Gacha Pity Calculator

Gacha games use randomized loot systems where players spend in-game currency (often purchased with real money) for a chance to obtain rare characters or items. The pity system guarantees a high-rarity pull after a set number of attempts, preventing indefinite bad luck.

Key formulas:

Probability of NOT getting the item in n pulls: P(fail all) = (1 − base_rate)^n

Probability of getting the item at least once in n pulls: P(success) = 1 − (1 − base_rate)^n

Expected pulls with no pity system at all: Expected Pulls = 1 ÷ base_rate (geometric distribution)

At a 0.6% rate that works out to 167 pulls on average, which is exactly why pity exists. Once the soft pity ramp is counted the real average drops to about 62.

Currency cost: Real Money Cost = Pulls Needed × Currency per Pull × Real Money per Currency Unit

What each variable means:

• Base Rate — base probability of getting the target item per pull (0.6% in Genshin Impact for a 5-star).
• Soft Pity — the pull at which the rate starts climbing, pull 74 in Genshin. The calculator ramps the rate by roughly 6 percentage points per pull past that point, which is close to the curve players have measured.
• Hard Pity — the guaranteed pull. Genshin Impact is 90. Honkai: Star Rail is 90 on character banners but 80 on light cone banners, so check which one you are pulling on before you plan a budget.
• 50/50 — many games give the pity pull a 50% chance of being the featured item. Lose it and the next 5-star is guaranteed to be the one you wanted.

Worked example (Genshin Impact): Target: the featured 5-star character. Base rate 0.6%, soft pity from pull 74, hard pity 90, 50/50 on the featured slot.

Average case: with the soft pity ramp counted, a 5-star lands after about 62 pulls. Half the time it is the character you wanted; the other half you lose the 50/50 and need a second 5-star, which is then guaranteed. Averaged out, that is roughly 93 pulls for the specific character.

Worst case: 90 pulls to hit hard pity, lose the 50/50, then 90 more for the guarantee = 180 pulls.

At roughly $1.60 per pull:

• Average: 93 × $1.60 ≈ $149
• Worst case: 180 × $1.60 = $288

Those dollar figures move with top-up bundle promotions and regional pricing, so treat them as a ballpark rather than a quote. The pull counts are the part that does not change.