Magriel's NYT Columns

It is often difficult psychologically for a backgammon player to actively look for winning variations in an unpromising position. Although it takes perhaps greater concentration to focus on a game that seems already lost, this ability is critical — for if you’ve already given up, you may miss seeing extraordinary opportunities.

In the diagrammed position, Black is hopelessly far behind in the race. It is vital, therefore, for Black to hit White and prevent White from coming home.

Black to play 2-1.

Unfortunately, with the roll of 2-1, Black is unable to hit White’s blot on the 9-point. Indeed, with this particular number, Black is unable even to safety his own blot on the 13-point.

Disappointed, Black may automatically play 13/10, moving closer to White in order to give White only a 1-shot (11 chances out of 36) to hit. Considering White’s strong home board, this certainly seems prudent. However, if Black thinks about his situation carefully, he may realize that he is not interested in decreasing his chances of being hit — but rather in increasing his chances of hitting White later. After all, Black is not likely to be gammoned even if he is hit.

The correct play is 7/4, leaving Black’s blot on the mid-point (13-point). This leaves Black exposed to a direct 4-shot (15 chances in 36), and so at first appears foolhardy because Black is more likely to be hit.

To understand this move, let’s look at a crucial but often neglected concept in backgammon — that of control. Each spare man exerts a sphere of influence on those points that are in direct range — that is, those points between one and six pips ahead. If Black plays 13/10, then White will either hit or move behind Black to the 11-, 12-, or 13-points, out of direct range of Black’s men on the 20-point. As a result, the only combinations that force White to leave a direct shot are 6-5 and 6-6 (3 chances out of 36).

But by playing correctly 7/4 and staying on the 13-point, Black retains control of his outer board, as well as White’s outer board. As a result, if White is unable to hit Black, he will be left with no safe landing space. Indeed, 15 combinations will force White to leave a direct shot on his next roll because Black exercises control of the 10-, 11-, and 12-points. Thus, Black has created significantly increased winning opportunities by actively looking for rolls that play poorly for White.

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