# CumulativeDropProbability

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## Template page

Syntax: {{CumulativeDropProbability|<p=0.001>}}

|p= is the probability of the item drop rate as a decimal number. This defaults to 0.001 = 0.1% = 1 / 1000.
Probability of at least one drop in X kills
Number of Kills 100 288 406 693 1386 2302 2995 4603 9206
Cumulative Probability 9.5% 25% 33% 50% 75% 90% 95% 99% 99.99%
The probabilities shown here are cumulative. The drop rate does not increase as you kill additional monsters.

This table shows the cumulative probability of getting at least one desired item while killing a particular number of monsters that drop the desired item with a constant probability p.

Mathematically, the probability of not getting the desired drop as a direct consequence of any particular kill is (1-p). We assume that each mob drops the item independently of any previous mobs killed, so the probability of not getting a drop as a direct consequence of any of N kills is (1-p)^N. The opposite of this -- the probability of getting at least one drop as a consequence of all of N kills -- is 1 - (1-p)^N. This probability converges to 1 as N goes to infinity; one is not guaranteed to get a drop in a finite number of kills.

The above describes cumulative probability P as a function of number of kills N; we can also describe N as a function of P:

P = 1 - (1-p)N
N = log(1 - P)/log(1 - p)
N should be rounded up: can't loot half a dead monster.