How to Use This Calculator
This calculator finds the cumulative probability of getting at least one success when pulling n times with a fixed per-pull rate p. It applies to gacha pulls, event drops, and any independent probability events.
The formula is 1 - (1 - p)^n. Even a low single-pull rate accumulates quickly over many attempts, but never quite reaches 100%.
Example: 1% Rate Cumulative Odds
| Pulls | Cumulative Odds |
|---|---|
| 50 | 39.5% |
| 100 | 63.4% |
| 200 | 86.6% |
| 300 | 95.0% |
Frequently Asked Questions
Does pulling the expected average guarantee success?
No. Pulling the average (1/p times) gives only ~63.2% cumulative probability. Success is never guaranteed without a pity system.
How many pulls for 99% probability?
n = log(0.01) / log(1-p). For 1%, you need about 459 pulls.