A sick math problem I can't seem to wrap my brain around.

Ruien · #12 04-01-2020, 08:43 AM

The OP seems to be asking how to calculate the number of attempts at a mob before getting at least N drops, given a drop rate.
That is the cumulative distribution function (CDF) of a negative binomial distribution. Scilab has this as the cdfnbn function.

This gives us the number of failures before a certain number of successes. The total number of attempts is the sum of the failures and successes.

For example, if we want 3 drops at 8% success per attempt, then it will require 48 attempts to be 75% sure of getting them:

Code:

successes = 3
success_chance = 0.08
confidence = 0.75
attempts = successes + cdfnbn("S", successes, success_chance, 1.0-success_chance, confidence, 1.0-confidence)

    attempts  =   48.031623

If the average time between attempts (including fighting) is 90 minutes, then this will require 72 hours. To be 95% sure, it increases to 77 attempts (115.5 hours).

If we want 3 drops at 1% success per attempt, then it will require 391 attempts to be 75% sure of getting them:

Code:

successes = 3
success_chance = 0.01
confidence = 0.75
attempts = successes + cdfnbn("S", successes, success_chance, 1.0-success_chance, confidence, 1.0-confidence)

    attempts  =   391.07841

If the average time between attempts (including fighting) is 6 minutes, then this will require 39.1 hours. To be 95% sure, it increases to 628 attempts (62.8 hours).

A few results:

Code:

1% chance, 1 success, 50% confidence: 69 attempts
1% chance, 1 success, 75% confidence: 138 attempts
1% chance, 1 success, 95% confidence: 298 attempts
1% chance, 1 success, 99% confidence: 458 attempts

5% chance, 1 success, 50% confidence: 14 attempts
5% chance, 1 success, 75% confidence: 27 attempts
5% chance, 1 success, 95% confidence: 58 attempts
5% chance, 1 success, 99% confidence: 90 attempts

10% chance, 1 success, 50% confidence: 7 attempts
10% chance, 1 success, 75% confidence: 13 attempts
10% chance, 1 success, 95% confidence: 28 attempts
10% chance, 1 success, 99% confidence: 44 attempts

This is sort of off the top of my head; it might be wrong. Can anyone confirm?