Lottery Odds Calculator
Find your odds of winning a lottery by computing how many equally likely ticket combinations exist. Use it before buying a ticket to see exactly how unlikely the jackpot really is.
Last updated: May 2026
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About this calculator
A standard 'pick k from n' lottery draws k distinct numbers from a pool of n, with order ignored. The number of possible tickets is the combination C(n, k) = n! / (k! · (n − k)!), and since exactly one combination wins, the probability that a single ticket matches all numbers is 1 / C(n, k). Here n is Total Numbers in the pool and k is Numbers Drawn. The calculator evaluates k! · (n − k)! / n!, which is algebraically identical to 1 / C(n, k). Because order does not matter, you must use combinations, not permutations; using permutations would overcount by a factor of k! and make the odds look far better than they are. Edge cases: if k = n there is only one possible ticket (probability 1), and if k = 0 the formula degenerates and is not meaningful for a real draw. The model assumes every number is equally likely and drawn without replacement, and it counts only the top 'match all' prize — it ignores bonus balls, secondary tiers, and multi-draw games. Real lotteries with bonus numbers or 'powerball' pools require multiplying separate combination counts.
How to use
Example 1 — a classic 6/49 lottery. Enter Total Numbers = 49 and Numbers Drawn = 6. Compute C(49, 6) = 49! / (6! · 43!) = 13,983,816. The probability of one ticket winning is 1 / 13,983,816 ≈ 0.00000715%, i.e. about 1 in 14 million. Verify by building up: (49·48·47·46·45·44) / (6·5·4·3·2·1) = 10,068,347,520 / 720 = 13,983,816. Example 2 — a 6/59 lottery. Enter Total Numbers = 59 and Numbers Drawn = 6. Compute C(59, 6) = (59·58·57·56·55·54) / 720 = 45,057,474. The odds are 1 / 45,057,474, roughly 1 in 45 million — more than three times worse than the 6/49 game. Verify the trend: adding ten numbers to the pool while still drawing six dramatically inflates the combination count, which is why bigger pools mean longer odds.
Frequently asked questions
Why do lottery calculators use combinations instead of permutations?
Because the order in which the winning numbers are drawn does not matter — a ticket of {3, 11, 27, 32, 40, 45} wins regardless of the sequence the machine produces. Combinations C(n, k) count each unordered set once, whereas permutations P(n, k) count every ordering separately and so overcount by a factor of k!. Using permutations is the most common mistake and makes the odds look k! times better than reality; for a 6-number game that is a 720× error. The single correct denominator for the 'match all' probability is C(n, k). Only use permutations if a game genuinely requires matching numbers in the exact drawn order, which ordinary lotteries do not.
Does this account for bonus balls, powerballs, or secondary prizes?
No — it computes only the probability of matching all k main numbers, the top jackpot tier. Games with a separate bonus pool (like Powerball or EuroMillions) multiply the main combination count by the number of bonus options, so the true jackpot odds are longer than this tool reports. Secondary prizes (matching 5, 4, or 3 numbers) have their own, much higher probabilities calculated with the hypergeometric distribution. If you want the odds of 'any prize', you must sum the probabilities across every winning tier. Treat this calculator as the headline jackpot figure for a single simple draw, not the full prize structure.
How much do my odds improve if I buy more tickets?
Odds scale linearly with the number of distinct tickets: buying m different tickets gives a winning probability of m / C(n, k). For a 6/49 game, ten tickets move you from 1 in 14 million to 10 in 14 million — still about 1 in 1.4 million, a negligible practical change. People dramatically overestimate this effect; you would need to buy millions of unique combinations to make winning likely, at a cost far exceeding most jackpots. Buying duplicate tickets does not help at all, since a repeated combination cannot win twice in the main draw. The math shows why 'buying more tickets' is not a viable strategy.
Are some number combinations more likely to win than others?
No. In a fair lottery every combination, including 1-2-3-4-5-6, is exactly as likely as any other, because the draw is uniform over all C(n, k) sets. The persistent belief that 'spread out' or 'random looking' numbers are luckier is a misconception with no mathematical basis. What choosing unusual combinations can affect is the prize you would share: picking numbers others avoid reduces the chance of splitting a jackpot, but it never changes your odds of winning. So combination choice is about payout-sharing, not probability. Treat any 'hot' or 'due' number system as entertainment, not strategy.
When should I NOT use this lottery odds calculator?
Do not use it for games that are not simple 'pick k from n' draws — scratch cards, raffles, keno with variable picks, and multi-pool games all need different models. It also should not be used to estimate the odds of any prize, only the jackpot, since lower tiers follow the hypergeometric distribution. Avoid relying on it for expected-value or 'is the jackpot worth it' decisions without also factoring in jackpot size, tax, and the probability of splitting the prize. Finally, never treat the output as a reason to expect a win: even favorable-looking expected value does not change the near-certainty of losing any single ticket. Use a dedicated expected-value model for financial questions.