Racing Tactics 
The Importance of Middlemen

From Backgammon Times, Volume 3, Number 2, Summer 1983. 
 Black to play 22. 
The first step in playing the 22 correctly is to bear off as many men as possible. With three of the 2's, Black bears off men from the 2 and 4points. The second step is to choose the correct man to move with the fourth 2, and in this case each of Black's three possible choices produces a different number of winning doubles.
 Black has one more 2 to play. 
The best choice is 2/off, 4/off, 5/3 (Play A), moving the man on the 5point to produce four winning doubles: 33, 44, 55, and 66. The worst choice is moving the man on the 3point (Play B), because both 33 and 44 are eleminated as winning rolls. In between is moving the man on the 6point (Play C). This move eliminates 33 but not 44.
If Black is familiar with endgame positions or takes the time to analyze the situation, he will make the right play. However, near the end of a close, exciting race, it can be very difficult to patiently examine all possible moves and then accurately count the number of winning doubles for each.
To help in this situation, the author has devised a shortcut method of finding the play that maximizes the number of winning doubles when there are exactly three men left in a player's home board.
The key factor is the location of the second highest (middle) man of the remaining three. The best place for this man is the 2point, followed by the 3point and then in order, the 4, 5, 6, and 1points.
To verify this preference order (2, 3, 4, 5, 6, 1), look at Black's three possible plays with the 22. After each play, the three remaining men wind up on the following points: A (3, 3, 6), B (1, 5, 6), and C (3, 4, 5). Therefore the middle man in each case is A (3), B (5), and C (4). According to the preference order the choices are, from best to worst: A, C, B—the correct ranking as previously determined.
In case of a tie, break the tie by applying the preference order to the highest man. For example, if Black rolled 33 instead of 22, he would bear off men from the 3 and 6 points, leaving a fourth 3 to play.
 Black to play a 3. 
If a player's lead is large enough that he is likely to have at least two more chances to roll, the preference order may not apply. Sometimes a different arrangement is better for protecting the lead.
Dr. Jeff Ward, a former professor of geology, has written several books on backgammon, notably The Doubling Cube. He is also head of the Backgammon Special Interest Group of MENSA.
More articles by Jeff Ward
More articles on racing tactics
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