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<blockquote data-quote="Rothe" data-source="post: 2979727" data-attributes="member: 39813">I can tell you the exact complex formula <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f609.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=";)" title="Wink&nbsp; &nbsp; ;)"&nbsp; data-smilie="2"data-shortname=";)" /> It was also floating around here before the crash.&nbsp; However if you have some programing acumen, the quickest way to do it is probably simulating to just 10,000 rolls.&nbsp; Since I have no prgramming skills anymore, and still like algebra, here is the precise formula or generating function for the distribution.For n dice expand out the expression&nbsp;&nbsp; (aX +aX^2 + aX^3 + aX^4 + aX^5 +aX^6)^nwhere for a fair d6, a=1/6.&nbsp; Unlike what you might be used to, the X is a dummy variable, you don't need to solve for it.&nbsp; The number that you want will be the coeficient in front of a specific X.&nbsp; If you are looking for the probability of rolling 10 on 10 d6 look at the coeficient in front of the X^10.&nbsp; If looking for the probability of rolling 31, it is the coeficient in front of the X^31 term.&nbsp;&nbsp; As you can see, once you get to high n the algebra becomes fairly tedious unless you can program it into Mathematica.&nbsp; One thing I like about generating functions is you can use them to get the probability distributions for mixed dice, unfair dice, and even mixed unfair dice.</blockquote>

[QUOTE="Rothe, post: 2979727, member: 39813"] I can tell you the exact complex formula ;) It was also floating around here before the crash. However if you have some programing acumen, the quickest way to do it is probably simulating to just 10,000 rolls. Since I have no prgramming skills anymore, and still like algebra, here is the precise formula or generating function for the distribution. For n dice expand out the expression (aX +aX^2 + aX^3 + aX^4 + aX^5 +aX^6)^n where for a fair d6, a=1/6. Unlike what you might be used to, the X is a dummy variable, you don't need to solve for it. The number that you want will be the coeficient in front of a specific X. If you are looking for the probability of rolling 10 on 10 d6 look at the coeficient in front of the X^10. If looking for the probability of rolling 31, it is the coeficient in front of the X^31 term. As you can see, once you get to high n the algebra becomes fairly tedious unless you can program it into Mathematica. One thing I like about generating functions is you can use them to get the probability distributions for mixed dice, unfair dice, and even mixed unfair dice. [/QUOTE]

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