🎰Gacha Probability Calculator

Why don't you always win even after pulling 1% probability 100 times

When pulling a 1% drop rate gacha 100 times, the probability of getting at least one copy is about 63.4%, not 100%. Each draw is independent, and there's a probability of losing all 100 times (0.99 to the 100th power, about 36.6%).

• Formula for at least one win probability：The probability of getting at least one copy is calculated as "1 − (1 − drop rate) to the power of pulls". With 1% drop rate, you need 230 pulls to reach about 90% and 459 pulls to reach about 99%.

What is expected pulls (expected value)

Expected pulls is the average number of pulls needed to get your target item when repeating the same gacha many times. Expected pulls is calculated as "100 ÷ drop rate (%)", so with 1% drop rate it's 100 pulls, and with 3% it's about 33.3 pulls.

• Expected pulls are not a guarantee：Even if you pull 10 times (the expected pulls) on a 10% drop rate gacha, the probability of getting at least one copy is only about 65.1%.

Why the number of pulls needed for completion becomes so large

The number of pulls to get all types is often many times the number of types. As you collect more items, new items become harder to get, and the last item takes longer, which is called the Coupon Collector Problem.

• Case of 10 equal probability items：For a gacha with 10 items at 10% each, the expected pulls to complete all is about 29.3, which is about 2.9 times the number of types.
• When drop rates differ：When drop rates differ, the least common item increases the count, and with 3 types at 1%, 2%, and 3%, the expected pulls become about 121.7.