Gaming Calculators
Gacha and loot box expected cost.
Enter the published drop rate and what each pull costs. If the game guarantees the item at a fixed number of pulls (hard pity), add that too. You get the average number of pulls and spend, the number to be 50% and 90% sure, and the worst case. Runs in your browser; nothing is sent or stored.
Inputs
Result
Fill the form and press Calculate.
Worked example
An item with a 0.6% rate and a hard pity of 90 pulls at $2.50 a pull: the expected number of pulls is (1 - 0.994^90) / 0.006 = 69.7, so the expected spend is $174.25, and the worst case is 90 pulls, $225.00. With no pity and a 2% rate the expected number of pulls is 1 / 0.02 = 50 ($125.00), but 90% certainty takes 114 pulls ($285.00).
How it works
With a fixed rate p, the number of pulls until the first success follows a geometric distribution whose mean is 1/p (the Geometric distribution - Wikipedia article gives the mean and the probability that the k-th trial is the first success). A hard pity H caps the run, which gives expected pulls = (1 - (1 - p)^H) / p. The pulls for a given confidence level c are ceil( ln(1 - c) / ln(1 - p) ), limited to H when there is a hard pity. Expected cost is pulls multiplied by cost per pull.
The Gacha game - Wikipedia article describes hard pity as a guarantee after a fixed number of pulls and notes it works as an effective price ceiling, while soft pity raises the rate gradually after a threshold. Soft pity is not modelled here, so games that use it will cost less on average than the figure shown. Some games also add "50/50" featured-item rules on top, which this does not include. Check the game's published rates; this is a probability estimate, not financial advice, and spending on randomised items carries real risk.
Sources: Geometric distribution - Wikipedia; Gacha game - Wikipedia. Each opened 2026-10-08.
Planning guide only, not professional advice. Figures are estimates from the inputs you enter.
FAQ
How do I calculate the expected cost of a gacha item?
Divide 1 by the drop rate to get the average pulls without pity, then multiply by the cost per pull. With a hard pity H use (1 - (1 - p)^H) / p instead.
What does hard pity do to the cost?
It guarantees the item by pull H, which caps the worst-case spend at H times the cost per pull and lowers the average.
Why is 90% certainty so much more than the average?
Without pity the number of pulls is spread out: the average is 1/p, but being 90% sure takes about 2.3 times as many pulls.
Does this include soft pity or 50/50 rules?
No. Soft pity raises the rate after a threshold and would lower the average cost. Featured-item rules can raise it. Both vary per game.
Are drop rates always published?
Many jurisdictions require item rarities and rates to be public, but not all. Use the rate the game publishes, and treat unpublished rates as unknown.