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Gacha Pity & Pull Budget Calculator

Expected pulls and currency to reach a target, accounting for soft/hard pity — for players and economy designers.

Expected pulls per copy
Expected pulls (all copies)
Expected currency needed

Pure rate gives expected pulls = 1/rate (a 0.6% rate → ~167), but hard pity guarantees the drop by pull N, capping the unlucky tail and lowering the true average. This is an approximation; real gacha add soft pity (rising rate near the cap) and 50/50 banner mechanics that need game-specific modeling.

Formula

without pity, expected = 1/rate; hard pity caps the worst case at the guarantee, pulling the true expectation below 1/rate
References: Geometric distribution with absorbing pity barrier; Public gacha rate disclosures (regulatory)

Disclaimer: This tool is for general informational and estimation purposes only and is not professional financial, tax, accounting or legal advice. All figures are estimates — verify with a qualified professional before making decisions. Read the full disclaimer.

About Gacha Pity & Pull Budget Calculator

Gacha budgeting is geometric probability with a safety net. Without pity, expected pulls to land a 0.6%-rate character is 1/0.006 ≈ 167 — but a hard-pity guarantee at pull 90 caps the unlucky tail and pulls the true average down. This calculator estimates expected pulls and currency to reach your target copies, helping players plan savings and designers tune the rate/pity/price triangle that drives gacha revenue. (It approximates the common hard-pity model; soft pity and 50/50 banner rules vary by game and need title-specific modeling.)

How to use Gacha Pity & Pull Budget Calculator

  1. 1Enter your values into Gacha Pity & Pull Budget Calculator — sensible, domain-typical defaults are pre-filled so you see a real result immediately.
  2. 2The result recomputes live using the formula shown on the page; there is no button to press.
  3. 3Adjust any input to compare scenarios, then read the worked example to see the substituted numbers.

Why use Gacha Pity & Pull Budget Calculator?

  • Computes Gacha Pity & Pull Budget instantly in your browser — no sign-up, no upload, no server round-trip.
  • 100% free and unlimited, with the exact formula shown: without pity, expected = 1/rate; hard pity caps the worst case at the guarantee, pulling the true expectation below 1/ra.
  • Runs entirely client-side, so every value you enter stays private on your device.
  • Live recompute as you type, with a worked example and authoritative references for trust.

Frequently asked questions

Why does pity lower the expected number of pulls?+

Without pity, the geometric distribution has a long tail — some players need far more than 1/rate pulls. Hard pity truncates that tail by guaranteeing the drop at a fixed pull count, so the unlucky outcomes that inflate the average are capped. The true expectation falls below the naive 1/rate as a result.

What's the difference between soft and hard pity?+

Hard pity is an absolute guarantee at a fixed pull (e.g. pull 90). Soft pity is a sharp rate increase in the pulls leading up to it (e.g. the rate ramps from ~0.6% to ~6%+ after pull 74 in some games), so most 'pity' drops actually happen during soft pity, before the hard cap. This calculator models hard pity; soft pity lowers the real average further.

What is the 50/50 system?+

On many character banners, winning the rate-up roll is itself a coin flip: hit the drop and there's a 50% chance it's the featured character, 50% a 'lost 50/50' giving a standard unit — with the NEXT drop then guaranteed featured. This roughly multiplies expected pulls for a guaranteed featured copy by ~1.5×, on top of the pity math here.

How should designers tune rate, pity and price together?+

They define the worst-case spend (hard pity × price) and the average spend (this tool's expectation × price). Players anchor on both: the average for routine pulls, the worst case for 'how much could this cost me?'. Tuning the triangle balances revenue against the perceived fairness that retains players — too punishing a worst case drives churn.

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