Odds for any pick-N-from-M lottery: jackpot odds, match-3/4/5 odds and the expected value of a ticket.
The classic example is 6 picks from 49 numbers. Add a bonus ball below if your game has one.
Jackpot odds
—How to use this tool
How many numbers a ticket picks, and how many numbers are in the pool — 6 from 49 is the classic example.
In Advanced, enter how many bonus balls must also match; the jackpot odds multiply accordingly.
Jackpot odds sit at the top, with match-3, match-4 and match-5 odds beneath.
Enter the jackpot and ticket price to see what a ticket is worth on average — almost always less than its price.
Formula & worked example
6 from 49: C(49, 6) = 13,983,816 combinations, so the jackpot is 1 in 13,983,816. Matching exactly 3 numbers is 246,820 ÷ 13,983,816, about 1 in 56.66. A $10 million jackpot makes a $2 ticket worth about $0.72 on jackpot value alone.
Limitations — read this before you rely on it
Expected value here covers the jackpot only, not smaller prizes, taxes, or the chance of splitting a jackpot with other winners — all of which lower what you actually take home. Odds assume one random draw with no repeated numbers on a ticket.
Frequently asked questions
For 6 numbers from 49 it is 1 in 13,983,816. Every game format is different — enter your game's picks and pool to get its exact odds.
No. Every combination is equally likely in a fair draw, and past draws do not influence future ones.
Jackpot × jackpot probability, minus the ticket price. It is almost always negative, which is how lotteries fund their prizes.
With the hypergeometric formula: ways to match 3 of your numbers times ways to miss the other 3, divided by all combinations — about 1 in 56.66 for 6 from 49.
Yes — the jackpot must then also match the bonus draw, so the jackpot combinations multiply by the number of bonus balls.