I want to calculate probabilities of X dice rolling successes in groups of dice rolls.

Assuming I have 10 dice and 1-2 is Fail and 3-6 is success, how do I calculate the number of combinations that can lead to a given number of successful outcomes?

(Other than 0,1,9 or 10 as these are easy).

My Google-fu so far has only yielded results which talk math without decoding it.

It doesn't explain it but i've used this website before:
Dice Probablility calulator

Just multiply every result by 100 to get the %.

Yeah I've seen that but I don't want to just get the numbers out, I want to know the formula behind it

Can you clarify what data you want to achieve, not sure if your after % of success or combinationsof rolls that = succuss.

Quite a good explanation here, which I used a few years ago to create a dice rolling script for IRC in the #warhammer channel: http://gwydir.demon.co.uk/jo/probabilit ... e.htm#more

BANE wrote:Can you clarify what data you want to achieve, not sure if your after % of success or combinationsof rolls that = succuss.

EDIT: I think the two are interlinked. The number of scenarios for a given outcome is the same but the chance of it occurring changes if the to hit roll changes.

@Spack: the multiple dice bit in your link is for single tests on multiple dice (bell curve) (eg 2D6, 3D6 etc etc), I'm looking at multiple instances of single D6 tests......

Most of the content is on how to calculate combinations of results, not the simple sum of the results - you've focussed on one little part of that page under "Sum of two dice", you need to go down at start at the section under that. You can scale up to 10 using the the last section titled "More than two dice".

For instance, if you want to know the probability of getting a 4+ on all 10 dice, that would be

(probability on one dice) ^ (number of dice)

which is

0.5 ^10 = 0.0009765625

but you say you've already covered that one anyway


It's gets pretty messy with more than two dice, but it boils down to the same thing pretty much - generally you need to work out the probability of not getting the result you want due to duplication of results, and then take that result away from 1.

Admittedly that page doesn't go into this level, but at least it had some of the basics.

Did you stumble on this one? http://www.wikihow.com/Calculate-Multip ... babilities

{[P(F)^F]*[P(S)^S]*[F+S]!}/[F!*S!]

Where:
F = number of fails
P(F) = probability of failing
S = number of successes
P(S) = probability of successes

Now I need to figure out how to incorporate being allowed to re-roll a single fail...

http://www.fnordistan.com/smallroller.html

This is the one I use regularly, simple interface that shows the formula it creates and then gives answer.. there was an almighty headache one about multiple not chances over sequential variance stuff on warseer a few years back and I managed to satsify the bloke by finding the right page of formula.. but you have to search for yahtzee maths stuff for that.. nobody did it for 40k
EDIT ooh I'm late.. never mind

that bit where I (hopefully arrogantly) have to google myself.
http://www.warseer.com/forums/showthrea ... ies-please

Leads to
http://blog.plover.com/math/yahtzee.html