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Backgammon

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:

1-11-21-31-41-51-6
2-12-22-32-42-52-6
3-13-23-33-43-53-6
4-14-24-34-44-54-6
5-15-25-35-45-55-6
6-16-26-36-46-56-6

Figure 1. The rolls resulting in a move of 1.

1-11-21-31-41-51-6
2-12-22-32-42-52-6
3-13-23-33-43-53-6
4-14-24-34-44-54-6
5-15-25-35-45-55-6
6-16-26-36-46-56-6

Figure 2. The rolls resulting in a move of 2.

1-11-21-31-41-51-6
2-12-22-32-42-52-6
3-13-23-33-43-53-6
4-14-24-34-44-54-6
5-15-25-35-45-55-6
6-16-26-36-46-56-6

Figure 3. The rolls resulting in a move of 3.

1-11-21-31-41-51-6
2-12-22-32-42-52-6
3-13-23-33-43-53-6
4-14-24-34-44-54-6
5-15-25-35-45-55-6
6-16-26-36-46-56-6

Figure 4. The rolls resulting in a move of 4.

1-11-21-31-41-51-6
2-12-22-32-42-52-6
3-13-23-33-43-53-6
4-14-24-34-44-54-6
5-15-25-35-45-55-6
6-16-26-36-46-56-6

Figure 5. The rolls resulting in a move of 5.

1-11-21-31-41-51-6
2-12-22-32-42-52-6
3-13-23-33-43-53-6
4-14-24-34-44-54-6
5-15-25-35-45-55-6
6-16-26-36-46-56-6

Figure 6. The rolls resulting in a move of 6.

Some moves have no possible combinations:

13, 14, 17, 19, 21, 22, 23, 25, ...

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.