Calculate at least one success
With a 3% rate across 10 independent attempts, the chance of at least one success is about 26.26%.
It answers “what is the chance I get at least one success?”
This repeated probability calculator is useful when each attempt has the same success rate and one attempt does not change the next attempt. It shows both the chance of at least one success and the chance of missing every attempt.
The miss chance matters because repeated attempts can still leave a large amount of risk. A higher attempt count does not turn a low single-attempt rate into a guaranteed result.
How the repeated probability formula works
The calculator first estimates the chance of missing every attempt. It then subtracts that miss chance from 100% to estimate the chance of at least one success.
Worked example: 3% chance over 10 attempts
If one attempt has a 3% chance and you try 10 times, the calculator gives about 26.26% for at least one success. This also means the chance of missing every attempt is still about 73.74%.
The important point is that 3% over 10 attempts is not exactly 30%. Each attempt can miss, so the calculator uses the probability of missing all 10 attempts first: 0.97 to the 10th power.
When this model fits and when it does not
Use this calculator for independent attempts with a fixed success rate. It can fit simple classroom probability examples, repeated checks, or fixed-rate random attempts where the rate does not change.
Do not use this calculator for pity systems, changing odds, hidden rules, shrinking prize pools, or draws without replacement. Those situations need a different probability model.
Common mistakes and limitations
The most common mistake is multiplying the single-attempt rate by the number of attempts and treating that as the final probability. That shortcut can overstate the result, especially as the number of attempts grows.
- The model assumes each attempt is independent and has the same success rate.
- It does not handle pity systems, changing odds, shrinking prize pools, without-replacement draws, or hidden rules.
- It cannot predict a specific result or guarantee success.
FAQ
Why is 3% across 10 attempts not exactly 30%?
Because each attempt can miss. The formula calculates the chance of missing every attempt first, then subtracts that from 100%.
What does independent attempt mean?
It means one attempt does not change the success rate of the next attempt. If the rate changes after each attempt, this calculator is not the right model.
Can this calculator guarantee a result?
No. It explains probability under a simple model. Random outcomes can still miss even when the success percentage looks high.
What is miss chance?
Miss chance is the probability of failing every attempt. This calculator shows it because the remaining risk can still be large even after many attempts.
Can I use this for gacha or blind box odds?
Only when each attempt is independent and the success rate stays the same. If there is a pity system, changing rate, or shrinking pool, use a model built for that situation.