Short answer
Repeated attempt probability is often misunderstood because people try to add the same percentage again and again. The safer method is to calculate the chance of missing every attempt first, then subtract that from 100%.
- Repeated attempt probability is best understood by calculating the chance of missing every attempt.
- A 3% rate over 10 attempts gives about a 26.26% chance of at least one success, not exactly 30%.
- The model only applies when attempts are independent and the success rate does not change.
Last reviewed by Sha Toolbox on 2026-05-27.
Overview
Repeated attempt probability is often misunderstood because people try to add the same percentage again and again. The safer method is to calculate the chance of missing every attempt first, then subtract that from 100%.
The formula for at least one success
If each attempt has the same success rate and each attempt is independent, the chance of missing one attempt is 1 minus the success rate. The chance of missing every attempt is that miss chance multiplied by itself for the number of attempts.
The formula is: at least one success = 1 - (1 - single-attempt rate) ^ attempts. This is the same model used by the on-site repeated attempt probability calculator.
Example: 3% rate across 10 attempts
For a 3% success rate, the chance of missing one attempt is 97%. Across 10 independent attempts, the miss chance is 0.97 raised to the 10th power, which is about 73.74%.
The chance of at least one success is what remains: 100% minus 73.74%, or about 26.26%. This is lower than simply multiplying 3% by 10 because repeated attempts can all miss.
When this model does not apply
The repeated attempt formula assumes that the success rate stays the same and one attempt does not affect the next attempt. It is not the right model for shrinking prize pools, guaranteed pity systems, changing rates, or draws where previous results change the remaining pool.
- Use a without-replacement model for shrinking prize pools.
- Check the official rules when rates change after a certain number of attempts.
- Treat hidden rules or incomplete data as a major limitation.
Responsible interpretation
A higher percentage is still not a guarantee. A calculator can show risk more clearly, but it should not be used to justify chasing a random outcome. If money is involved, decide a budget before testing larger attempt counts.
Summary
- Repeated attempt probability is best understood by calculating the chance of missing every attempt.
- A 3% rate over 10 attempts gives about a 26.26% chance of at least one success, not exactly 30%.
- The model only applies when attempts are independent and the success rate does not change.
FAQ
Why not just multiply the rate by attempts?
Multiplication ignores the fact that every attempt can miss. The miss-chance formula handles repeated independent attempts more accurately.
Does a higher success chance guarantee a hit?
No. Probability describes the model, not a promise about your individual result.
Can this model handle prize pools without replacement?
No. A prize pool that removes items after each draw needs a different model because each draw changes the remaining pool.