Generic gacha math · user-supplied inputs

At Least One Drop Probability Calculator

Answer the basic “one or more” probability question with a stable closed-form calculation instead of repeated simulation.

Quick answer

Example: At a constant 0.6% rate across 90 independent pulls, the chance of at least one drop is about 41.8%, while the expected count is 0.54.

Chance of at least one drop —

Chance of zero drops —

Expected number of drops —

What this calculator does

For independent pulls with a constant rate, the easiest event to calculate is the opposite one: missing every pull. Raising the miss probability to the number of pulls gives the zero-drop chance; subtracting it from one gives at least one drop.

Expected drops and probability are different. An expectation of 0.54 drops does not mean a 54% chance unless the surrounding distribution happens to make them close. The calculator reports both quantities so they are not confused.

Do not use this constant-rate model for a banner whose rate changes with a pity counter. It is intended for fixed-rate scenarios entered by the user.

Formula

P(at least one) = 1 − (1 − per-pull rate) ^ pulls

Example: At a constant 0.6% rate across 90 independent pulls, the chance of at least one drop is about 41.8%, while the expected count is 0.54.

FAQ

Why is 0.6% times 90 not the final probability?

Multiplication gives the expected count. At-least-one probability must account for the possibility of multiple successes.

Are pulls assumed independent?

Yes. A changing pity rate violates that assumption and needs a different model.

Does a 100% result mean an official guarantee?

The display can round very high probabilities; only the entered mathematical model is being evaluated.

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