Gacha Probability Calculator

Frequently Asked Questions

How many pulls should I save?

Budget the pulls-for-confidence figure at a confidence you can accept (90% is common) rather than the expected value, which leaves you short more than a third of the time.

Does pity make this calculation wrong?

Real games with soft pity raise the effective rate near the cap. Treat this calculator as a conservative floor and the hard-pity ceiling as your guaranteed worst case.

Why did I hit it on pull 3?

Variance. The geometric distribution has a long tail, so early jackpots and brutal dry streaks are both completely expected outcomes across many banners and players.

Should I do a 10-pull or singles?

Mathematically the per-pull odds are identical. 10-pulls only matter if the game guarantees a minimum rarity per batch.

What if the banner shares the rate across many characters?

Enter the rate for the specific item you want, not the combined featured rate. A 50/50 split or shared pool can halve or quarter the chance the formula reports.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How It Works

Gacha and loot-box systems advertise a per-pull drop rate, but players really want to know "what are my odds across a whole batch of pulls?" That is a classic at-least-one probability problem. Each pull is an independent trial with success probability p, so the chance of never hitting it in N pulls is (1 − p)^N, and the chance of getting it at least once is the complement, 1 − (1 − p)^N.

This tool also reports the expected number of pulls (1 ÷ p, the mean of a geometric distribution) and inverts the formula to tell you how many pulls you need to reach a chosen confidence level - the honest way to budget currency before you spend it.

An optional pity counter adds your already-accumulated pulls to N, since those failed attempts still count toward the same independent-trial pool. A true hard-pity guarantee is a separate ceiling this simple model does not enforce but the hard-pity number serves as your guaranteed worst case.

Use Cases

This calculator helps players make informed decisions about spending gacha currency:

Deciding whether to spend remaining currency on a banner or save it for the next one given the current pull count.

Calculating how many pulls to save before a new banner to have a 90% or higher chance of success.

Checking whether a limited-time banner is worth spending on versus waiting for a guaranteed rerun.

Comparing two banners with different rates to find which is more currency-efficient for the desired item.

Understanding how the pity counter already accumulated affects your current odds and remaining budget.

Tips

Budget to confidence, not expected value: The expected pulls figure leaves you short more than a third of the time - plan using the pulls-for-confidence at 90% for a realistic safety margin.

Pity makes this model conservative: Real games with soft pity raise the effective rate near the ceiling, so your true odds late in a pity cycle are better than this independent model says.

10-pulls vs. singles are mathematically equal: Per-pull odds are identical. 10-pulls only matter if the game guarantees a minimum rarity per batch.

Enter the rate for your specific item: A 50/50 split or a shared 5-star pool can halve or quarter the chance the formula reports - using the combined rate is the most expensive mistake new players make.

Variance is expected: Early jackpots and brutal dry streaks are both completely expected outcomes when you sum across many banners and many players. The math is working correctly either way.

FAQ

How many pulls should I save?

Decide on a confidence you can accept (90% is common) and budget the pulls-for-confidence figure rather than the expected value, which leaves you short more than a third of the time. The gap is often several dozen pulls on a 0.6% banner.

Does pity make this calculation wrong?

Real games with soft pity raise the effective rate as you approach the cap, so your true odds at high counts are better than this independent model says. Treat the calculator as a conservative floor and the hard-pity ceiling as your guaranteed worst case.

Why did I hit it on pull 3?

Variance. The geometric distribution has a long tail, so early jackpots and brutal dry streaks are both completely expected outcomes across many banners and players.

Should I do a 10-pull or singles?

Mathematically the per-pull odds are identical. Ten singles and one ten-pull have the same chance of success, so 10-pulls only matter if the game guarantees a minimum rarity in each batch.

What if the banner shares the rate across many characters?

Enter the rate for the specific item you want, not the combined featured rate. A 50/50 split or a shared pool can halve or quarter the chance the formula reports.

Gacha Probability Calculator

Frequently Asked Questions

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