Gacha probability calculator
Enter the probability of winning on a single draw and the number of draws to calculate the chance of winning at least once or the number of draws needed to reach your target probability. Configure constant-probability draws and a draw limit that guarantees the first win separately. View the average number of draws, and the distribution of win counts for independent draws.
What you can do
Calculate win probability and required draws
Check both the probability of winning at least once in a specified number of draws and the number of draws needed to reach a target probability.
Check probability by number of wins
For draws with the same probability each time, display the probability of exactly or at least a given number of wins, and the distribution for all win counts.
Include a first-win guarantee limit in the conditions
Supports a first-win guarantee when losses continue. You can specify the guaranteed draw count and the consecutive losses so far.
How to use
Enter win probability and draw count
Enter the win probability per draw, the number of draws from now, and the target probability of winning at least once.
Change conditions as needed
In advanced settings, set the win count to examine or the first-win guarantee limit, then click “Calculate.”
Check probability and required draws
The average number of draws does not guarantee obtaining the target. Check the results and calculation conditions, then copy or save them if needed.
Useful when
Compare before deciding how many draws to make
With the same win probability, change the number of draws to 10, 30, or other counts to check differences in the probability of winning at least once.
Check the draws needed for a target probability
Specify a target such as 90% and check how many draws are needed to reach that probability.
Differences between win probability, averages, and guarantee limits
Probability for one draw and multiple draws
For independent draws, the probability of winning at least once is “1 − probability of losing every draw.” Drawing 10 times with a 3% probability is not a simple 3% × 10 calculation.
The average draw count is not a guarantee
With independent draws at 3%, the average until the first win is about 33.33 draws. This number does not guarantee a win; reaching 90% requires 76 draws.
Where the guarantee limit applies
The supported condition guarantees the first win for the same target on the specified draw if losses continue. Probability increases during the draws, other prizes, and guarantee limits for the second or later win are not included.
Frequently asked questions
Does drawing the average number of times guarantee a win?
The average is a guide over many trials, not a number that guarantees a win. Check it separately from the number of draws required for the target probability.
What if I have already lost several draws?
If there is a guarantee limit for the first win, enter this in “Consecutive losses so far” in advanced settings. For independent draws without a guarantee limit, past losses do not change the probability of winning the next draw.
What happens to the distribution when I set a guarantee limit?
With a first-win guarantee, the tool displays the probability of the first win, required draw count, average draw count, and draws remaining until the guarantee. It does not show probabilities of multiple wins or the distribution of the number of wins.
Can I calculate complex game-specific mechanics?
This screen supports independent draws with the same probability each time and a fixed guarantee limit for the first win only. Game-specific rules such as probability increases or changing targets are not included.
Input and results
- Input
- Win probability, draw count, and target probability. Optionally, the win count to examine or the first-win guarantee conditions.
- Results
- Calculated values such as probability, required draws, and averages. Independent draws also show a probability distribution by number of wins.
- Save
- Copy the calculated values rounded for display and the full distribution, or save them as .txt.