Burying vs. Bearing In
by Douglas Zare

The 7-5-3 Bearoff Position

In a large fraction of backgammon games, at some point the players break contact and race. Some people think racing is pure luck, but there is still some skill left: handling the cube and positioning one's checkers properly. Since it comes up so frequently, one should know the basics of bearing in correctly.
Experts rarely make large errors in non-contact checker plays, but beginners often cost themselves a noticeable amount in each game. This is easy to avoid once one knows what the correct goals are.
What is the fastest way to bear off 15 checkers?

 

A novice will think of the top position, and an expert will think of the bottom, the 7-5-3 position. Certainly no matter who is on roll, the top player is a big favorite. However, one never has a choice between these two positions. While bearing in, you have no control over the pip count. The top player has a pip count of 15, and the bottom player has a pip count of 79. A more reasonable comparison is between the following sides:

 

Which side would you choose?
Now, the pip count is 15 for both players, and the bottom player will be off in 2-3 rolls, whereas the top player will probably take 6-7 rolls. Clearly the bottom position is better, even though not all rolls take at least two checkers off.
Of course, one almost never sees someone try to put 15 checkers on the ace point. However, one probably would not stumble upon the 7-5-3 position (at bottom in the first diagram) by chance. It was checked by a computer, and you can simply rely on the fact that among all bearoff positions with 79 pips, the 7-5-3 position is in some sense the most efficient, bearing off fastest on average. Whether you are ahead or behind in the race, the 7-5-3 position is a good goal.