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Expected Pulls Calculator

Enter the drop rate and a target confidence to estimate the pulls you need.

How it is calculated

The drop rate p is entered in percent (0.6 means 0.6%, not 60%) and must be above 0 and at most 100. The average number of pulls until the first success is E = 1 / (p ÷ 100), shown to two decimals. The pulls needed for a chosen confidence c (also in percent) come from n = ln(1 − c/100) / ln(1 − p/100), rounded up to a whole pull, because you cannot make part of a pull.

The confidence is the chance of getting at least one drop within those n pulls. It must be above 0 and below 100; if the field is empty or outside that range, the second result shows a dash. At a 100% drop rate the answer is always 1 pull. The model assumes every pull is independent with the same rate: pity counters, rate-ups that change after a miss and guaranteed-after-N systems are not modelled.

Worked example

A character has a 0.6% drop rate and you want 90% confidence of getting at least one. The average is 1 ÷ 0.006 = 166.67 pulls. For the target, n = ln(1 − 0.90) / ln(1 − 0.006) = ln(0.1) / ln(0.994) = −2.3026 / −0.006018 ≈ 382.6, which rounds up to 383 pulls. So you would need to budget well over twice the average to be 90% sure.

Try this example →

Common mistakes

  • Typing the rate as a fraction: 0.006 is read as 0.006%, which gives about 16,667 expected pulls. Enter 0.6 for 0.6%.
  • Treating the average as a safe budget: 166.67 pulls is only the mean, and the 50% point is lower (116 pulls at 0.6%) while 90% needs 383 and 99% needs 766. About 63% of players get the drop by the average.
  • Entering 100 or 0 as confidence: the confidence must be strictly between 0 and 100, otherwise the second result shows a dash because certainty needs infinite pulls.
  • Using the base rate on a game with pity: if the game guarantees a drop after a fixed number of pulls, the real worst case is that cap, and this tool will overstate the pulls needed.
  • Combining several wanted items as one rate: for a specific item inside a drop pool, enter the chance of that exact item, not the chance of any drop in the pool.

About this calculator

In gacha-style games, each pull is an independent trial with a fixed drop rate p, so the number of pulls until the first success follows a geometric distribution: the expected (average) number of pulls is 1/p, and the probability of getting at least one success within n pulls is 1 − (1 − p)^n. Rearranging that second formula for n gives the number of pulls needed to reach a chosen confidence level, such as 90% or 99%.

This calculator takes a drop rate and a target confidence level and returns the expected number of pulls and the pulls needed to hit that confidence. Gacha and loot-box game players use it to budget how much currency or how many pulls to save before a banner, and game economy analysts use the same geometric-distribution math when modeling expected player spend against a given drop rate during monetization design.

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Comments (1)

  • Editorial team

    The tool answers for one copy only, but you can scale it by hand. Two copies of the same item average twice the single-copy figure, so at a 1.6% rate the 62.50-pull average becomes 125 pulls, while the 90% budget of 143 pulls for one copy does not simply double. Multiply pulls by what a pull costs to turn the number into a budget. Does the banner you are planning for have a pity counter?

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