At Least One Success
Calculator
Results
- Probability of at least one success
- 64.151407
- Probability of no success
- 35.848592
- Expected successes
- 1
Gaming results
| Probability of at least one success | 64.151407 |
| Probability of no success | 35.848592 |
| Expected successes | 1 |
formula-map diagram
- Probability of at least one success
- 64.151407
- Probability of no success
- 35.848592
- Expected successes
- 1
Game math relationship
Formula
P(≥1) = 1 − (1 − p)^n= 64.151407759146
Note
This is a simplified model: it applies the standard probability or game-math formula to the numbers you entered. Real games add pity systems, drop-rate tiers, rounding, server-side variance and balance patches, so treat the result as an estimate rather than a guarantee.
More in Gaming and probability
See all →Frequently asked questions
What does "at least one success" mean in a probability calculation?+
It's the probability that a specific event happens one or more times across multiple independent attempts, as opposed to happening a specific exact number of times.
Why is it easier to calculate via the complement (no successes at all)?+
Directly summing the probabilities of exactly one success, exactly two, and so on gets complicated quickly, but the probability of zero successes across all attempts is a simple product, and subtracting that from 1 gives "at least one" directly.
What's the formula for at-least-one-success probability?+
If p is the probability of success on a single attempt and n is the number of independent attempts, the probability of at least one success is 1 − (1 − p)^n.
Why does the probability approach but never reach 100%?+
Each additional attempt multiplies the "no success" probability by (1 − p) again, which shrinks that term toward zero but never makes it exactly zero for a finite number of tries with p less than 1, so there's always some residual chance of failure.
How many attempts are needed to reach a 50% or 90% chance of success?+
Solve 1 − (1 − p)^n for the target probability by taking logarithms: n = log(1 − target) / log(1 − p); this tells you, for instance, how many loot box openings you'd need for a 90% chance at a low-probability drop.