Gacha Pity Calculator

Base rate per pull, %

Guaranteed at pull

Pulls already spent

Price per pull

Result

Average pulls to a drop69.7
Pulls to the guarantee70
Expected cost11,152
Worst-case cost14,400
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.

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 starting around the seventy-fifth pull, present in several games. It pulls the real average below the calculated one.

Does the counter carry between banners?

In most games the pity counter carries between banners of the same type but not across different types. The exact rules vary by game.

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.

Worked example

A typical banner

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

Output: 69.7 pulls on average, an expected cost of 11,154

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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Gacha Pity Calculator

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