Probability and Odds Calculator
The chance of something happening at least once, a dice total, or a lottery win.
Good to know. A 1-in-6 chance, tried six times, still misses a third of the time.
How it works
In plain words
The chance of something happening at least once is 1 minus the chance of it never happening, and never happening means missing every time: (1 − p) multiplied by itself once per try. Dice totals count every way the dice can fall. Lottery odds are the number of possible tickets, which is “pool choose pick”.
The formula
at least once = 1 − (1 − p)ⁿ lottery = C(pool, pick) × extra-ball pool · C(n, k) = n! ÷ (k! (n − k)!) dice: count the combinations that make the total ÷ sidesⁿ
Worked example
A 10% chance, tried 10 times: the chance of missing every time is 0.9¹⁰ = 34.87%, so the chance of at least one hit is 65.13%, not 100%.
Sources
No outside data or rates: this is plain arithmetic.
6 automated tests check its answers on every change.
About the probability and odds calculator
Probability is the everyday maths people most often get wrong. A 10% chance tried 10 times does not add up to 100%: the tries overlap, and there is still about a one-in-three chance of never succeeding. This calculator gets three common questions right: at least once in several tries, dice totals, and lottery odds.
For repeated tries, work with the chance of failing. If each try succeeds with probability p, all n fail with probability (1 − p)ⁿ, and at least one succeeds with 1 minus that. It works for anything independent: a 1-in-6 roll, a spam filter, a game drop rate, a component that fails 1% of the time.
For dice, the calculator counts every combination. With two six-sided dice, 7 is the most likely total (6 of the 36 combinations, 16.67%) and 2 and 12 the least (1 in 36). The table shows every total for the dice you choose.
Lottery odds are the number of different tickets. Choosing 6 numbers from 49 can be done 13,983,816 ways, so one ticket has a 1 in 13,983,816 chance of the jackpot. A separate bonus ball multiplies that: US Powerball, 5 from 69 and 1 from 26, is 1 in 292,201,338. Buying ten tickets makes it ten times more likely, still roughly nothing.
Questions people ask
What is the chance of rolling a 6 in 6 tries?
66.51%: 1 − (5/6)⁶. Even with six tries there is a one-in-three chance of no 6.
What are the odds of winning a 6/49 lottery?
1 in 13,983,816 for the jackpot with one ticket.
What is the most likely total with two dice?
7, with a chance of 1 in 6 (16.67%). 2 and 12 are the least likely, 1 in 36 each.
How do I convert odds to a percentage?
For “1 in N”, divide 100 by N: 1 in 20 is 5%. For “a to b against”, the chance is b ÷ (a + b).