Gacha Probability Calculator – Pity and 50/50

How to use the Gacha Probability Calculator

Pick a probability model preset, or choose "Custom" and enter the rates and pity rules.
Enter how many pulls you plan to do and how many copies you want (e.g. 1, or 7 for max constellations / eidolons).
If you already have pity built up or a guarantee, enter "Current pity" and tick "Guaranteed".
Your success chance, average pulls and pulls needed appear instantly; add a cost per pull to convert to currency.

Examples

90-pull character banner: chance to get the featured unit in 90 pulls

Input

Model: 90-pull character banner | 90 pulls | 1 copy | 0 pity, no guarantee

Output

Chance: 59.4%
Average: 93.5 pulls
50% odds: 80 pulls | 90% odds: 155 pulls
Worst case: 180 pulls

A 1% rate with no pity — will 100 pulls hit?

"1% means 100 pulls guarantees it" is a common myth — there is about a 36.6% chance of getting nothing.

Input

Rate 1% | no pity | 100 pulls

Output

Chance of at least one: 63.4%
Average: 100 pulls

How pity and 50/50 work

Hard pity guarantees a top-rarity drop after a set number of pulls without one (for example pull 90). Soft pity raises the rate on each pull as you approach hard pity (for example +6% per pull from pull 74), so most drops land between pulls 74 and 80. 50/50: each top-rarity drop has a chance (for example 50%) to be the featured unit; if you lose, the next one is guaranteed. Getting one featured unit therefore takes at most two pity cycles (180 pulls) and about 93 pulls on average.

The calculator runs an exact dynamic-programming model over pity count × guarantee × copies obtained — not a simulation — entirely in your browser.

Specs & key facts

Method	Exact dynamic programming (not Monte Carlo)
Rules	Base rate, soft pity ramp, hard pity, featured rate, guarantee after losing
Presets	90-pull character banner (0.6%, +6%/pull from 74, 50/50); 80-pull weapon / light cone banner (0.8%, +7%/pull from 66, 75/25)
Output	Chance within N pulls, average pulls, pulls for 50 / 90 / 99%, worst case, cumulative chart
Copies	1 to 7
Data note	Soft pity values come from community statistics; official announcements take precedence

FAQ

With a 1% rate, are 100 pulls guaranteed to hit?

No. With independent pulls, the chance of at least one hit in 100 pulls is 1 − 0.99¹⁰⁰ ≈ 63.4%, so about 36.6% of players get nothing. You need about 459 pulls for 99% odds.

Why is the "consolidated rate" 1.6% when the base rate is 0.6%?

The consolidated rate includes pity: on average a top-rarity drop takes about 62 pulls, which is roughly 1.6% per pull. This calculator uses the base rate plus pity rules and matches that figure.

I already have 60 pity. How do I account for it?

Enter 60 in "Current pity". Existing pity brings hard pity closer and reduces the pulls you need; if you lost your last 50/50, also tick "Guaranteed".

Which games does it work for?

Any gacha with independent pull rates plus pity — just enter the game's published rates. Presets fit 90-pull character banners with 50/50 and 80-pull weapon / light cone banners with 75/25.

What is the difference between "average pulls" and "50% odds"?

The average is pulled up by very unlucky cases; 50% odds is the point by which half of players succeed. When saving currency, plan for the 90% figure.