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Backgammon Maths
 
Arrow Backgammon Maths
 
A dice has six faces. When two diced are used there are 36 possible combinations on numbers. These are shown below in table 1.
Table 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
  • There are 11 ways in which a specified number may be thrown; hence the chance of throwing a 5 is 11 in 36 (simple odds 9-4)
  • There are two ways in which a combination of two ordinary numbers may be thrown; hence the chance of throwing a 2 and a 1 (2-1 or 1-2) is twon in 36 (simple odds 17-1)
  • There is only one way in which a particular double may be thrown; hence the chance of throwing 5-5 is one in 36 (simple odds 35-1)

Table 2 shows the exact odds, the simplified odds and the percentage chance of being able to move a specific number of points (provided that your opponent has not blocked any of them along the way).

Table 2 

Number of points to be moved Throws against / for Simple odds % Chance
1 25/1     9-4 31%
2 24/12     2-1 33%
3 22/14     3-2 39%
4 21/15     7-5 42%
5 21/15     7-5 42%
6 19/17     9-8 47%
7 30/6     5-1 17%
8 30/6     5-1 17%
9 31/5     6-1 14%
10 33/3   11-1 8%
11 34/2   17-1 5.5%
12 33/3   11-1 8%
15 35/1   3%
16 35/1   3%
18 35/1   3%
20 35/1   3%
24 35/1   3%

It is absolutely essential for a player to be familiar with table 2, and it is particularly important to be aware of the true chances of success or failure when offering or refusing a double. If a player is ignorant of the possible consequences of throwing any particular roll (i.e. a particular combination of dice), he will be at a decided disadvantage-especially if his opponent is aware of them.

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