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Message: <blockquote data-quote="Darren" data-source="post: 1820866" data-attributes="member: 22701">Ditto tarchon.If there were a single elegant formula, my probability and statistics textbook would be rather thinner... Using a computer to generate the numbers and crunch them isn't really that uncommon.I'll give die distributions a quick shot though...Each side on a d6 (properly weighted) has equally likely outcome - 1/6.The number on the face of one die does not depend in any way on the number on another die.  In probability terms, the outcomes are independent, meaning we can simply add and multiply outcomes of individual die rolls to find results for multiple die rolls.  (If this were no so, the outcomes would be said to be dependent, and the math would get more complicated.)So, how many ways to get a 3 on a 3d6?Just one: 111The probability to roll this is (1/6)*(1/6)*(1/6) = 1/216, or about 0.46%This is also the probability of rolling any three given numbers.So how many ways to get a 5 on a 3d6?There are 6 ways:113131311122212221The probability for any one of these is 1/216, but there are 6 outcomes that sum up to 5, so we can add the individual probabilities: The odds of rolling a five on a 3d6 is 6/216 or about 2.78%Basically, I'm just counting up the number of outcomes that gives me the result I'm interested in, then dividing that by the total number of outcomes possible.  With dice, you can usually draw a little table and figure out how things work, unless you have very many dice or are interested in many different outcomes.  Then it may be simpler to have a computer crunch numbers, or take a sample to get a close estimate.Averages are a bit simpler if no result goes below one.  2d6-1, for example.  In this case it really is just the average of the die, then subtract 1.  Each d6 has average of 3.5, so the average of 2d6 is 7, subtract 1 for 6.  To get the average of 4d6-10, you would have to add up the outcome of each roll and divide by the number of all possible outcomes.</blockquote>

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