How this calculator works
Each run is treated as an independent trial with the same drop chance. The chance of no drop in one run is 1 minus the drop chance, and the chance of no drop in every run is that figure raised to the number of runs. The chance of at least one drop is the complement of that. Expected drops are simply runs times the drop chance, which is a different question: you can have a 63 percent chance of at least one drop and still expect only one drop over a hundred runs at one percent.
Formula
P(at least one in n runs) = 1 - (1 - p)^n, where p is the per-run chance as a fraction. P(no drop) = (1 - p)^n. Expected drops = n x p. Runs for a target chance C = ceiling(ln(1 - C) / ln(1 - p)). Per-run chance for a target C in n runs = 1 - (1 - C)^(1 / n).
Worked example
At a 1 percent drop rate over 100 runs, the chance of at least one drop is 1 - 0.99^100 = 0.634, or 63.4 percent. Over 300 runs it rises to 95.1 percent. For a 90 percent chance at the same rate, you need ceiling(ln(0.1) / ln(0.99)) = 230 runs. For a 50 percent chance, 69 runs are enough.
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Frequently asked questions
Does a 1 percent drop mean I get one in 100 runs?
No. On average you get one drop per hundred runs, but the chance of at least one drop in exactly 100 runs is only about 63.4 percent. About 36.6 percent of players would still have nothing after a hundred runs, which is why bad luck streaks feel so common.
How many runs give a 99 percent chance?
At a 1 percent rate, ceiling(ln(0.01) / ln(0.99)) = 459 runs. At 0.1 percent it is 4,603 runs, and at 0.01 percent it is 46,050 runs. The required count grows in proportion to 1 divided by the rate once the target is high.
Are drop rates really independent?
Sometimes not. Pity systems, guaranteed drops after a set number of pulls, and loot boxes with a rotating pool break the independence assumption. This page models a plain independent drop. If the game states a guarantee or a pity counter, use the game rules rather than this formula.
Why do rates differ between game versions?
Developers rebalance drop tables in patches and events, and the published rate may apply only to a specific boss, difficulty or event window. Check the rate against the current version and the exact activity. A figure from an old guide can be badly out of date.
Is the expected number of drops the same as the most likely number?
Not usually. The expected value is a long-run average and need not be a whole number. The most likely single outcome is the floor of (n + 1) times p, which can be a different value entirely. Use the chance curve when you care about the spread, not just the average.