Lottery Odds Calculator
Compute your exact odds of winning a lottery jackpot based on pool size, numbers drawn, and bonus ball rules. Helps you understand just how unlikely a jackpot win really is.
About this calculator
Lottery odds are determined by combinatorics. When you choose r numbers from a pool of n, the number of possible combinations is C(n,r) = n! / (r!(n−r)!). If the lottery includes a separate bonus ball drawn from a pool of b additional numbers, the total combinations multiply to C(n,r) × b. If the bonus ball is drawn from the same main pool (without replacement), the multiplier is (n − r), the count of remaining numbers. Your win probability is simply tickets_bought / total_combinations. For a typical 6/49 lottery, C(49,6) = 13,983,816, meaning one ticket gives roughly a 1-in-14-million chance — less likely than being struck by lightning twice.
How to use
Model a Powerball-style game: 69 main numbers, 5 drawn, plus a separate bonus ball pool of 26. Set total_numbers = 69, numbers_drawn = 5, bonus_ball = 'separate', bonus_pool_size = 26, tickets_bought = 1. C(69,5) = 11,238,513; multiplied by 26 gives 292,201,338 total combinations. Probability = 1 / 292,201,338 ≈ 0.0000000034, or about 1 in 292 million. Buying 10 tickets raises the probability to roughly 1 in 29 million — still vanishingly small.
Frequently asked questions
How do lottery odds change when a bonus ball is added to the draw?
A bonus ball multiplies the number of distinct winning combinations, dramatically increasing the odds against a jackpot win. If the bonus is drawn from a separate pool of b numbers, total combinations multiply by b. If drawn from the remaining main-pool numbers, they multiply by (n − r). For example, adding a bonus ball from a pool of 26 to a 5/69 game increases combinations from ~11 million to ~292 million. This design lets lottery operators offer bigger jackpots by making wins far rarer.
Does buying more lottery tickets significantly improve my chances of winning?
Buying additional tickets improves odds linearly: 10 tickets give exactly 10 times the probability of 1 ticket. However, because baseline odds are so extreme (often 1 in hundreds of millions), even 100 tickets still leaves you with a probability below 0.00004%. The expected value of a lottery ticket is almost always negative once taxes and lump-sum discounts are factored in, meaning lotteries are statistically poor investments. Buying more tickets is only strategically worthwhile if the jackpot is large enough to produce a positive expected value after tax.
What is the difference between lottery odds and lottery probability?
Odds and probability express the same information differently. Probability is the ratio of favorable to total outcomes: P = 1/C(n,r). Odds against winning are expressed as (C(n,r) − 1) : 1, meaning the number of losing outcomes relative to winning ones. For a 6/49 lottery, the probability is about 1/13,983,816 ≈ 0.0000000715, while the odds against are roughly 13,983,815 to 1. Probability is more useful for calculations; odds are more intuitive for comparison and are commonly used by bookmakers.