Magriel's NYT Columns

In backgammon, even the most elementary position, such as a bearoff without opposition, may contain hidden complexities. Indeed, here is a case in which a little knowledge can be dangerous. An experienced player is more likely than a novice to go astray in the diagrammed position.

Black to play 6-1.

Both players have already begun to bear off. Black’s highest priority each turn is to take off as many men as possible. Accordingly, with the roll of 6-1, Black first uses the 6 to take a man off the 6-point. With the 1, however, Black misses (cannot take a man off). The general rule — when it is not possible to bear a man off — is to fill in gaps (points without men) in order to avoid misses on future rolls. Following this rule, the inexperienced player would play 2/1 to eliminate the gap on the 1-point.

A more knowledgeable player may first stop to assess his overall chances and realize that he is in dire straits. To see why, evaluate the number of rolls left on each side to complete the bearoff.

After Black completes this play and takes one man off, each side will have exactly eight men left. Thus, if both sides take two men off each roll (neither side rolls a double or misses), both players would complete the bearoff in exactly four rolls. Because it is now White’s turn, White will win the race by one roll. Black’s only hope, then, is to recoup an entire roll by taking off four men in one turn; in other words, Black needs to roll a high double.

As a result of this pessimistic evaluation, an experienced player may attempt a drastic remedy in hopes of improving his chances. Because Black needs to take four men off, he may play 6/off, 5/4, to prepare for 4-4’s by stacking four men on the 4-point. In fact, he may secretly congratulate himself for his clever maneuver. Unfortunately, the logic is faulty and so the remedy actually worsens his already poor condition.

The correct play is still 6/off, 2/1. Even though a roll behind, filling the gap on the 1-point has higher priority than preparing for immediate double 4’s. In order to understand why, it is necessary to examine in detail which variations are better for each play.

First, consider what happens if Black next rolls his best, either 6-6 or 5-5. In this case Black stands considerably better after playing 2/1. 5/4 leaves Black with a dangerous gap on the 1-point, and as a result Black is only a small favorite. By contrast, 2/1 leaves Black with an essentially winning position — White will be hard-pressed to accept an immediate redouble.

Next, consider what happens if Black rolls a double immediately. Of course Black gains by playing 5/4 (because he can now take four men off), but even so, Black is still in jeopardy of rolling a 1 and losing.

Finally, consider the critical variations in which Black first rolls a 1. These variations occur much more frequently than starting with a high double, and all favor 2/1. 5/4 leaves a gap on the 1-point, so a 1 will cost Black a full roll. Now Black will never be able to catch up, even if he later rolls a big double. By correctly playing 2/1, Black still gives himself winning chances for several rolls. 5-5’s, 6-6’s, and later 4-4’s will be effective even after rolling a 1.

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