simple bear-off

This week we are going to look at a relatively simple bear-off. In the position; should black double? Should white take if doubled?

In bear-offs we can’t use our Race/Threat/Position/Opponent criteria to evaluate positions. We should still factor in the opponent but most of what we know about bear-offs we know through study and the accumulation of reference positions.

So for example we know that a 3-roll vs 3-roll ending as shown below is a double for black and a drop for white.

White wins only 21.2% of the time which nowhere near the 25% he needs to take. Also white never gets to redouble.

In the 4-roll vs 4-roll position shown below the cube action is now double/take:

White now wins about 27% of the time and sometimes gets to use the cube to good effect. However beware. If we change the position by one pip to:

The cube action reverts to double/drop. This is because double ones no longer take off four men and white may also throw four successive 1’s and on the last turn will not be able to bear-off his last checker. Small differences can mean a lot in backgammon.

When we make judgements in a bear-off we mentally refer to positions such as the ones above and do comparisons. In our first position both sides have five checkers each so initially we might think it is a 3-roll vs 3-roll position and use that benchmark. But black in particular may well take 4 rolls (for example look what happens if black roll 42 followed by 42). It looks as if it is roughly a 3½ roll vs 3-roll position. This should give you the answer that white will have a comfortable take.

Does black have a double? Just – the position is volatile enough that by next turn black may well have lost his market so he must double now. Snowie’s database confirms this:

Chris Bray
May 2007