The jackpot calculation
In a 6/49 game you choose 6 numbers from 1 to 49. The number of different 6-number sets is the combination C(49, 6) = 49! ÷ (6! × 43!) = 13,983,816. With one ticket, your chance of matching all six is 1 in 13,983,816.
For entertainment only. Lotto draws are random; no generator, wheel or statistic can predict results. 18+ only. Play within a budget.
Odds of matching fewer numbers
Matching exactly k of the 6 drawn numbers uses C(6, k) × C(43, 6 − k) ÷ C(49, 6). Exactly 3 matches works out to about 1 in 57, exactly 4 about 1 in 1,032, and exactly 5 about 1 in 54,201. Bonus-ball prizes add other tiers depending on the game.
Other formats
The same method applies to any lotto: C(n, k) for choosing k from n. Games with a separate bonus pool multiply by that pool's size. That is why big multi-state jackpots have odds in the hundreds of millions.
Putting the number in perspective
Buying 10 tickets a week for a year is 520 sets, giving a chance of roughly 1 in 26,900 at a single jackpot that year. Coverage grows linearly with spending.
Understanding combinations
A combination counts selections where order does not matter. Choosing numbers 3, 15, 22, 31, 40, 44 is the same ticket as 44, 40, 31, 22, 15, 3. That is why we use C(49, 6) rather than 49 × 48 × 47 × 46 × 45 × 44, which would count every ordering. Dividing that product by 6! = 720 gives the 13,983,816 figure.
Comparing games
Smaller lotto games have better odds and smaller prizes. For example, a 5/35 game has C(35, 5) = 324,632 combinations. A game with a separate bonus ball from a pool of 10 multiplies its main odds by 10. Comparing odds across games helps you see why huge jackpots come with very long odds.
Making informed choices
If you enjoy lotto, choosing a game with better odds and smaller prizes can give more frequent small wins, while big jackpot games offer a dream at very long odds. Neither has positive expected value. Choose the one you find fun and keep to your budget.
Calculating smaller prizes yourself
For exactly 3 matches: C(6, 3) × C(43, 3) = 20 × 12,341 = 246,820 winning combinations, and 13,983,816 ÷ 246,820 ≈ 56.7. For exactly 4: C(6, 4) × C(43, 2) = 15 × 903 = 13,545, giving about 1 in 1,032. For exactly 5: 6 × 43 = 258, about 1 in 54,201. Working through these once makes the prize tables on lottery websites much easier to understand.
Bonus balls
Many 6/49 games draw a seventh bonus number used for a second-tier prize, typically 5 main numbers plus the bonus. The chance of that is 6 ÷ 13,983,816, about 1 in 2,330,636, because 6 of the 258 five-match combinations also contain the bonus. Check your game's rules, since bonus formats vary.
Odds of matching nothing
The chance of matching none of the six numbers is C(43, 6) ÷ C(49, 6), about 43.6%, so most tickets match at least one number.
Why understanding odds matters
Clear odds help you treat lotto as entertainment and resist claims of systems that 'guarantee' wins. Nothing changes the mathematics of a fair draw.
Frequently asked questions
Why 13,983,816?
It is the number of ways to choose 6 from 49.
Do quick picks have worse odds?
No. Every set has the same chance.
Does the same set lose forever if it lost before?
No. Each draw is independent.
What are the odds of 3 matches?
About 1 in 57.
Does buying two tickets double my chance?
Yes, if they are different sets; it also doubles the cost.