# 2 Dice Rolls Probability/Statistics - Backgammon Style

The following is the probability associated with 1 unbiased die being rolled twice or 2 unbiased dice being rolled at the same time and the result recorded. The order of the results are irrelevant. The two resulting values from the dice are then added together with the final results being the 2 numbers on the dice and the sum of the two dice (eg a roll of 2 and 5 brings a positive result for 2, 5 and 7).

In backgammon, rolling doubles (eg two 5s) results in being able to make 4 moves (eg if two 5s are rolled you have the possibility of moving up to 20 spaces).

There are 6 outcomes per die roll - 1, 2, 3, 4, 5 or 6. Each die roll does not affect the outcome of further rolls. There are a total of 36 possible combinations for 2 rolls which creates 17 possible end results.

Aim specifies the result we are aiming for.
Successful indicates the probability for our aim being meet.
Not Successful indicates the probability for our aim being missed.

AimSuccessfulNot Successful
1
30.56%
(11/36)
69.44%
(25/36)
2
33.33%
(12/36)
66.67%
(24/36)
3
38.89%
(14/36)
61.11%
(22/36)
4
41.67%
(15/36)
58.33%
(21/36)
5
41.67%
(15/36)
58.33%
(21/36)
6
47.22%
(17/36)
52.78%
(19/36)
7
16.67%
(6/36)
83.33%
(30/36)
8
16.67%
(6/36)
83.33%
(30/36)
9
13.89%
(5/36)
86.11%
(31/36)
10
8.33%
(3/36)
91.67%
(33/36)
11
5.56%
(2/36)
94.44%
(34/36)
12
8.33%
(3/36)
91.67%
(33/36)
15
2.78%
(1/36)
97.22%
(35/36)
16
2.78%
(1/36)
97.22%
(35/36)
18
2.78%
(1/36)
97.22%
(35/36)
20
2.78%
(1/36)
97.22%
(35/36)
24
2.78%
(1/36)
97.22%
(35/36)

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