Gacha probability calculator

How to read your gacha odds

This calculator answers two questions: given a drop rate, how likely are you to get at least one copy in a set number of pulls, and how many pulls do you need to reach a chance you are happy with?

Using the calculator

1. Enter the drop rate as a percentage. A 0.6% rate is typed as 0.6, not 0.006. Decimals down to 0.01 work.
2. Enter the number of pulls you plan to make or can afford. A ten-pull counts as 10.
3. Read Chance of at least one and Expected number. The expected number is pulls × rate: the average number of copies you would get if you repeated the same attempt many times.
4. Under Pulls needed for a target chance, enter a target between 1% and 99%. The result is rounded up to a whole number of pulls.

What the calculator assumes

The maths treats every pull as an independent event with the same fixed rate. Under that assumption, the chance of missing n times in a row is (1 − rate)^n, and the pulls needed for a target chance T is ln(1 − T) ÷ ln(1 − rate), rounded up. The calculator does not know about pity, guarantees, rate-ups or 50/50 rules. That makes it exact for systems with no pity and only a rough guide for games that have one.

Worked example

Take a 0.6% rate and 90 pulls. The chance of missing on a single pull is 0.994, so missing all 90 is 0.994^90 ≈ 0.582. The chance of at least one is 1 − 0.582 ≈ 41.8%, and the expected number is 90 × 0.006 = 0.54. To reach a 50% chance you would need 116 pulls; 90% takes 383. With independent pulls the chance never quite reaches 100%, however many pulls you make.

Pity and soft pity

Many gacha games add a pity system on top of the base rate:

• Hard pity guarantees a top-rarity drop by a fixed pull count, for example pull 90.
• Soft pity raises the rate sharply once you pass a certain count, before hard pity is reached.
• 50/50 or featured guarantees decide whether a top-rarity drop is the featured character or item. Some games guarantee the featured one after you lose a 50/50.

Pity changes the maths a lot. In the example above, a game with a 0.6% base rate and hard pity at 90 gives a 100% chance of a top-rarity drop within 90 pulls, not 41.8%. So when pity applies, this calculator understates your chances, especially as you approach the pity threshold. Whether pity carries over between banners, and the exact soft-pity point, vary by game, so check the game's own rate details.

Getting closer numbers

• If you only want the featured item and it gets half of all top-rarity drops, enter half the rate (0.3% instead of 0.6%) to estimate it without guarantees.
• Some games publish a "consolidated" rate that includes pity. Using it gives a better long-run expected number, but the at-least-one figure will still be off near pity thresholds.
• If you already have pity built up, what matters is how many pulls remain until the guarantee. If your budget covers that, the drop is certain.

Common mistakes

• Typing the rate as a decimal. Entering 0.01 for a 1% rate gives odds 100 times too low.
• Multiplying rate by pulls and calling it a probability. That is the expected number, which can go above 1 even when your chance is well below 100%.
• The gambler's fallacy. With no pity, a long losing streak does not make the next pull more likely to hit. With pity it does, which is exactly what pity is for.
• Deciding the budget after pulling. Choose the chance you are willing to accept and the pulls you can afford first, then stick to it.

More calculators are in the gaming tools collection.