Editing Probability (section)

====In general====
Now, I am a stats nerd with an undergrad education. I have spent several hours trying to figure out the exact probabilities for the sums of dice, which is probably more than any sane person would spend on this article. So I'm sure you don't care either. Plus, the math involves Greek letters, and I'm quite attached to my kneecaps.

Fortunately, other stats nerds get tired of this shit too, so they discovered a good approximation: the normal distribution. This works well for 3dX and gets better the more dice you roll.

Looking at my notes, for an adX the mean (average) is [[File:Probability Eq11.png|x50px]], and the "standard deviation" is [[File:Probability Eq12.png|x50px]]. That's all you need [https://www.wolframalpha.com/input/?i=normal+distribution+calculator&assumption=%7B%22F%22%2C+%22NormalProbabilities%22%2C+%22z%22%7D+-%3E%22-1%22&assumption=%7B%22F%22%2C+%22NormalProbabilities%22%2C+%22mu%22%7D+-%3E%220%22&assumption=%7B%22FVarOpt%22%7D+-%3E+%7B%7B%22NormalProbabilities%22%2C+%22sigma%22%7D%2C+%7B%22NormalProbabilities%22%2C+%22z%22%7D%2C+%7B%22NormalProbabilities%22%2C+%22mu%22%7D%7D to get an answer from Wolfram Alpha], but with a few caveats: You can't ask it for the probability that you'll roll ''exactly'' a number (it will pedantically tell you 0), but you can ask it the probability of rolling ''less than or equal'' or ''more than or equal'' to some number, and it doesn't respect the range of the dice pool (it will say it's possible, if unlikely, to roll a negative number, for example).

So if, for whatever reason, you're doing a check roll for 12 or better on a 4d6, know that the mean is (4+4*6)/2 = 14 and the standard deviation is the square root of 182/3 (about 7.8), so the chance of passing the check is about [https://www.wolframalpha.com/input/?i=probability+that+x+%3E%3D+12+given+x+is+normally+distributed+mean%3D14+standard+deviation%3D7.8 60%].