How is at-least-once probability calculated?

Each attempt independently succeeds with probability p equals 1 divided by N. The chance of getting nothing in n attempts is (1 minus p) to the power n, so the chance of at least one drop is 1 minus that. This is the correct geometric or binomial result, not n times p.

Why isn't the chance just attempts divided by drop rate?

Multiplying attempts by p overcounts because it ignores the possibility of multiple drops and exceeds 100 percent past N attempts. The real formula 1 minus (1 minus p) to the power n caps correctly at just under 100 percent and accounts for repeated successes.

What does the dry-streak figure mean?

It is the probability that after your entered number of attempts you still have zero of the item. At exactly N attempts on a 1-in-N drop this is about 36.8 percent, which is why being dry past the drop rate is completely normal.

How many attempts give a 50 percent chance?

Roughly 0.693 times N attempts gives a 50 percent cumulative chance, because that is N times the natural log of 2. For a 1-in-5000 drop, about 3,466 attempts puts you at even odds of having it.

Is the expected number of drops the same as guaranteed?

No. Expected drops is attempts times p, the long-run average. An expected value of 1 still leaves about a 37 percent chance of zero drops, because outcomes vary around the average. Nothing is guaranteed until the item actually drops.

RuneScape 3 Drop Rate & Probability Calculator

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RuneScape rare drops follow a fixed per-attempt chance, and players badly misjudge the odds by multiplying attempts by the rate. This calculator uses the correct binomial model so you can see your true chance of at least one drop and understand why long dry streaks are normal.

How it works

If the drop rate is 1 in N, each attempt succeeds with probability p = 1 / N. Attempts are independent, so:

p            = 1 / N
P(none)      = (1 − p)^attempts
P(at least 1)= 1 − (1 − p)^attempts
expected     = attempts × p

The at-least-once formula correctly approaches but never reaches 100 percent, unlike the naive attempts / N which would wrongly exceed certainty past N attempts.

Example and tips

On a 1-in-5000 drop, 5000 kills give a 1 − (1 − 1/5000)^5000, about a 63.2 percent chance of at least one — not 100 percent. To reach 50 percent you need only about 3,466 attempts, and to reach 90 percent about 11,513. Expect to sometimes go far past the drop rate empty handed: that is the geometry of independent rolls, not bad luck protection failing.