# 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.

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.