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Heroes Community > Library of Enlightenment > Thread: WOW Mighty Gorgon is da best!!
Thread: WOW Mighty Gorgon is da best!! This thread is 3 pages long: 1 2 3 · «PREV
rechet
rechet


Hired Hero
posted June 22, 2004 08:30 AM

One apparent problem with the probabilities presented above - their sum is above 100%, which is of course impossible. So let's do some maths...

Chance for one Moo to do its trick = p = 0.1
The "otherwise" chance being thus q = 1-p = 0.9
Number of Moo's is N

Only extra constraint to a perfect binomial probability distribution is that no more than N/10 (rounded up) enemies can be killed by one stack of moo's.

So, to calculate the chance for N Moo's killing EXACTLY x units - let's call it p(N,x) - is as follows. Operator nCr is the "number of combinations in a subset of a set", it takes into account the fact that it doesn't really matter in which order those numbers are rolled. "Kill - no kill - no kill" is the same as "no kill - kill - no kill" when only the number of kills matters.

p(N,x) = (N nCr x) * p^x * q^(n-x)

Substituting some values (21 moo's, zero to three kills), we get

p(21,0) = 0.11 (read: 11% chance to kill no one with 21 moo's)
p(21,1) = 0.26
p(21,2) = 0.28
p(21,3) = 0.20 (actually 0.35, see below)

Sum of these is only 0.85, so the 'remaining' chance gets added to the last one. I'm assuming that if one gets lucky with the rolls and would score more than n/10 kills, game truncates the number of kills to the highest possible, thus giving a bit of an extra chance to score the highest # of kills possible.

One noteworthy breakpoint is that when the number of Moo's gets at or above 51 - the chance of scoring zero kills goes below 1 percent.

The reported occasion where 15 moo's couldn't score a kill supports the fact that the probabilities aren't cumulatively additive, as that would mean that a pack of 10 moo's would ALWAYS score one kill.

I'm accepting counter-theories with proof as of now. =)
____________
--
Jukka Mikkonen a.k.a Sir Rechet

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csarmi
csarmi


Supreme Hero
gets back
posted June 22, 2004 09:11 AM
Edited By: csarmi on 22 Jun 2004

The numbers were right.

Xarfax gave the chance of killing at least k creatures and called it p(n,k).

For instance,
p(21,1)=89%
p(21,2)=63.5%
and...

of course the remaining numbers are added to the highest, cause it probably goes like this: Moo1 rolls the dice (kill or not), Moo2 rolls the dice, ... this goes until no Moo's left OR at least n/10 rounded up enemies are killed.

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rechet
rechet


Hired Hero
posted June 23, 2004 12:13 PM

A couple extra notes:

As the binomial probability distribution goes towards a bell curve as N goes towards infinity, AND the cut-off point just happens to be the same as p (one tenth vs one tenth of N), it can be stated that the probability of scoring the max number of kills is 50% when the stack is "sufficiently large", that is, in the order of several hundreds or thousands.

Also, the probability of scoring low # of kills in relation to the maximum gets smaller and smaller as N goes up. For example, already at N=200, the combined chance to score less than 11 kills is below one percent, while less than 14 kills (combined) is still below 10% chance. Maximum here is of course 20 kills, and it has 53,45% chance of happening.
____________
--
Jukka Mikkonen a.k.a Sir Rechet

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csarmi
csarmi


Supreme Hero
gets back
posted June 23, 2004 01:35 PM
Edited By: csarmi on 23 Jun 2004

For example, for large n, the chance to score n/10-0.7*sqrt(n) converges to 0.99.

That means, that for large stack sizes you will have a 99% chance to score between n/10 and n/10-0.7*sqrt(n), for n=1000, for example, this is 77 to 100 kills.

This is undescriptive for smaller n's, but in these cases we can tell that you have a very fair chance to score almost maximal, partially due to the fact that the max is the same for 20 as for 28, for example.


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jeremiahcfelt
jeremiahcfelt

Tavern Dweller
posted June 25, 2004 11:21 PM

oh my...

oh my goodness... look what I started just by saying ghost dragons were better!!!

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Xarfax111
Xarfax111


Bad-mannered
Supreme Hero
The last hero standing
posted September 16, 2007 12:26 AM

i want a Quality Point
____________

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sachelos
sachelos


Known Hero
posted September 16, 2007 06:39 AM

Quote:
i want a Quality Point


what for?

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roy-algriffin
roy-algriffin


Supreme Hero
Chocolate ice cream zealot
posted September 17, 2007 05:12 AM

I think he meant you know, in general terms, Like Gief quality point for XXXX plx
____________
"Am i a demon? No im a priest of the light! THE BLOODY RED LIGHT"

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