal | Fractional | American | Implied probability | Return on KES 100 |
|---|---|---|---|---|
| 1.20 | 1/5 | −500 | 83.33% | KES 120 |
| 1.40 | 2/5 | −250 | 71.43% | KES 140 |
| 1.6667 | 2/3 | −150 | 60.00% | KES 166.67 |
| 2.00 | 1/1 | +100 | 50.00% | KES 200 |
| 2.25 | 5/4 | +125 | 44.44% | KES 225 |
| 3.50 | 5/2 | +250 | 28.57% | KES 350 |
| 6.00 | 5/1 | +500 | 16.67% | KES 600 |
| 21.00 | 20/1 | +2000 | 4.76% | KES 2,100 |
Going the other way: from probability to odds
The formula turns round without trouble. A probability of 25% corresponds to decimal odds of 1 ÷ 0.25 = 4.00. A probability of 60% corresponds to 1 ÷ 0.60 = 1.67.
This is handy for a sanity check. If you think an outcome happens about one time in three, a price with no margin would be about 3.00. Any price below that pays less than your own estimate says it should, before you even ask whether your estimate is any good.
Why the implied probability is too high
Take an event with two outcomes that are equally likely. Fair prices would be 2.00 and 2.00, and the two implied probabilities would add up to 100%. A bookmaker might instead offer 1.90 and 1.90. Each price now implies 52.63%, and together they imply 105.26%.
Nothing can happen 105.26% of the time. The extra 5.26% is the bookmaker's margin, spread across the prices. That is why a single implied probability always overstates the chance the price was built on. How to measure and remove the excess is covered in the guide on calculating the bookmaker's margin.
Common slips in the arithmetic
- Forgetting the "+ 1". Fractional and American prices state profit. Without adding the stake back you get the profit ratio, not decimal odds, and the probability comes out wrong.
- Mixing the two American cases. For plus prices the number goes on top (X ÷ 100); for minus prices it goes underneath (100 ÷ X).
- Reading return as profit. KES 100 at 1.40 returns KES 140, but the profit is KES 40. The stake was yours already.
- Treating the percentage as a forecast. It is the break-even win rate of the price, inflated by the margin. It says nothing certain about what will happen.
- Rounding too early. Keep four decimal places until the last step. 1.67 and 1.6667 give 59.88% and 60.00%.
What to do with the number
The honest use of implied probability is to see the cost of a bet clearly. Once every price is a percentage, you can add up a market, find the margin and work out the long-run average result of a stake, which is the subject of the guide on the expected value of a bet.
It is not a tool for finding winners. A percentage does not know anything about form, injuries or luck, and a price that looks generous against your own guess may simply mean your guess is off. Prices are set by people with more data than a single bettor has.
The law adds one fixed number to all of this. Section 71(1) of the Gambling Control Act, 2025 says a player in an online gambling activity shall not bet less than twenty shillings in a competition, so every return in the table above scales from a stake of at least KES 20; see the note on the minimum online stake.
Questions and answers
What is the quickest way to get the implied probability from decimal odds?
Divide 100 by the decimal odds. Odds of 4.00 give 100 / 4.00 = 25%, and odds of 1.25 give 100 / 1.25 = 80%.
Do lower odds mean the outcome is certain to happen?
No. Lower odds mean a higher implied probability, not certainty. Odds of 1.25 correspond to 80%, which still leaves the outcome failing about one time in five even if the price were perfectly fair.
Why do the probabilities of all outcomes add up to more than 100%?
Because each price is set a little lower than a fair price would be. The excess over 100% is the bookmaker's margin, also called the overround.
Are fractional odds of 1/1 and decimal odds of 2.00 the same?
Yes. 1/1 means one shilling of profit per shilling staked, so the total return is two shillings per shilling: decimal 2.00, American +100, implied probability 50%.
Does Kenyan law say how odds must be shown?
Regulation 23(1) of the Gambling Control (Conduct of Gambling Operations) Regulations, 2026 requires a licensee to clearly display betting odds, rules and terms applicable to each bet. It does not prescribe a particular odds format.