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Backgammon Mathematics – Part 2
2008-07-14
Baran Gülçiçek
Baran Gülçiçek
We are pleased to publish Part 2 of Baran Gülçiçek's article on backgammon mathematics.
Probabilities Of Making A Point (putting two checkers on the same board)
Consecutive Checkers = 11/36 = 12,21,23,32,34,43,45,54,56,65,11(12)
Double Consecutive Checkers = 10/36 = 13,31,24,42,35,53,46,64,11(13),22(42)
3 Interval Checkers = 7/36 = 14,41,25,52,36,63,33(63)
4 Interval Checkers = 5/36 = 15,51,26,62,22(62)
5 Interval Checkers = 2/36 = 16,61
You need to consider the above probalities, especially when you want to make a point by leaving a blot.
For example, when the dice is 4,5 when you play 13/9 and 13/8, you are going to find
Especcially in the cases where you leave a blot for the sake of making a point, you need to consider both of these probabilities. Therefore the dice will give you a higher chance to play your game.
Probabilities of making a blot by hitting in the starting position
Blot in board 20 = 5/36 = 13,31,11,33,44
Blot in board 21 = 4/36 = 24,42,22,44
Blot in board 22 = 3/36 = 35,53,55
Blot in board 23 = 3/36 = 46,64,44
Blot in board 24 = 1/36 = 55
Blot in board 18 = 5/36 = 16,61,11,33,66
Blot in board 16 = 2/36 = 22,44
Blot in board 15 =1/36 = 33
Blot in board 14 =1/36 = 22
In the starting positions, your opponents probability of hitting you and making a point is highest at the boards 20 and 18. It is a 5/36 probability, 14% in other words.
On the other hand the probabilties are lowest at 24 and 14. In these kinds of positions your opponents chances for hitting you and making a point is only 1/36.
In the cases where you will lose a game because of your opponent hitting you and making a point, you need to consider these probabilites.
If your goal is to make a point at 20 and 18 at a second roll, then you need to consider your opponents' points and then risk that single checker inside.
