# Changes: Template:CumulativeDropProbability

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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 100 288 401 693 1386 2302 2995 4603 9206
Cumulative Probability 9.5% 25% 33% 50% 75% 90% 95% 99% 99.99%
Neither the drop rate nor cumulative probability increases based on the number of monsters you have already killed.

## Computing the probabilities Edit

The 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.

Note that as the mobs drop items independently of each other, the process is essentially memoryless: having killed (N-1) mobs without getting a drop, the probability of the item dropping on N'th kill is still p, as opposed to the cumulative probability for N 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 to an integer: can't loot half a monster.