Probability and Trial Calculator
Calculate the chance of at least one success from a rate and number of trials.
This calculation assumes independent trials with the same success rate each time. It does not include pity systems, changing rates, guaranteed rewards, or duplicate protection. The expected count is an average, not a guaranteed result.
Common values
Repeated trials at 1% per trial
| Trials | At least one | No success |
|---|---|---|
| 10 | 9.562% | 90.438% |
| 25 | 22.218% | 77.782% |
| 50 | 39.499% | 60.501% |
| 69 | 50.016% | 49.984% |
| 100 | 63.397% | 36.603% |
| 200 | 86.602% | 13.398% |
| 299 | 95.046% | 4.954% |
| 459 | 99.008% | 0.992% |
About this tool
Enter the success rate per attempt and the number of independent trials to calculate the chance of at least one success, the chance of no success, and the expected count. It also shows the trials needed to reach common target probabilities.
Enter the success chance for one attempt. For example, for 100 attempts at a 1% rate, enter 1 for the rate and 100 for the number of trials.
The chance of at least one success is one minus the chance of no successes. The expected count is a long-run average and may not match the outcome of any one set of trials.
FAQ
- What is the chance of winning at least once in 100 trials at 1%?
- It is 1 − (1 − 0.01)^100, approximately 63.3968%. Multiplying 100 trials by 1% does not produce a 100% chance.
- How many 1% trials are needed to reach 50%?
- The smallest count for at least 50% is 69 trials. At 69 trials, the chance is approximately 50.0163%.
- How does expected successes differ from chance of at least one?
- Expected successes is probability times trials and represents a long-run average count. Chance of at least one subtracts the all-failure probability from one.
- Must the trials be independent?
- Yes. The formula assumes the same success probability each time and no effect from earlier results. Changing or linked probabilities require another model.
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