Fine Holding Game Requires Getting Wagons in a Circle
Paul Magriel, 1980
New York Times, May 4, 1980
Backgammon Often in backgammon a player will fall behind in a race yet still have good chances of winning. The basic strategy in such cases is to play a holding game. In such a game the player who is behind seeks to hinder his opponent from coming home safely by holding certain key points on the opponent’s side of the board.

To play an effective holding game, it is necessary to plan ahead in order to create the best defensive formation.

In the diagrammed position, White has gained a significant lead in the race and has already doubled Black. Thus, Black’s main winning chance is to wait and hope for a shot. White may have trouble bringing home all three men on his mid-point, the 12-point. White will be able to move the first man easily, but then “clearing” the point with the remaining two men will be difficult. In fact, with Black holding the 20- and 13-points, White will need a double to come home safely. If White fails to roll a double in time, he will be forced to leave a man exposed.

Black to play 2-2.
With the roll of 2-2, one plan for Black is to improve his home board by playing 8/4(2), making the 4-point and so building a powerful 5-in-a-row prime (from the 3-point to the 8-point). Another plan is to make a different holding formation by switching from the 20-point to the 18-point. The remaining 2’s could be played 6/4. By making the 18-point, White’s bar-point, Black also prevents White from coming home safely without a double.
(a) 8/4(2)
(b) 20/18(2), 8/4
Which formation is better? If we view Black’s position from a static point of view — that is, if Black does not have to move — then both formations give Black about equal chances for a shot. From a dynamic point of view, however, making the 18-point is far superior.

The holding formation Black now has requires Black to hold both the 20-point and the 13-point. Unfortunately, Black lacks the time to hold both. Black will soon run out of constructive moves on his side of the board and be forced to give up the 13-point. When Black gives up the 13-point, White can bring his last two men on the 12-point down one at a time, exposing himself at most to an indirect 8-shot.

By contrast, the 18-point alone is sufficient to stop White’s men on the 12-point. Thus, by making the 18-point, Black creates a holding position that he will be able to keep; Black frees his men on the 13-point, giving himself a good holding game. Failure to plan ahead will result in a position that, although superficially adequate, will not be able to be maintained.

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Tom Keith 2013 
Money play
Black owns 2-cube
Black rolls 2-2

1296 games with VR
Checker play: 2-ply
Cube play: 3-ply Red

2-2: Game BG   Equity
1 20/18(2), 8/4 W
−0.3483 x  (b)
8 8/4(2) W
−0.3859 (0.0376)  (a)

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