Bearing off (The Last Lap)

Introduction to Bearing Off

In this first article on bearing-offs we are going to look at the final stages (or endgame) of a backgammon game. As a reminder you cannot bear off any checkers until you have all fifteen of them in your home board. If, during the course of bearing off, you have a checker hit and sent to the bar, it must make the return journey from the bar all the way back into your home board before you can bear off any more checkers.

We will look at the type of bear-offs that can occur and then at some of the very basics. In subsequent articles we will look in depth at an area of the game that might seem simple but which is actually quite complex.

Bear Off Types

There are really four types of bear-off:

Without Opposition (a simple race)
Against an anchor (your opponent holds one point in your home board)
Against a checker (or checkers) on the bar
Against a back game (your opponent holds two – or more – points in your home board)

As with all backgammon games effective use of the doubling cube is critical to success and we will make sure we cover the use of the doubling cube in future articles

The Basics of Bearing Off

For the time being we won’t worry about the opposition and we’ll assume we’re in a simple race. You can’t bear your checkers off before you’ve borne them in and therefore our first priority is to get them into our home board.

During the normal course of a game you will have made some points in your home board and the only decision that you then have to make is where to try to put the other checkers as your bear them in.

It might seem intuitively obvious to spread them evenly across the your home board as shown below:

bop1.1

In fact red’s distribution is much better than black’s. It is important to have the extra checkers, i.e. more than two per point, on the three highest points in your home board.

This is because of a concept we call “wastage” which we will explore in more depth later but to take a trivial example imagine you have your checkers on your ace point. Now you bear off two or four checkers (when you roll a double) each turn but the numbers on the dice are irrelevant as a 6 is as good as a 1. Every time you roll a six you ‘waste’ 5 pips. To bear off efficiently we seek to keep wastage to a minimum.

There’s an old saying in backgammon that you can never have too many men on your 4-pt for the bear-off. To see why look at the following diagram:

bop1-2

Here black has borne in very inefficiently and he has too many men on his 2-pt and 3-pt. Every time he rolls a 4 he will have to play either 6/2 or 5/1. Subsequently he may bear those checkers off by rolling 3’s, 4’s, 5’s or 6’s incurring significant wastage.

The position that creates the least wastage is shown in the next diagram:

bop1-3

This positioning of the black checkers - 7 on the 6-pt, 5 on the 5-pt and 3 on the 4-pt is the theoretically best position. You are unlikely to achieve it in practice but it does reinforce the basic tenet that extra checkers belong on the higher points.

Once you have all fifteen checkers in your home board taking them off is relatively straightforward and most of the time you will bear off a checker from the point that equates to the number on the dice. For example, there is no bear off position where it is incorrect to bear a checker off the ace point if there is a checker on the point to bear off.

Very occasionally subtleties come into the bear off. The following is an example:

bop1-4

Black has a 63 to play. He could play 6/off, 4/1. The problem with this play is that when he rolls his next 3 he will not be able to use the number to take a checker off. As he has an even number of checkers left this may cost him a whole roll, i.e. he will take an extra roll to take off all his men.

However, the rules of backgammon allow you to play your numbers in either order and therefore black can make the much better move, 6/3, 4/off. The checker that he puts on his 3-pt with this move may save him that whole roll.

Summary

The basic Backgammon Strategy for an unopposed bear off is quite simple. Get them in and get them off. Whilst the prior play in the game will have defined where some of your checkers are in your home board it is important that the remainder are borne in to the higher points (the 4,5 and 6-pts).

Remember the old adage – you can never have too many men on your 4-pt. Finally remember that backgammon allows you to play the numbers on your dice in either order, this sometime helps you to fill gaps.

Chris Bray - May 2006

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