Here is a handy trick, courtesy of Robert Goodhand of Somerset, UK. First put on a row six ones surrounded by five zeros on either side, as follows:
One-Die Probabilities
Dice Total123456 One Die0000011111100000
This represents the number of combinations for rolling a 1 to 6 with one die. I know, pretty obvious. However, stick with me. For two dice, add another row to the bottom, and for each cell take the sum of the row above and the five cells to the left of it. Then add another five dummy zeros to the right, if you wish to keep going. This represents the combinations of rolling a total of 2 to 12.
Two Dice Probabilities
Dice Total23456789101112 One Die000001111110000000000 Two Dice000001234565432100000
For three dice, just repeat. This will represent the number of combinations of 3 to 18.
Three Dice ProbabilitiesExpand
Dice Total3456789101112131415161718 One Die00000111111000000000000000 Two Dice00000123456543210000000000 Three Dice000001361015212527272521151063100000
To get the probability of any given total, divide the number of combinations of that total by the total number of combinations. In the case of three dice, the sum is 216, which also easily found as 63. For example, the probability of rolling a total of 13 with three dice is 21/216 = 9.72%. So for d dice, you’ll need to work your way up through 1 to d-1 dice. This is very easily accomplished in any spreadsheet.