What are fair odds, and why bookmakers never offer them
Fair odds are the decimal price that gives an average profit of exactly zero: 1 divided by the true probability of the outcome. An outcome with a 50% chance has fair odds of 2.00. Offered prices sit below fair odds, and the gap is the cost of betting.
What fair odds are
Fair odds are the price at which a bet would cost nothing on average. They are worked out from the true probability of an outcome: fair decimal odds = 1 ÷ probability. If you can turn a price into a chance, as shown in the guide on converting betting odds into probability, you can turn a chance back into a price.
"True odds" and "fair odds" are two names for the same thing. Both describe a price with no margin built in.
Why fair means zero average profit
Stake KES 1 on an outcome with probability p at decimal odds D. With chance p you get D back, and with chance 1 − p you get nothing. The average return is p × D.
Put D = 1 ÷ p and the average return is p × (1 ÷ p) = 1. You get back exactly what you staked, so the average profit is zero. That is the definition of fair, and it is the same idea as an expected value of zero, covered in the guide on the expected value of a bet.
Simple cases with known chances
Where the chances are known, fair odds are easy to state. The table uses games of pure chance, because a sports result has no known probability.
| Event | Probability | Fair decimal odds |
|---|---|---|
| Fair coin lands heads | 1 in 2 (50%) | 2.00 |
| Fair die shows a six | 1 in 6 (16.67%) | 6.00 |
| Fair die shows an even number | 3 in 6 (50%) | 2.00 |
| Card drawn is a heart | 13 in 52 (25%) | 4.00 |
Anything priced below these numbers carries a charge. A coin-toss bet priced at 1.90 returns 0.5 × 1.90 = 0.95 per shilling staked on average, so KES 50 of every KES 1,000 is kept by the other side.
Why offered prices are never fair
A priced market sits below fair on every outcome. The implied probabilities (1 ÷ price) of all outcomes therefore add up to more than 100%, and the excess is the overround, explained in the glossary entry on what overround is. If the prices were fair, they would add up to exactly 100% and the other side of the bet would earn nothing on average from the money staked.
The margin is not hidden. 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. The prices are visible, so the margin can be worked out.
Fair prices against offered prices
Illustrative example: a three-way match
Suppose, for the sake of the sum, that the true chances were 50%, 30% and 20% for home win, draw and away win. Real chances are never known, so these are invented. The fair odds are 1 ÷ 0.50 = 2.00, 1 ÷ 0.30 = 3.33 and 1 ÷ 0.20 = 5.00.
The invented offered prices are 1.90, 3.10 and 4.60. The average return on KES 1,000 staked on each outcome is chance × price × 1,000.
| Outcome | True chance | Fair odds | Offered odds | Average return on KES 1,000 | Average cost |
|---|---|---|---|---|---|
| Home win | 50% | 2.00 | 1.90 | KES 950 | KES 50 |
| Draw | 30% | 3.33 | 3.10 | KES 930 | KES 70 |
| Away win | 20% | 5.00 | 4.60 | KES 920 | KES 80 |
Every row loses on average, and the longer the price, the larger the cost in this example. The implied probabilities are 1 ÷ 1.90 = 52.63%, 1 ÷ 3.10 = 32.26% and 1 ÷ 4.60 = 21.74%, which total 106.63%. The overround is 6.63%, and the payout percentage is 100 ÷ 1.0663 = 93.78%, as laid out in the guide on bookmaker payout percentage.
Estimating fair odds from offered prices
Since the true chances are unknown, a common shortcut is to remove the margin in proportion. Divide each implied probability by the total, then take 1 divided by the result.
- Write the implied probabilities: 0.5263, 0.3226 and 0.2174.
- Add them: the total is 1.0663.
- Divide each by 1.0663: 0.4936, 0.3025 and 0.2039. These now add up to 1.
- Take 1 divided by each: 2.03, 3.31 and 4.90.
These are margin-free estimates, not true odds. Notice that they differ from the invented true values of 2.00, 3.33 and 5.00. The method spreads the margin by proportion, and a real market may not do that, so treat the result as a reference point. The full method is in the guide on calculating the bookmaker's margin.
What fair odds do not mean
- Not a prediction. A fair price for a 20% outcome still loses four times out of five.
- Not a safe bet. Even at a fair price the average profit is zero, and single results swing far from the average.
- Not observable. The true chance of a sports result cannot be measured, so nobody can know that a price is fair.
- Not a way to make money. Comparing offered prices with fair prices explains the cost of betting. It does not turn betting into income.
How far results can drift from the average is covered in the guide on variance and losing streaks.
Using the idea to stay in control
Fair odds give you a yardstick. The gap between the fair price and the offered price is the average cost of each shilling staked, and that cost is a reason to decide a spending limit before you start. Set an amount you can afford to lose and stop at it.
Questions and answers
Are fair odds the same as true odds?
In betting maths the two terms mean the same thing: the price implied by the real probability of an outcome, with no margin. The catch is that the real probability is never known for a sports event, so fair odds can be estimated but not observed.
Can I find the fair odds of a match from the bookmaker's prices?
Only as an estimate. You can divide each implied probability by the total to make them add up to 100%, which gives margin-free prices. This assumes the margin is spread in proportion to the prices, and that is a modelling choice, not a fact about the match.
Does a bet at fair odds win more often?
No. Fair odds do not change how often an outcome happens. They only mean that the price pays back exactly what the chance deserves, so the average result is zero. A single bet at fair odds still wins or loses.
Is a bet at fair odds a good bet?
It is a bet with no average cost, which is the best case the maths allows. It is still a bet: results swing around the average, and you can lose the whole stake.
Do the Kenyan regulations set a maximum margin?
The regulations read for this guide do not set a figure. Regulation 23(1) requires a licensee to display betting odds, rules and terms clearly for each bet, which is what allows you to work out the margin yourself.