How to convert a probability into odds
Divide 1 by the probability to get decimal odds: 25% (0.25) gives 1 / 0.25 = 4.00. Subtract 1 for the fractional profit ratio: 3/1. These are odds with no bookmaker margin, so a real price for the same event will be lower.
The idea in one line
A probability says how often something should happen. Odds say what a winning bet pays. Fair odds link the two so that, over many repeats, the average result is exactly zero, and that single requirement produces every formula below.
This is the reverse of the sums in the guide on converting betting odds to implied probability. You can check each step by hand or use the odds converter for the same arithmetic.
Step 1: write the probability as a decimal
Divide a percentage by 100, or write a "1 in n" chance as 1 ÷ n. Call the result p, a number between 0 and 1.
Step 2: divide 1 by p to get decimal odds
The reasoning is the break-even test. A KES 1 stake at odds D wins with chance p, so the average return is p × D shillings. Setting that equal to the KES 1 staked gives D = 1 ÷ p.
Illustrative example
An outcome with a 40% chance: D = 1 ÷ 0.40 = 2.50. Check by repeating the event 10 times with KES 100 each time, a total stake of KES 1,000. It wins 4 times, each win returning 100 × 2.50 = KES 250, so the total return is 4 × 250 = KES 1,000. Stake in, same amount out: zero.
Step 3: get fractional odds
Fractional odds state profit per unit staked, so take the chance of failing and divide it by the chance of winning. The result is the same as D − 1.
For p = 0.20: (1 − 0.20) ÷ 0.20 = 0.80 ÷ 0.20 = 4, so the odds are 4/1. For p = 0.35: 0.65 ÷ 0.35 = 13/7 (that is 1.857 as a decimal), and the decimal price is 1 + 13/7 = 20/7 = 2.857.
Step 4: get American odds
American odds are built around a base of 100, and the sign depends on which side of 50% you are on.
At p = 0.25, D = 4.00, so the American price is +(4 − 1) × 100 = +300. At p = 0.80, D = 1.25, so it is −100 ÷ 0.25 = −400. For more on that format, see the guide on American moneyline odds to decimal.
Reference table
Each row applies the steps above. Decimal figures are exact except where rounded to four places, and the last column is the total return, stake included, on KES 100.
| Probability | Decimal | Fractional | American | Return on KES 100 |
|---|---|---|---|---|
| 80% | 1.25 | 1/4 | −400 | KES 125 |
| 75% | 1.3333 | 1/3 | −300 | KES 133.33 |
| 60% | 1.6667 | 2/3 | −150 | KES 166.67 |
| 50% | 2.00 | 1/1 | +100 | KES 200 |
| 40% | 2.50 | 3/2 | +150 | KES 250 |
| 25% | 4.00 | 3/1 | +300 | KES 400 |
| 20% | 5.00 | 4/1 | +400 | KES 500 |
| 12.5% | 8.00 | 7/1 | +700 | KES 800 |
| 10% | 10.00 | 9/1 | +900 | KES 1,000 |
A full worked example
Illustrative example
A fair six-sided die lands on a particular face with probability 1 in 6. So p = 1 ÷ 6 = 0.1667 (rounded) and D = 1 ÷ (1 ÷ 6) = 6.00 exactly. The fractional price is 6 − 1 = 5/1, and the American price is +(6 − 1) × 100 = +500.
In shillings: KES 100 at 6.00 returns KES 600 on a win, a profit of KES 500. Over 6 rolls with KES 100 each (KES 600 staked), one win is expected on average, returning KES 600. Again the average result is zero, which is why 6.00 counts as the fair price.
Why a real price will be lower
The odds you calculate here are margin-free. A bookmaker shortens them, so the same chance is quoted at a lower decimal figure, and the shortfall is the margin. The sums for that are in the guides on overround and on calculating the bookmaker's margin.
Illustrative example
An event with a true chance of 1 in 3 has a margin-free price of 3.00. Suppose the price shown is 2.80. Its implied probability is 1 ÷ 2.80 = 35.71%, which is 2.38 percentage points above 33.33%.
The average return per KES 100 staked at 2.80, with a true chance of 1/3, is 100 × 2.80 ÷ 3 = KES 93.33. That is an average shortfall of KES 6.67 on every KES 100.
Where the probability comes from
The conversion is only as good as the probability going in. Dice, coins and cards have chances you can derive exactly. For sport, any figure you pick is an estimate, and it can be wrong in either direction.
A calculated price therefore does not say a bet is good or bad. It only turns a belief into a number you can compare against a quoted price. To see what win rate a quoted price needs just to break even, read the guide on the break-even win rate for given odds.
Common slips
- Using the percentage as if it were a decimal. Dividing 1 by 25 gives 0.04, not 4.00. Convert 25% to 0.25 first.
- Confusing "1 in 4" with "4/1". A 1-in-4 chance is p = 0.25, and the fractional odds are 3/1, not 4/1, because the stake is returned separately.
- Dropping the "− 1". Decimal 4.00 includes the stake. The fractional profit ratio is 4.00 − 1 = 3.
- Rounding too soon. Keep four decimal places. 0.33 gives 3.03, while the exact 1/3 gives 3.00.
- Treating the result as a promise. A fair price describes a long-run average. Any single bet either returns the stake plus profit or returns nothing.
What the law adds
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. Section 71(1) of the Gambling Control Act, 2025 sets the minimum online bet at twenty shillings.
Betting is for adults aged 18 and over. Gambling is addictive: converting a probability into odds shows the arithmetic of a price, and it does not make any bet safer or more likely to pay.
Questions and answers
What is the formula to convert a probability into decimal odds?
Decimal odds = 1 divided by the probability written as a decimal. A probability of 20% is 0.20, so the odds are 1 / 0.20 = 5.00. A KES 100 stake would return KES 500 in total at those odds, of which KES 400 is profit.
How do I convert a percentage into fractional odds?
Divide the chance of not happening by the chance of happening. For 20%, that is 80 / 20 = 4, so the odds are 4/1. For 35%, it is 65 / 35, which reduces to 13/7.
Why is the price I see lower than the odds I calculated?
The odds you calculate from a probability contain no margin. A bookmaker builds a margin into its prices, so the price shown for the same chance is shorter. At a true chance of 1 in 3 the margin-free price is 3.00, and a shown price of 2.80 would be an example of a shorter one.
Can a probability of 100% or 0% be converted?
Not into useful odds. At 100% the decimal odds are 1 / 1 = 1.00, which pays no profit. At 0% the sum would divide by zero, so no odds exist.
Does Kenyan law say how odds must be shown?
Regulation 23(1) of the Gambling Control (Conduct of Gambling Operations) Regulations, 2026 says a licensee shall clearly display betting odds, rules and terms applicable to each bet. It does not name a format.