Lottery Odds Calculator
Find the odds of winning a lottery by calculating how many possible ticket combinations exist. Use it before buying a ticket to understand just how unlikely a jackpot win is.
About this calculator
In a typical lottery you choose k numbers from a pool of n, and the draw is made without replacement and without regard to order. The total number of possible combinations is the binomial coefficient C(n,k) = n! / (k! × (n−k)!). This calculator returns that value — your odds of winning the jackpot are 1 in C(n,k). For example, a 6/49 lottery has C(49,6) = 13,983,816 combinations, so your chance with one ticket is roughly 1 in 14 million. The formula grows extremely fast: doubling the pool size or adding even one extra number can multiply the odds against you by millions.
How to use
Consider a standard 6/49 lottery: 49 total numbers, 6 drawn. Enter totalNumbers = 49 and numbersDrawn = 6. The calculator evaluates 49! / (6! × 43!) = 13,983,816. Your odds are 1 in 13,983,816, or about 0.0000072%. Buying ten tickets improves your odds tenfold — to roughly 1 in 1.4 million — still vanishingly small, illustrating why jackpots can accumulate for weeks.
Frequently asked questions
What are the odds of winning a 6/49 lottery with one ticket?
With 49 numbers and 6 picks, there are C(49,6) = 13,983,816 possible combinations. One ticket covers exactly one of those combinations, giving a win probability of about 1 in 14 million, or 0.0000072%. To put that in perspective, you are roughly 60 times more likely to be struck by lightning in a given year than to win a 6/49 jackpot with a single ticket.
How does buying more lottery tickets affect your probability of winning?
Each additional unique ticket adds one more covered combination, so your probability increases linearly. Buying 10 tickets gives 10 in 13,983,816 odds, buying 100 gives 100 in 13,983,816, and so on. While the relative improvement is real, the absolute probability remains tiny. To have even a 50% chance of winning 6/49 you would need to buy nearly 7 million tickets — an investment far exceeding any jackpot prize.
Why do lottery odds get so much worse when more numbers are added to the pool?
Because C(n,k) grows combinatorially, not linearly. Adding just one number to the pool multiplies the total combinations by (n+1)/(n+1−k). For a 6-pick game, going from 49 to 50 numbers increases combinations by a factor of 50/44 ≈ 1.14 — about 14% harder. Larger pools have even steeper scaling, which is why lotteries that expand their number pool see jackpots roll over far more often.