What are the real chances of winning an accumulator?
Multiply the winning chance of every leg. Five legs that are each 80% likely win together with probability 0.8 x 0.8 x 0.8 x 0.8 x 0.8 = 32.77%, about 1 time in 3. Every extra leg lowers the chance, and one lost leg loses the whole bet.
The rule in one line
An accumulator wins only if every leg wins. For legs that do not influence each other, the chance of that is the product of the individual chances. The guide on converting odds to probability shows where each leg's chance comes from.
Here p is a chance written as a decimal: 80% is 0.80. The second line counts every outcome where at least one leg fails, which is the outcome that loses the bet.
Why the chance falls so quickly
Each chance is below 1, so each multiplication shrinks the running total. The loss is not a fixed amount per leg: it is a fixed share of what remains. Nine legs that are each 90% likely look safe one by one, yet 0.9 to the power 9 is only 38.74%.
The table gives the chance that all legs win when every leg has the same chance. The figures are exact powers rounded to two decimals, and they are mathematics, not a description of any real market.
| Chance per leg | 2 legs | 3 legs | 5 legs | 10 legs |
|---|---|---|---|---|
| 50% | 25.00% | 12.50% | 3.13% | 0.10% |
| 60% | 36.00% | 21.60% | 7.78% | 0.60% |
| 70% | 49.00% | 34.30% | 16.81% | 2.82% |
| 80% | 64.00% | 51.20% | 32.77% | 10.74% |
| 90% | 81.00% | 72.90% | 59.05% | 34.87% |
A leg at 90% fails once in ten. Ten such legs together fail in about 65 of every 100 attempts (100% − 34.87% = 65.13%).
Step by step with different legs
Real legs rarely share one chance. Multiply them one at a time and keep four decimal places until the end.
Illustrative example
Five invented legs with chances of 80%, 70%, 65%, 60% and 55%.
| Leg | Chance | Working | Running chance |
|---|---|---|---|
| 1 | 0.80 | 0.80 | 80.00% |
| 2 | 0.70 | 0.80 × 0.70 | 56.00% |
| 3 | 0.65 | 0.56 × 0.65 | 36.40% |
| 4 | 0.60 | 0.364 × 0.60 | 21.84% |
| 5 | 0.55 | 0.2184 × 0.55 | 12.01% |
The accumulator wins with probability 0.1201, so it loses with probability 1 − 0.1201 = 0.8799, or 87.99%. On average it wins about once in 1 ÷ 0.1201 = 8.3 attempts. No single leg looked unlikely, yet the bet as a whole is a long shot.
The weakest leg sets the ceiling
The product can never be higher than the smallest chance in it. Four legs at 90% have a combined chance of 0.9 to the power 4 = 65.61%. Add one leg at 50% and the result is 0.6561 × 0.50 = 32.81%, which is half of the previous figure.
So a single doubtful selection halves the chance of the whole bet. Removing the weakest leg raises the chance, but it also lowers the combined odds, as the guide on accumulator odds and payout shows.
Reading the chance from the odds
The combined decimal odds contain the same information. The implied chance of the whole bet is 1 divided by the combined odds, because the odds are a product of the legs' odds and each leg's implied chance is 1 divided by its odds.
Illustrative example
Combined odds of 25.00 imply a chance of 1 ÷ 25.00 = 0.04, or 4%, about 1 time in 25.
This implied figure includes the bookmaker's margin, so it overstates the real chance. The size of that gap is explained in why accumulators carry more margin and in the guide on what overround is.
How many legs until losing is the likelier result
Find the smallest n where p to the power n falls below 0.5. With equal legs, the table shows when the bet becomes more likely to lose than to win.
| Chance per leg | Last count above 50% | Next count | Result |
|---|---|---|---|
| 90% | 0.96 = 53.14% | 0.97 = 47.83% | Below 50% from 7 legs |
| 80% | 0.83 = 51.20% | 0.84 = 40.96% | Below 50% from 4 legs |
| 70% | 0.71 = 70.00% | 0.72 = 49.00% | Below 50% from 2 legs |
Even when every leg is a strong favourite, the bet turns into a likely loser within a few legs.
When the legs are not independent
The multiplication rule needs legs that do not affect one another. For two legs the general form is: chance of A and B = chance of A × chance of B given that A has happened.
Illustrative example
Leg A has a chance of 60% and leg B 70% on their own. If B is 80% likely once A has won, the pair wins with probability 0.60 × 0.80 = 48%, not 0.60 × 0.70 = 42%.
The direction of the error depends on the link between legs, and the true conditional chances are not published. For legs taken from the same match, treat any simple product as a rough guide only.
From chance to cost
The chance of winning is only half of the picture. The other half is the payout, and the two together give the average result, set out in the expected value guide. A low chance of winning paired with fair odds is not a reason to expect a profit.
The stake does not alter any probability. Section 71(1) of the Gambling Control Act, 2025 sets twenty shillings as the least a player may bet online in a competition, and a KES 20 accumulator has the same chance of winning as a KES 2,000 one. Regulation 23(1) of the Gambling Control (Conduct of Gambling Operations) Regulations, 2026 requires a licensee to clearly display betting odds, rules and terms for each bet, so read how a cancelled leg is treated before you stake.
Because the usual result is a loss, decide the total you can afford to lose first, using the guide on setting a betting budget and limits. Gambling is addictive. Play responsibly.
Questions and answers
What is the chance of winning an accumulator?
It is the product of the chances of its legs, if the legs do not influence each other. Three legs with chances of 70%, 60% and 50% give 0.7 x 0.6 x 0.5 = 0.21, or 21%.
Why does adding a leg lower the chance?
Each leg is multiplied in, and every chance is below 1 (below 100%). Multiplying by a number below 1 always makes the result smaller, so a longer accumulator has a smaller chance than the shorter one it is built from.
How many legs make an accumulator more likely to lose than win?
When every leg has chance p, the accumulator wins less than half the time once p to the power n drops below 0.5. At p = 0.9 that happens at 7 legs (0.9 to the power 7 = 0.478). At p = 0.8 it happens at 4 legs (0.8 to the power 4 = 0.410).
Can I work out the chance from the combined odds?
Yes, as an approximation. The implied chance is 1 divided by the combined decimal odds. It includes the bookmaker's margin, so the real chance is a little lower than the implied one.
Does the multiplication rule work for legs from the same match?
Not reliably. The rule needs independent legs. When two legs come from one match, the second chance depends on whether the first leg wins, so the simple product can be too low or too high.
Does the minimum online stake change the chance?
No. Section 71(1) of the Gambling Control Act, 2025 sets twenty shillings as the least a player may bet online in a competition. The stake size has no effect on the probability of the legs winning.
Sources
- Gambling Control Act, 2025 (No. 14 of 2025), s.71(1), accessed 2026-10-05
- Gambling Control (Conduct of Gambling Operations) Regulations, 2026, r.23(1), accessed 2026-10-05