Okay, so there are a lot of backgammon pages out there. I'm just adding this because I wanted to show the probabilities to a friend, so I might as well post them for all to see.
It is critical to determine probabilities of certain moves taking place, however, because each die is a separate move, it is necessary to consider all possible cases.
Normally, most people are aware that the probabilty of getting a 7 on a roll of two die is 1/6. However, the probability of getting a 6 as some combination is significantly higher—17/36 or almost 50%. All combinations which contain at least one move of 6 include:
| 1-1 | 1-2 | 1-3 | 1-4 | 1-5 | 1-6 |
| 2-1 | 2-2 | 2-3 | 2-4 | 2-5 | 2-6 |
| 3-1 | 3-2 | 3-3 | 3-4 | 3-5 | 3-6 |
| 4-1 | 4-2 | 4-3 | 4-4 | 4-5 | 4-6 |
| 5-1 | 5-2 | 5-3 | 5-4 | 5-5 | 5-6 |
| 6-1 | 6-2 | 6-3 | 6-4 | 6-5 | 6-6 |
Figure 1. The rolls resulting in a move of 1.
| 1-1 | 1-2 | 1-3 | 1-4 | 1-5 | 1-6 |
| 2-1 | 2-2 | 2-3 | 2-4 | 2-5 | 2-6 |
| 3-1 | 3-2 | 3-3 | 3-4 | 3-5 | 3-6 |
| 4-1 | 4-2 | 4-3 | 4-4 | 4-5 | 4-6 |
| 5-1 | 5-2 | 5-3 | 5-4 | 5-5 | 5-6 |
| 6-1 | 6-2 | 6-3 | 6-4 | 6-5 | 6-6 |
Figure 2. The rolls resulting in a move of 2.
| 1-1 | 1-2 | 1-3 | 1-4 | 1-5 | 1-6 |
| 2-1 | 2-2 | 2-3 | 2-4 | 2-5 | 2-6 |
| 3-1 | 3-2 | 3-3 | 3-4 | 3-5 | 3-6 |
| 4-1 | 4-2 | 4-3 | 4-4 | 4-5 | 4-6 |
| 5-1 | 5-2 | 5-3 | 5-4 | 5-5 | 5-6 |
| 6-1 | 6-2 | 6-3 | 6-4 | 6-5 | 6-6 |
Figure 3. The rolls resulting in a move of 3.
| 1-1 | 1-2 | 1-3 | 1-4 | 1-5 | 1-6 |
| 2-1 | 2-2 | 2-3 | 2-4 | 2-5 | 2-6 |
| 3-1 | 3-2 | 3-3 | 3-4 | 3-5 | 3-6 |
| 4-1 | 4-2 | 4-3 | 4-4 | 4-5 | 4-6 |
| 5-1 | 5-2 | 5-3 | 5-4 | 5-5 | 5-6 |
| 6-1 | 6-2 | 6-3 | 6-4 | 6-5 | 6-6 |
Figure 4. The rolls resulting in a move of 4.
| 1-1 | 1-2 | 1-3 | 1-4 | 1-5 | 1-6 |
| 2-1 | 2-2 | 2-3 | 2-4 | 2-5 | 2-6 |
| 3-1 | 3-2 | 3-3 | 3-4 | 3-5 | 3-6 |
| 4-1 | 4-2 | 4-3 | 4-4 | 4-5 | 4-6 |
| 5-1 | 5-2 | 5-3 | 5-4 | 5-5 | 5-6 |
| 6-1 | 6-2 | 6-3 | 6-4 | 6-5 | 6-6 |
Figure 5. The rolls resulting in a move of 5.
| 1-1 | 1-2 | 1-3 | 1-4 | 1-5 | 1-6 |
| 2-1 | 2-2 | 2-3 | 2-4 | 2-5 | 2-6 |
| 3-1 | 3-2 | 3-3 | 3-4 | 3-5 | 3-6 |
| 4-1 | 4-2 | 4-3 | 4-4 | 4-5 | 4-6 |
| 5-1 | 5-2 | 5-3 | 5-4 | 5-5 | 5-6 |
| 6-1 | 6-2 | 6-3 | 6-4 | 6-5 | 6-6 |
Figure 6. The rolls resulting in a move of 6.
Some moves have no possible combinations:
What makes the game more interesting is when you have a number of covered points in front of the piece you are intereted in moving.
Anyway, the next three graphs show the probabilities of certain moves as a result of the given combinations, with the last figure giving to sum of the probabilities. Each square represents a probability of 1/36.
Here is a pdf of the four charts and you should also consider visiting Wikipedia's Backgammon page.
