Gacha pity calculator
Enter the banner rules: the base chance of a top-rarity item, where soft pity starts and how much it adds per pull, the hard pity, and the share of top items that are the featured one. Add how many pulls you have already made since the last top item and how many you can afford. The calculator works out the exact chance, plus the average and worst-case number of pulls.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Enter the base chance and the pity rules of the banner, as published by the game.
- Enter the share of top items that are the featured one and whether losing it gives a guarantee.
- Enter your current pity count and whether you are on a guarantee.
- Enter how many pulls you can make and read the chance; the other lines show how many pulls a 50 % and a 90 % chance take.
The model
On pull i since the last top item the chance is the base rate; from the soft pity it grows by the step each pull (base + step × (i − soft + 1)), capped at 100 %, and on the hard pity pull it is 100 %. A top item is the featured one with the given share, or always if a guarantee is active. The calculator propagates the probability of every state (pity count, guarantee) pull by pull, so the chance, average, median and 90 % figures are exact for these rules.
Worked example
Default banner, starting from zero with no guarantee, 80 pulls saved:
- chance of the featured item within 80 pulls: 51 %;
- average pulls needed: 93.4; half the time it takes 80 or fewer, 90 % of the time 155 or fewer;
- worst case: lose the 50/50 on pull 90, then the guarantee at pull 180.
Tips
- Your pity count carries over between banners in many games; enter it, it changes the result a lot.
- If you are on a guarantee, tick that box: with the default banner the chance within 80 pulls jumps from 51 % to 91.8 % because no 50/50 is left.
- Plan with the 90 % line, not the average, if you must have the item before the banner ends.
Frequently asked questions
What is soft pity and hard pity?
Hard pity is the pull that always gives a top-rarity item if none came before. Soft pity is the point after which the chance grows on every pull. The calculator raises the chance by the set step on each pull from the soft pity onward until it reaches 100 % or the hard pity.
How does the 50/50 guarantee work?
When you get a top item, it is the featured one with the chance you set (50 % by default). If it is not, many games make the next top item the featured one; switch the guarantee on for that rule. Then the worst case is two full pity cycles.
What do the default numbers mean?
They are an example of a common banner design: 0.6 % base, soft pity from pull 74 with +6 % per pull, hard pity at 90 and a 50/50 with a guarantee. From zero, 80 pulls give about 51 %, the average is 93.4 pulls and the worst case is 180. Check the rates your game publishes and enter them.
Why is the average far above the base rate suggests?
1 ÷ 0.6 % would be 167 pulls, but pity cuts that down to about 62 for any top item; the 50/50 then adds roughly half of another cycle on average.
Is the result exact?
Yes, for the rules as entered: it tracks every possible pity count and guarantee state pull by pull instead of simulating. Real games may use other ramp shapes, so the result is as good as the rules you enter.