Probability Calculator: Chance in Many Tries
Enter the chance of one try and how many tries you make. The calculator gives the chance of at least one, of exactly a number, of that many or more or fewer, and of a streak, with a coin, a die, a colour and your own figures as starting points.
What the calculator does
Some questions repeat the same try again and again: flip a coin, roll a die, play a round that wins with a fixed chance. Give the calculator the chance of one try and the number of tries. It works out the chance that the event happens at least once, exactly a number of times, that many times or more, or that many or fewer. It also gives the chance of a streak, and how many tries it takes before at least one is likely.
The count of times an event happens in repeated tries follows a pattern called the binomial distribution. You do not need the name. It only means that every try has the same chance and does not depend on the ones before it.
How to use it
Type the chance of one try as a percentage (one in six is 16.67%), then the number of tries, then pick the question. For “exactly”, “or more” and “or fewer” also type how many times. Add a streak length to see how likely that many in a row is.
The tiles answer your question and give the average count and the range 95 runs out of 100 fall in. The table shows every count around yours. The tries-needed table shows how long you must keep trying before at least one is 50%, 90% and 99% likely. Pretend runs at the bottom check the exact figures by playing the tries with random numbers.
A worked example: ten coin flips
Ten flips of a fair coin, 50% each:
| Heads | Exactly | This many or more | This many or fewer |
|---|---|---|---|
| 2 | 4.39% | 98.9% | 5.47% |
| 3 | 11.7% | 94.5% | 17.2% |
| 4 | 20.5% | 82.8% | 37.7% |
| 5 | 24.6% | 62.3% | 62.3% |
| 6 | 20.5% | 37.7% | 82.8% |
| 7 | 11.7% | 17.2% | 94.5% |
| 8 | 4.39% | 5.47% | 98.9% |
Exactly 5 heads happens in 24.6% of runs, which is 252 of the 1,024 equally likely sequences. An even split is the likeliest single count and still only about one run in four. The chance of at least one head is 99.9%, and 95 runs out of 100 give between 2 and 8 heads. A streak of 5 heads in a row turns up somewhere in 10.9% of runs.
Flip 100 times and exactly 50 heads falls to 7.96%, while the range for 95 runs in 100 widens to 40 to 60 heads. A streak of 7 or more heads in a row turns up in 31.8% of runs of 100 flips.
Waiting does not build up a chance
A 1% chance tried 100 times gives a 63.4% chance of at least one hit, not 100%. It takes 69 tries before at least one is more likely than not, 230 before it is 90% likely and 459 before it is 99% likely. That does not make the 70th try “due”. Each try keeps its own 1%. The at-least-one figure is the chance over the whole stretch, worked out as 1 minus the chance of missing every single time.
Why streaks are normal
Streaks look suspicious and are not. Play 200 rounds that each have a 49% chance of a win, and a run of 6 wins in a row turns up somewhere 76.6% of the time. A run of 8 turns up 28.4% of the time. Long streaks of either kind are what random rounds look like, and the streaks page of the prediction simulator draws them so you can see.
What it cannot tell you
The calculator assumes every try has the same chance and does not depend on earlier tries. It does not fit drawing cards from a deck, where the chances change as cards leave, or a list of events with different chances. It cannot predict the next try, and nothing can. The chance is the one you type: if you do not know a game’s real chance, treat the answer as an illustration and use the figure your own app states.
To see what a session of rounds costs, use the expected-loss calculator. The Martingale calculator uses the streak chance to show how often a doubling plan breaks, and the odds converter turns a price into the chance it implies. The hacks and predictors overview explains why a record of past tries cannot reveal the next one, and the games guide lists four questions that show what any game costs. The rest of the free tools are one click away.
Common questions
How do I work out the chance of at least one success?
Take the chance of missing on one try, raise it to the number of tries, and subtract from 1. For a 10% chance tried 20 times that is 1 − 0.9^20 = 87.8%. The calculator shows this in its tiles, along with the chance of none, which is the part you subtract.
Why is exactly half heads so unlikely when I flip many coins?
Many counts sit close to half and they share the chance between them. In 10 flips, exactly 5 heads is 24.6%. In 100 flips, exactly 50 heads is 7.96%. The middle count is still the likeliest single one, but the counts beside it are almost as likely.
Does a long run of misses make a hit more likely?
No. Each try keeps its own chance, whatever happened before. After 20 misses at 10%, the next try is still 10%. The chance of 20 misses in a row was 12.2%, which is why a hit feels due. That is a different question from the next try.
How do I type one in six or one in 37 as a percentage?
Divide 100 by the second number. One in six is 100 ÷ 6 = 16.67%, and one in 37 is 2.70%. Type the percentage in the chance box. Decimals are fine, and 16.67 gives the same answers as one in six to three figures.
How many tries does it take for a 1% chance to come up?
69 tries make at least one more likely than not, 230 make it 90% likely and 459 make it 99% likely. Even then it is not certain, and the next try is still 1%. The tries-needed table in the results shows this for any chance you type.
Are the chances and tries I type saved or uploaded?
No. Everything is worked out in your browser and nothing is saved. If you press the copy-link button, the figures go into the link after the # sign, a part that a website never receives.