A general calculator for repeated attempts
This page answers two common questions: what is my chance after a certain number of tries, and how many tries do I need to reach a target probability? It is the cleanest version of the math behind gacha pulls, blind box estimates, random prize entries, and many collectible pack decisions.
The key assumption is that every attempt has the same success rate. If the rate changes over time, a prize is removed from a pool, or a guarantee activates after enough attempts, you need a more specific model. For ordinary independent attempts, this calculator keeps the answer simple and transparent.
The reverse calculation is especially useful for planning. A 1% chance per attempt needs 69 attempts to pass a 50% chance, while a 5% chance needs only 14 attempts. Seeing that difference can help you avoid unrealistic expectations before you buy.
Formula
P = 1 - (1 - r)^n; attempts needed = ln(1 - target probability) / ln(1 - r) The first formula calculates the probability of at least one success after n attempts. The reverse formula rearranges the same relationship to estimate how many attempts are needed for a chosen target probability.
The result for attempts needed is rounded up because you cannot make a fraction of a pull, box, or draw. For example, if the math says 13.52 attempts, the practical answer is 14 attempts.
Example use cases
1% success rate
At 1% per attempt, 10 attempts gives about 9.56%. You need 69 attempts to reach at least a 50% chance.
3% success rate
At 3% per attempt, 10 attempts gives about 26.26%. You need 23 attempts to reach at least a 50% chance.
5% success rate
At 5% per attempt, 20 attempts gives about 64.15%. You need 14 attempts to reach at least a 50% chance.
Responsible use
Probability can help you understand risk, but it cannot guarantee a win. If you are buying pulls, boxes, packs, or prize tickets, set a budget first and avoid spending more than you can afford. A calculator is a planning aid, not a reason to chase losses or ignore your limit.
FAQ
What does at least one success mean?
It means one or more successful outcomes. Getting two, three, or more successes is still counted as a success for this calculation.
Why does the reverse calculator use logarithms?
The number of attempts is inside an exponent in the original formula. Logarithms let the calculator solve for that attempt count.
Can I use this for prize draws?
Use it for independent draws where each attempt has the same rate. For a shrinking ticket pool, use the Ichiban Kuji-style calculator.
Can the attempts needed ever be infinite?
If the success rate is 0%, success is impossible. The calculator requires a rate above 0 and below or equal to 100.
Related tools
Gacha Calculator
Calculate your chance of getting at least one target item from gacha pulls based on drop rate and number of pulls.
Expected Cost
Estimate how much you may spend to reach a target probability in gacha pulls, blind boxes, or random packs.
Ichiban Kuji Calculator
Estimate your chance of drawing a target prize from an Ichiban Kuji-style prize pool without replacement.
Helpful guides
How Gacha Probability Works
Learn how gacha probability works, why repeated pulls do not add up directly, and how to read at least-one-success odds.
Blind Box Odds Explained
Understand blind box odds, equal variant assumptions, secret item limits, duplicate risk, and how to compare boxes with resale prices.