Calculating Probability of different totals of three dice

2Zons

New member
Joined
Feb 15, 2018
Messages
3
I'm an avid craps player and I have an intrinsic knowledge of the probabilities of 2 dice. I was thinking one day about what a 3 dice craps game would be like. I understand how to calculate the total combinations (6X6X6 = 216 total combinations). I built a spread sheet to manually total the probabilities of individual dice totals and got the expected bell curve centering on 10 and 11 both having 27/216 probability and 3 and 18 having 1/216. I am just wondering how I would do the math to calculate for any value. So here is my question specifically:

How do I calculate the probability of a total of X being rolled on 3 dice, X being anything from 3 to 18?

You may be able to tell from my question that I am not a matholigist(sic). It has been a long time since I studied probability ( in high school ~1987). I did math in my post secondary education but not any probability stuff that I can recall. I am sure this is a very basic question and the answer should be straight forward but my googling didn't return any useful results.
 
I don't know how you would do it with 2 dice, I just know the probabilities intrinsically. 1 way to make a 2, 2 to make a 3, 3:4, 4:5, 5:6, 6:7, 5:8, 4:9, 3:10, 2:11, 1:12. total of 36 combinations, but not a bell curve (I think its too low resolution to form a curve). It's a low enough amount of combinations you can just think about it and figure it out. When you get to 216 combinations (3 dice) you need to calculate.
 
I would have thought this was pretty straight forward probability math. Does no one have any ideas?
 
Top