Gacha Pity Calculator

Written byOleh Soloninupdated 5 October 2026

Base rate per pull, %

Guaranteed at pull

Pulls already spent

Price per pull

Result

Pulls still to go on average, given those spent57.3
Pulls to the guarantee70
Still to spend9168 on average, 11200 at most
Average pulls from the start of the cycle69.7
Expected cost from the start of the cycle11,152
Cost of the guarantee from zero14,400
Chance before pity, %41.47%
Chance from pulls spent, %11.34%

Pity changes the whole arithmetic

Works out the average number of pulls to a drop with a pity system in place, and what that costs.

Without pity, a 0.6 percent rate would take 167 pulls on average. A guarantee at ninety cuts the tail off the distribution and brings the average down to about seventy: an enormous difference, and precisely the reason the system exists.

Two numbers are worth reading together. The average says what a drop usually costs; the pity cost says what you need on hand in the worst case. Budget on the second.

How to use

Enter the base rate for a single pull and the pull number at which pity triggers.
Say how many pulls you have already made in the current cycle.
Add the price of one pull to see the expected and the worst-case spend, both from the start of the cycle and from where you are now.
Note that the model holds the rate flat until pity: if your game ramps the rate up near the end, the real average will be lower.

What a pity counter does to the expected pull count

Each row is a run of this calculator at a pull price of 160. The expectation is summed honestly across every pull from the first to the pity, where the drop becomes certain.

Pity shortens more than the worst case — it cuts the long tail, and with it the mean. At a 0.6 percent rate with no pity the average would sit near 167 pulls; with pity at 90 it falls to 69.7, less than eighty percent of the pity count itself.

Runs of this calculator at a pull price of 160.
Base rate	Pity at pull	Mean pulls	Chance before pity	Expected spend	Worst case
0.6%	90	69.7	41.47%	11,152	14,400
1.6%	90	47.86	76.2%	7,658	14,400
0.6%	80	63.69	37.84%	10,190	12,800
3%	50	26.06	77.52%	4,170	8,000
5%	10	8.03	36.98%	1,284	1,600

What this calculator shows

The average number of pulls to a drop with pity included
The expected cost and the worst-case cost
The chance of hitting before pity, and the chance from the pulls already spent

What to keep in mind

The model uses hard pity: the drop is certain on the stated pull. The soft rate increase that some games apply just before pity is not modelled.
It does not distinguish a targeted drop from a random one: fifty-fifty systems need double the budget half the time.

FAQs

How many pulls does it take on average?

At a 0.6 percent rate with pity at ninety, about seventy. Without pity the expectation would be 167.

What is soft pity?

A gradual rate increase before the hard guarantee, which some games have; where it starts depends on the game and banner. It pulls the real average below the calculated one — this calculator models only a constant base rate followed by hard pity.

Does the counter carry between banners?

That is a rule of the particular game: whether the counter carries over, and between which banners, is set out in the banner's details.

How do I budget a fifty-fifty system?

Multiply by one and a half: half the time the first guarantee gives the wrong item and a second cycle is needed. A certain outcome costs two full pity cycles.

What is pity?

The pull number at which the item is granted for certain if it has not dropped already. At a 0.6 percent rate with pity at 90, roughly 59 percent of players reach that pull and get the item there.

Why is the mean pull count lower than the pity number?

Because some players get the item earlier. At a 0.6 percent rate, 41.47 percent land it before pity, and their short runs drag the mean down to 69.7 against a pity of 90.

Worked example

A typical banner

Input: 0.6% rate, pity at 90, 20 pulls spent, 160 per pull

Output: From the start of the cycle 69.7 pulls and 11,152 on average; after the 20 already made, 57.3 more pulls, 9,168 on average and 11,200 at most

Note: Only 41 percent of players hit before pity — most reach the ninetieth pull. So the number to plan around is 14,400, the full cost of the guarantee.

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