How is the at-least-once probability calculated?

Each run is independent, so the chance of zero drops over N runs is (1 minus p) to the power N. The at-least-once probability is one minus that. With a 5 percent rate over 20 runs, that is 1 minus 0.95 to the 20th, about 64 percent.

Why is it not just rate times attempts?

Multiplying rate by attempts double-counts the chance of multiple drops and can exceed 100 percent, which is impossible. The correct method uses the complement of getting nothing, which always stays between 0 and 100 percent.

What is the expected number of drops?

Expected drops is simply per-attempt rate times the number of attempts. Unlike at-least-once probability, this can exceed 1 and tells you the average count of items you would get across many farming sessions.

How many runs do I need to almost guarantee a drop?

The tool solves for the runs needed at 50, 90, and 95 percent confidence using N equals log of (1 minus target) divided by log of (1 minus rate). A rare item can need dozens of runs for 90 percent, which is why farming feels long.

Does Destiny 2 use bad-luck protection?

Some sources do increase odds after dry streaks, which this independent-trial model does not include. For pure random drops the model is exact; for pity-style sources use a pity calculator instead.

Destiny 2 Drop Rate & Probability Calculator

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Destiny 2 farming feels random because it is, and a flat per-run drop rate hides how many runs you actually need. This calculator uses the correct independent-trial math to show your true cumulative odds, the average number of drops, and how many runs it takes to be reasonably confident.

How it works

Runs are independent, so the chance of getting nothing is the per-run miss rate raised to the number of runs:

pMiss        = 1 − rate
atLeastOnce  = 1 − pMiss^attempts
expectedDrops = rate × attempts
runsForTarget = ln(1 − target) / ln(1 − rate)

The at-least-once formula always stays between 0 and 100 percent, unlike the common mistake of multiplying rate by attempts, which can wrongly exceed 100.

Example and tips

A 5 percent drop over 20 runs gives about a 64 percent chance of at least one, and an average of 1 drop. To reach 90 percent confidence you need roughly 45 runs at that rate. If a target confidence demands an unreasonable run count, look for a higher-rate source or a pity-based version of the item, since pure random drops have no ceiling on how unlucky a session can get.