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

[Ruien]

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:

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:

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:

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?

[magnetaress]

Originally Posted by Dogma [You must be logged in to view images. Log in or Register.]

Took me over 600 hours camping Jail in KC before I got my first Tstaff drop. That's only counting actual hours camping it tho. I haven't tried keeping track since.

Got a few leveling on random toons in the zone and a few logging in drunk at 2am just wandering around.

Then again I was randomly given a Spirit Wracked Urn for free also. So idk. Luck is weird.

Be good, hope for the best and be okay when it isn't. Bout all you can do.

Originally Posted by Ruien [You must be logged in to view images. Log in or Register.]

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:

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:

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:

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?

These posts are so awesome and I have total and absolute faith in them.

And ya, nothing is certain. So it's possible to never ever get an AC ring. (scary)

Thank you so much for the lengthy math explanation. That is what I was most curious about. I have a very hard time understanding that stuff, and my math teach gave me a passing grade by 1 point because she just didn't want to ever see me again. So I greatly appreciate you taking the time to try and teach me.