Generic gacha math · user-supplied inputs

Copies Within Pulls Probability Calculator

Model a multi-copy target with the binomial distribution rather than multiplying a single-hit percentage.

Quick answer

Example: At a constant 1% target rate over 200 pulls, the expected count is 2, but the chance of receiving at least two copies is a separate binomial result.

Chance to reach copy target —

Expected copies —

Target minus expected copies —

What this calculator does

A multi-copy target asks for the probability of two, three, or more successes, not merely one. The calculator sums the relevant binomial outcomes from the requested copy count through the total number of pulls.

The expected copy count is pulls multiplied by the target rate. It is a long-run average, while the target probability measures how often an entire pull session would reach the chosen threshold.

This page assumes a fixed target rate and independent attempts. It deliberately does not import constellation, dupe, featured-loss, or pity rules from any particular game.

Formula

P(copies ≥ k) = 1 − sum of binomial probabilities for 0 through k − 1 copies

Example: At a constant 1% target rate over 200 pulls, the expected count is 2, but the chance of receiving at least two copies is a separate binomial result.

FAQ

Why can expected copies equal the target while probability stays below 50%?

Expectation is an average across many sessions and can be pulled upward by sessions with more than the target count.

Can copies wanted exceed pulls?

Yes, but the returned probability is zero because that outcome is impossible.

Does this include guarantees after a miss?

No. Every pull uses the constant independent rate you enter.

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