Chance of at least one win in several bets: the arithmetic

Find the chance that every bet loses, then subtract it from 1. For n independent bets that each win with probability p, the chance of at least one win is 1 - (1 - p)^n. Ten bets at 10% each give 65.13%. A win is not the same as a profit, and more bets do not raise expected value.

By BetSmart Kenya Editorial (prepared with AI tools under our editorial policy) · Last updated 2026-10-30

The rule in one line

To find the chance of at least one win in several bets, work out the chance that all of them lose and subtract it from 1. If one bet wins with probability p, it loses with probability 1 − p. Where each bet's chance comes from is covered in the guide on converting odds to probability.

Here p is written as a decimal: 20% is 0.20. The rule assumes the bets are independent, which means the result of one does not change the chance of another.

Why subtract from 1

"At least one win" covers many outcomes: only the first bet wins, only the second, any pair, all of them. There is exactly one outcome where nothing wins. Because all outcomes together add up to 1, the chance of at least one win equals 1 minus the chance of that single losing outcome.

The chance that every bet loses is a product, because independent events multiply. Three bets that each lose with probability 0.70 all lose with probability 0.70 × 0.70 × 0.70 = 0.343.

Table: at least one win for equal chances

Each figure is 1 − (1 − p)ⁿ, rounded to two decimals. They are exact powers, not a description of any real market.

The chance rises with every extra bet, but by smaller steps each time. At p = 20% the second bet adds 16 percentage points, while going from 5 bets to 10 adds about 22 points over five more bets.

Step by step with different chances

Real bets rarely share one p. Multiply the losing chances one by one, then subtract the product from 1.

The chance of at least one win is 1 − 0.2250 = 0.7750, or 77.5%. Note that it is higher than the best single bet (50%) and lower than the sum of the three chances (40% + 25% + 50% = 115%, which is impossible as a probability). Adding chances overcounts the outcomes where several bets win together.

How many bets for a target chance

Rearrange the rule to solve for n. For a target chance T, you need (1 − p)ⁿ ≤ 1 − T. The table lists the smallest whole number of bets, checked by multiplying out the powers.

A long losing run is therefore normal when p is small. The guide on variance and losing streaks shows the same arithmetic from the other side.

A win is not the same as a profit

The formula counts bets that win, whatever they pay. Whether one win covers the money staked depends on the odds. Take the break-even idea from the break-even win rate guide: with decimal odds of 3.00, the implied chance is 1 ÷ 3.00 = 33.33%.

• Chance that all five lose: 0.70⁵ = 0.16807, so at least one win has probability 1 − 0.16807 = 83.19%.
• One win returns KES 100 × 3.00 = KES 300, which is KES 200 less than the KES 500 staked.
• Two wins return KES 600, so the series breaks even or better only from two wins.
• Chance of exactly one win: 5 × 0.30 × 0.70⁴ = 5 × 0.30 × 0.2401 = 0.36015.
• Chance of finishing with a net loss (zero or one win): 0.16807 + 0.36015 = 0.52822, or 52.82%.

So an 83.19% chance of "at least one win" sits next to a 52.82% chance of ending the series behind. The headline chance is a poor measure of how a series of bets will go.

More bets do not raise expected value

Expected value (EV) is the average result per bet: chance of winning × return, minus the stake. In the example above, one KES 100 bet has EV = 0.30 × 300 − 100 = −KES 10. Five such bets have EV = 5 × (−KES 10) = −KES 50.

EV adds up across bets, so each extra bet adds its own negative amount. Raising the number of bets lifts the chance of at least one win, but it also raises the total staked and the expected loss. The expected value guide sets out the full calculation.

The negative sign comes from the bookmaker's margin. Odds are set so that the implied chances add up to more than 100%, as explained in what overround is, and so the true chance of a bet is on average lower than the implied chance printed in its odds.

Limits of the formula

• Independence: bets on the same match or on related events can be linked, and the product of separate chances may then be wrong in either direction.
• Estimated p: the true chance of a win is unknown. Using the implied chance from odds overstates it by the margin, so the result is a ceiling, not a forecast.
• Past results: a losing run does not make a win more likely on the next bet. Each independent bet keeps its own p.
• Accumulators: an accumulator is a different question, because all legs must win. See the accumulator probability guide.

Using the arithmetic with a budget

Section 71(1) of the Gambling Control Act, 2025 states that a player in an online gambling activity shall not bet an amount of less than twenty shillings in a competition. The stake has no effect on any chance above: a KES 20 bet and a KES 2,000 bet have the same probability of winning, and only the money at risk differs.

Because the usual result over many bets is a net loss, set the total you can afford to lose before staking anything, using the guide on setting a betting budget and limits. Treat that total as money spent, not as a stake to be recovered by placing more bets. Gambling is addictive. Play responsibly.