Gacha Probability Calculator
Exact banner odds, pity included — no simulation, no guesswork. Set your rate and pulls, and read the real chance of going home with the character.
What This Calculator Does
Every gacha banner is a repeated experiment: each pull succeeds with a small fixed probability, and pity mechanics put a ceiling on how long a losing streak can run. This calculator turns that into exact answers. Set the base rate your game advertises, the number of pulls you can afford, and the hard pity (the pull at which a top-rarity drop is guaranteed — set 0 if your game has none), and it computes the chance of at least one success, the expected number of pulls per drop, your expected copies, and the pull counts you would need for 50%, 90% and 99% confidence.
Nothing here is simulated — the numbers come from the geometric distribution truncated by pity. Without pity, the chance of at least one success in N pulls is 1−(1−p)ᴺ. With a hard pity at P, no losing streak can exceed P−1, and the expected pulls per success collapses to the closed form (1−(1−p)ᴾ)/p. Soft pity — the rate ramp many games apply shortly before the cap — is deliberately ignored, which makes every number here a conservative floor: your real odds are at least this good.
How to Use It
The Mathematics of the Banner
The engine underneath every gacha is the geometric distribution: if each pull succeeds with probability p, the chance your first success arrives exactly on pull k is (1−p)ᵏ⁻¹p. Its famous property is memorylessness — the seventy pulls you already lost do not change pull seventy-one. Believing otherwise is the gambler's fallacy, the same illusion the streak counter on our Coin Flip page exists to demonstrate. What pity changes is not the memory but the tail: it amputates every losing streak at P−1, which is why a 0.6% banner with pity at 90 costs about 62 pulls per copy on average instead of the pityless 167.
The most useful number for planning is not the average but the confidence ladder. At 0.6% with pity 90, you cross 50% around pull 77 — later than most players guess, because low rates bunch successes near pity — while 99% is nearly indistinguishable from saving to the guarantee itself. That shape is why veteran players talk in guarantees rather than luck: the only number that never betrays you is hard pity. The same truncated-geometric mathematics applies unchanged to loot boxes, trading-card packs and RPG drop rates — set pity to zero and this page becomes a general drop-rate calculator, a close cousin of our exact-odds Dice Roller.
Reading Your Odds Honestly
Four habits keep gacha budgeting rational — all of them straight from the math on this page.
Budget in guarantees, not averages
The expected-pulls number is an average over many players; half do worse. If missing the character would genuinely sting, the only budget that cannot disappoint is the hard-pity count — everything short of it is a probability, not a plan.
Never chase a streak
Seventy losses do not make pull seventy-one luckier — only the pity counter improves, never the rate. Decide your total pull budget before you start, and let the confidence table, not frustration, set the number.
Respect the median
At 0.6% with pity 90, the halfway point sits near 77 pulls — meaning a majority of your attempts to "get lucky early" with 30 or 40 pulls will fail. Small speculative sessions feel cheap and lose often; the math prefers fewer, fully-funded attempts.
Count copies, not hopes
The expected-copies figure is linear: 180 pulls on a 62-pull-average banner yields about 2.9 copies on average. When a game asks for multiple copies to unlock a character's potential, multiply before you commit — the total is usually far larger than the single-copy cost that gets advertised.
FAQ
Is the gacha calculator free?
Yes — the calculator on vygam is completely free, with no download and no sign-up. Enter a rate, a pull count and a pity cap and the odds update instantly.
How does the calculator work?
It uses the exact mathematics of the truncated geometric distribution rather than simulation. Without pity, the chance of at least one success in N pulls is 1−(1−p)^N. With a hard pity at pull P, any run of P pulls is guaranteed a success, and expected pulls per success follows the closed form (1−(1−p)^P)/p.
What is pity in gacha games?
Pity is a guarantee mechanic: if you have not hit the top rarity after a set number of pulls (the hard pity, often 80–100), the next pull is guaranteed. The counter resets when you succeed. Many games also raise rates shortly before the cap (soft pity), which this calculator conservatively ignores — your real odds are at least as good as shown.
How many pulls do I need to be safe?
Truly safe means reaching hard pity: only the guarantee is certain. The calculator shows the pulls needed for 50%, 90% and 99% confidence — for a 0.6% rate with pity at 90, the 50% mark arrives near 77 pulls sooner than intuition suggests, but 99% effectively means saving to pity.
If I have pulled 70 times with nothing, am I due?
Outside of pity mechanics, no — each pull is independent, and 70 misses do not raise the next pull's base chance. That belief is the gambler's fallacy. What genuinely improves is your position relative to the hard-pity guarantee: at 70 of 90, at most 20 pulls remain until a certain success.
Why do my results feel worse than the advertised rate?
Because a 0.6% rate means the median player needs over a hundred pulls without pity — and half of all players do worse than the median. Advertised rates describe single pulls, not sessions. The expected-pulls number this calculator shows is the honest cost of one copy.
Does this apply to loot boxes and card packs too?
Yes — any repeated draw with a fixed success chance follows the same geometric mathematics: trading card packs, loot boxes, drop rates in RPGs. Set the rate, leave pity at none if the game has no guarantee, and the numbers carry over exactly.