Gacha Simulator: Pity, Pull Odds and Expected Pulls

This gacha simulator works out exactly how many pulls it takes to get the top-rarity item when the rate has soft and hard pity, and the chance that your pulls are enough for one copy or several. With a 0.6% base rate, soft pity from pull 74 and hard pity at 90, the item takes 62.3 pulls on average, an effective rate of about 1.6%, and 9 in 10 copies arrive by pull 80. Set your own rates below, or press Pull ×10 to try your luck.

What is pity in gacha?

Pity is a counter that raises your chance of the top-rarity item the longer you go without one, and resets when you get it. Hard pity is the pull where the item is guaranteed: with hard pity at 90, the 90th pull since your last top-rarity item always hits. Soft pity is a ramp before that: from a set pull, every pull adds a few percentage points to the rate. In the default preset the rate is 0.6% up to pull 73, then 6.6% on pull 74, 12.6% on pull 75, and so on, until hard pity makes it 100%.

A system with no pity is a flat rate. Every pull has the same chance whatever happened before, so a long dry run makes the next pull no more likely to hit.

How many pulls does it take to get the top-rarity item?

With soft pity from 74 and hard pity at 90 on a 0.6% base, it takes 62.3 pulls on average. Most copies come from the soft pity ramp: only 35.55% arrive by pull 73, while 56.29% land on pulls 74 to 80. Half of all copies have arrived by pull 76 and 9 in 10 by pull 80, so reaching hard pity itself is very rare.

The flat row shows what pity is worth. At 0.6% with no pity the average is 1 ÷ 0.006 = 166.7 pulls, only 41.82% of players have the item after 90 pulls, and 1 in 10 still waits past pull 383. With hard pity at 80 and no soft pity, 27.96% of copies come from the guarantee itself.

What is the effective rate in gacha?

The effective rate is one copy divided by the average pulls it takes, so it counts the pity pulls as well as the base rate. For the default preset it is 1 ÷ 62.3 = 1.61%, almost three times the 0.6% base. The simulator shows it next to the base rate. It is the right figure for budgeting over many copies, though not for one: a single copy is far more likely to arrive late, around pull 76, than at the average.

How many pulls for two or more copies?

The counter resets after each hit, so every copy is a fresh run and the averages add up: two copies take 2 × 62.3 = 124.6 pulls on average with the default preset. The spread does not double, though. Half of all pairs are done by pull 135 and 9 in 10 by pull 158, and a budget of 140 pulls is enough for both copies 52.89% of the time. Set the copies and your pulls above to see your own chance.

How the gacha maths works

Count k as the pulls since your last top-rarity item, this one included. The rate on pull k is

p(k) = min(1, base + max(0, k − softStart + 1) × step), and p(hardPity) = 1.

The chance that the first hit is on pull k is that rate times the chance that every earlier pull missed: P(k) = p(k) × (1 − p(1)) × … × (1 − p(k − 1)). The average is the sum of k × P(k), and the median and 90th percentile are the first pulls where the running total reaches 50% and 90%. For several copies the tool convolves that distribution with itself once per copy, which gives the exact chance of every total. With no pity at all it is the geometric distribution (average 1 ÷ rate) and, for several copies, the negative binomial. Nothing here is estimated by random runs; only the Pull ×10 log is random.

Is a pull ever due?

Only when pity says so. Under a pity system the rate really does rise with every miss, so a long run without the item makes the next pull more likely to hit. Under a flat rate it does not: 200 misses at 0.6% leave the next pull at 0.6%. Believing otherwise is the gambler's fallacy, which our gambling odds explained article covers.

Gacha pulls and Gift Club boxes

This page is neutral maths for a generic gacha pity system. Gift Club's boxes are a different thing: they are opened one at a time, not pulled from a banner, and have no pity counter for this simulator to model. Our mystery box game article explains how they work.

Frequently asked questions