Games · Gacha

Gacha Pull Expected Value

Most gacha calculators just do "expected number of pulls to hit pity, times cost per pull". This one compares up to four banners side-by-side and converts expected pulls to dollar cost including currency pack bonuses and tax-free thresholds. With optional pity guarantee, 50/50 loss, and a whaling simulator that tracks monthly spend vs budget.

Banner A (target)

Base rate p% (single pull)

Pity threshold (pulls)

Pity guarantees?

50/50 (loss to off-rate)

Pull cost (in-game currency)

USD per 100 currency

Banner B

Base rate p%

Pity threshold

Pity?

50/50?

Pull cost

USD/100c

Cost-per-hit comparison

Whaling simulator

Monthly budget $

Months to plan

Pulls/mo from gameplay

% who hit pity ≤ budget

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Median USD spent

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Median hits in horizon

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Advertisement slot · natural placement

Method note

Expected pulls to hit a target under hard pity is the standard mixture of geometric waiting time (rate per pull) capped at the pity threshold, with adjustment for 50/50 (multiply by 2 if lose). Concretely: E = (1 − (1−p^★)^k) / p^★ where p^★ = effective pull rate; with hard pity we cap at k, so the worst case is exactly k.

For dollar cost we multiply expected pulls by pull cost, then divide by per-100-currency USD, with an optional first-purchase bonus (max +50% extra) applied to the spending-only part. Whaling simulator runs 1,000 streams and reports mean/median cost.

Who uses this

F2P budgeters

Estimate which banner to pull on given limited saved currency. See when pity guarantees make the "wait" banner strictly better.

Whales / dolphins

Set a reasonable monthly budget and see the expected number of limited characters for it.

Game-econ students

Manipulate rates to see the gradient of revenue vs player perceived fairness.

When not to trust this

Soft pity "rate increase" curves are non-uniform and not modeled here.
Some banners have a "guaranteed on next 5★" mechanic that boosts the effective rate as pulls pile up.
First-purchase bonus structures vary by region — check your store before treating USD figures as ground truth.

FAQ

What's "50/50 loss"?

Some games give you a feature banner 5★ only half the time, the rest being a "standard" character. If you lose the 50/50, your next 5★ is guaranteed to be the featured one. The effective p★ halves; we show that as a 2× multiplier on expected pulls.

How does the whaling simulator work?

We simulate 1,000 deterministic pull sequences (without RNG; we precompute the distribution) and report where each player's monthly budget runs out versus when pity triggers. Median hit count tells you "50% of players got at least this many".