The Probability Of Moving
Each move in backgammon is governed by the roll of two dice. As each die has six faces,
it can land showing any number from 1 to 6. For both dice, this means there are 6 x 6
or 36 total combinations of dice throws. Some of these are duplicates, for example 1,2
is the same as 2,1. In total there are 21 different dice combinations.
A direct move covers six points or less, that is it can be made with a single die roll.
An indirect, or combination move, crosses more than six points, and always uses both dice.
Movement Probability Table
The table below shows the relative probability of moving any given distance:
From the probability table, you can see that you are far more likely to achieve a direct
move than an indirect one. In fact, there are 17 different ways in which it is possible
to move a distance of six points, which gives a probability of 17/36 or 47%!
This means that it is extremely dangerous to leave a blot six points away from your opponent
- but it will be relatively safe seven points away.
When you are playing a game, remember that not all combinations will be available,
because some points will be held by your opponent.
Key Points on the Board Bearing Off