Gacha Probability Calculator (Expected Value & Pity Simulator)

Gacha probability calculator: enter your drop rate, number of pulls, and pity counter to get exact binomial odds, expected draws, median draws, and expected cost.

What Is a Gacha Probability Calculator?

A gacha probability calculator answers a question that gut feeling gets wrong more often than you'd expect: if an item drops at a fixed rate, what are the real odds of pulling it within a given number of tries? Rather than guessing, this tool applies the binomial distribution — the same statistical model used for coin flips and dice rolls — to turn "a 3% drop rate over 90 pulls" into a precise, calculable percentage. It works for any repeated trial with a fixed, independent success probability, but it's especially useful for the gacha mechanics found in mobile and social games, where drop rates are usually published but rarely translated into something a player can act on.

Beyond the basic hit probability, this calculator also accounts for pity systems — the increasingly common safety net where a guaranteed drop kicks in after a set number of consecutive misses. Factoring in pity changes the math meaningfully: without it, the number of draws needed for a hit is theoretically unbounded, but with it, your expected and median draw counts become more realistic and typically lower. Add your desired item count and the cost of a single draw, and you'll also get a straightforward estimate of what reaching your goal is likely to cost.

How to Use the Gacha Probability Calculator

Enter the drop rate Input the official per-pull drop rate for the item you're after (for example, 3% or 0.6%). Most games publish this figure on their official site or within the game's rate-disclosure screen.
Enter the number of draws Enter how many pulls you're planning to make, or how many you've already made, so the calculator can evaluate the odds over that exact window.
Enter your desired count Leave this at 1 if a single copy is enough. If you're chasing duplicates for upgrades or "dupes," enter the total number you're aiming to collect.
Enter the pity count, if any If the game guarantees a hit after a certain number of consecutive misses, enter that threshold here. If there's no such system, just leave it at 0.
Review your results and the probability chart The calculator instantly displays your hit probability, expected and median draw counts, an expected cost estimate (if you entered one), and a chart showing how the odds climb as your draw count increases.

Tips for getting more out of it

Expected value and median frequently diverge, and the gap grows as the drop rate falls. That's because a small number of extremely lucky pulls drag the average upward, so for rare items the expected value will usually sit noticeably higher than the median.
Getting closer to your pity threshold can feel reassuring, but it's worth remembering that your odds on any individual pull before that point are still governed purely by the drop rate — pity only guarantees the outcome once you actually reach the ceiling.
If you're chasing multiple copies, most games reset the pity counter after every confirmed hit. This calculator assumes that reset happens each time, so its "desired count" results reflect pity restarting from zero after every hit.
If your game publishes the drop rate as a fraction rather than a percentage (for example, 1 in 166), convert it first by dividing 100 by 166 (about 0.6%) before entering it here.

When This Calculator Comes in Handy

Budgeting before you spend

Get a realistic estimate of how much you'd expect to spend to land a specific item before opening your wallet, so you can decide up front whether the odds are worth the cost.

Planning around a pity system

For games with a guaranteed-drop mechanic, see how factoring in pity brings your expected and median draw counts down to a more grounded, realistic figure.

Deciding whether a pull is worth it

Put a hard number on your odds within a given budget of draws, which can be exactly the reality check you need to walk away from a low-probability chase.

Teaching probability with a familiar example

Use a scenario most students already recognize to make the binomial distribution click, turning an abstract formula into something concrete and motivating.

Glossary

Drop Rate: The probability of pulling your target item on any single gacha draw. This figure is usually published officially by the game, either in-app or on an official rates page, and should be used as-is rather than estimated.
Pity: A safety-net mechanic that guarantees a hit on your next draw (or within a defined window) once you've missed a set number of times in a row. The term comes from English-language player communities describing the system as the game taking "pity" on unlucky players.
Binomial Distribution: The probability distribution describing how many successes occur when a trial with a fixed success probability p is repeated n independent times. It's the mathematical foundation this calculator uses to work out gacha hit probabilities.
Expected Value: The long-run average of a random outcome, calculated as the sum of each possible value weighted by its probability. Here, the "expected draws" figure represents the average number of pulls you'd need if you repeated the same scenario many times over.
Median: The middle value of a data set when sorted in order. The "median draws" figure means that half of all players would hit their target by that draw count or earlier, which often reflects typical player experience more closely than the average (expected value) does.

Frequently Asked Questions

No. A 3% drop rate over 100 pulls averages out to roughly 3 hits, but the actual outcome follows a binomial distribution and will vary — you could end up with zero hits or five or more. This calculator gives you the exact probability for any specific number of hits.

Without pity, the number of draws needed for a hit has no upper limit, even though it becomes vanishingly unlikely to keep missing forever. With pity, a hit is guaranteed by a fixed draw count, which pulls both the expected value and the median down to lower, more favorable numbers than the no-pity calculation would give.

It's worth checking both. Expected value tells you the long-run average, but for low drop rates a handful of extremely lucky outcomes can pull that average well above what most players actually experience — the median, representing the point at which half of all players have already hit, often lines up more closely with typical results.

Yes. Entering a desired count of 2 or more calculates the total expected draws under the assumption that pity resets after each confirmed hit. Since pity implementations vary by game, it's worth double-checking that assumption against your specific game's rules.

Yes. Rather than computing factorials directly, which can overflow or lose precision for large draw counts, this calculator builds up the binomial probability mass function through a recurrence relation, keeping results accurate even for drop rates well below 0.1%.

Side Note — Where "Gacha" Comes From, and How Its Odds Became Regulated

The word "gacha" is widely believed to be onomatopoeia — it echoes the mechanical "gacha-gacha" sound of turning the handle on a capsule-toy vending machine. Coin-operated capsule dispensers of this kind originated in the United States in the mid-1960s before being imported to Japan, where they evolved into a beloved pop-culture fixture in their own right. That same thrill of not knowing what you'll get was later carried over into the randomized item-draw systems of mobile and social games in the early 2010s, and the borrowed name stuck.

Gacha odds haven't always been a settled matter, either. In Japan, a particular mechanic known as "kompu gacha" — which encouraged players to collect a full set of rare cards by combining cheaper ones, with the completed set unlocking an especially desirable reward — drew regulatory scrutiny in the early 2010s under consumer protection law governing prize-linked sales schemes. Major publishers phased the mechanic out fairly quickly afterward, and industry self-regulation followed, pushing many social games toward the now-common practice of publishing their drop rates openly.

The rise of pity systems tracks closely with that same shift toward transparency. Once players could see exactly how low a drop rate really was, the experience of pulling dozens of times without success became a much sharper source of frustration — and a much bigger risk to player goodwill and spending. Guaranteeing a hit after a fixed number of attempts let developers keep the excitement of randomness while capping the worst-case outcome, and the approach has since become close to an industry standard.

Step back far enough, and calculating gacha odds is really just a modern costume on one of probability theory's oldest problems: repeated independent trials with a fixed chance of success. The binomial distribution that powers this calculator was formalized by the Swiss mathematician Jacob Bernoulli in the early 18th century, published posthumously in his 1713 work Ars Conjectandi. It's a small thrill to realize that a three-hundred-year-old mathematical framework, developed with no video games in sight, turns out to describe the mechanics of a smartphone gacha pull with total precision.

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