02-07-2009, 02:25 AM
Rare drops are a binomial distribution. In a binomial distribution, for every "event," you can have either a "success" or a "failure." In the case of PSO, an event = an enemy kill, a success = a rare drop, and a failure = no rare drop. The more events (enemy kills) you have, the more likely it is you're going to get a success (rare item), but there's no guarantee of that. You could hunt forever and never get your rare, as some players have experienced.
So, to calculate the actual odds of getting a certain number of rares after a certain number of enemy kills, you use the following formula.
P(n|N) = (N!) / (n! * (N - n)!) * p^n * (1-p)^(N-n)
P = "probability of" - it'll come out in a decimal; multiply by 100 to make it a percentage
n|N = "n successes in N tries" - that is, how many rares you want in how many enemy kills.
! = the factorial operator - basically, multiply a number by every number from it down to 1. So, 5! = 5*4*3*2*1 = 120. Also, 0! = 1 by definition.
p = the odds of a rare drop, eg. 1/2, 1/55, 1/205, 1/299594
^ = the exponent operator, like 5^3 = 5*5*5 = 125
You can see if that if n=1 and N=1, then P(n|N) = p. I also ought to note that this formula only gives the odds for that one exact pair of n|N. So, if you want to find the odds of getting at least 3 rares in some number of kills (say you need three God/Battles), then you've got to calculate P(3|N), P(4|N), P(5|N), etc. and add them all together. However, since that series goes to n = infinity, it'd be easier to simply calculate the odds of n = 0, 1, and 2, then add them together, and subtract that total from 100%.
Typically, what we care about is what are the odds of getting NO rares in some number of enemies? If we've killed 80 Pal Rappies and not gotten an Angel Harp (1/21) what are the odds of that happening? How pissed off should we be? In that case, the formula reduces to:
P(0|N) = (1 - p)^(N) = (20/21)^80 = 0.02017
That means, there's a 2.017% chance of getting no rares, and about a 98% chance that we should have gotten AT LEAST one. So, at that point, it's still not even 100%. It'll never be. But 98% is pretty damn good. You'd be happy with that score on a final exam! So, seeing as how you haven't gotten even one yet, you ought to be pretty pissed!
I hope that clears some things up!
So, to calculate the actual odds of getting a certain number of rares after a certain number of enemy kills, you use the following formula.
P(n|N) = (N!) / (n! * (N - n)!) * p^n * (1-p)^(N-n)
P = "probability of" - it'll come out in a decimal; multiply by 100 to make it a percentage
n|N = "n successes in N tries" - that is, how many rares you want in how many enemy kills.
! = the factorial operator - basically, multiply a number by every number from it down to 1. So, 5! = 5*4*3*2*1 = 120. Also, 0! = 1 by definition.
p = the odds of a rare drop, eg. 1/2, 1/55, 1/205, 1/299594
^ = the exponent operator, like 5^3 = 5*5*5 = 125
You can see if that if n=1 and N=1, then P(n|N) = p. I also ought to note that this formula only gives the odds for that one exact pair of n|N. So, if you want to find the odds of getting at least 3 rares in some number of kills (say you need three God/Battles), then you've got to calculate P(3|N), P(4|N), P(5|N), etc. and add them all together. However, since that series goes to n = infinity, it'd be easier to simply calculate the odds of n = 0, 1, and 2, then add them together, and subtract that total from 100%.
Typically, what we care about is what are the odds of getting NO rares in some number of enemies? If we've killed 80 Pal Rappies and not gotten an Angel Harp (1/21) what are the odds of that happening? How pissed off should we be? In that case, the formula reduces to:
P(0|N) = (1 - p)^(N) = (20/21)^80 = 0.02017
That means, there's a 2.017% chance of getting no rares, and about a 98% chance that we should have gotten AT LEAST one. So, at that point, it's still not even 100%. It'll never be. But 98% is pretty damn good. You'd be happy with that score on a final exam! So, seeing as how you haven't gotten even one yet, you ought to be pretty pissed!
I hope that clears some things up!
Too legit to quit.