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BACKGAMMON BY THE BAY
Problem #4 solution
  		Match to 11
Blue 1, White 0

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0123456bar789101112
     Blue to play 41

Candidate plays:

  1. 22/18 22/21
  2. 13/8
  3. 13/9 22/21
  4. 13/9 6/5
  5. 6/1*

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RK:
What's going on in this position? White has a racing lead, but has one back checker trapped. Blue's main concern is to prevent White's checker from escaping.

In situations like this, quite often the best approach is to attack (with a play like 5/1*). After all, Blue has a better board than White, is already behind in the race, and has an anchor, while White doesn't. What more can you ask for in an attacking play? Well, more builders, for one thing. Even if White doesn't hit back immediately, Blue has only 3 numbers to cover the ace point, and will be an underdog to cover for at least another roll or two. Plus, the two point will remain open.

A key point here is that White is not a favorite to be able to escape anyway, so Blue doesn't need to be so impatient. And Blue has an attractive use for his ace: advancing the anchor 22/21. If White had already escaped her back checker, it might be right to stay back on the 22 point in order to get more defensive shots, but here Blue has forward chances, so the more advanced anchor is better.

With the 4, advancing the other back checker with 22/18 is slightly better than bringing down a new builder. The checker is exposed to 6s and 1s, but these are the same numbers that White needs to advance her back checker, and most hits subject White to some return shots at a time when she definitely doesn't want another one hit. If not hit, that checker should be able to keep advancing, providing more coverage for Blue's outer board. In addition, playing 13/9 doesn't add many point-making numbers to Blue's arsenal. 

Pip counts:          Blue   146                     White  120

                     Blue                           White              
Candidate Plays      Equity   Win    G/BG    BG     Win    G/BG    BG  
22/18 22/21          +0.013   49.4%  11.6%   0.3%   50.6%   9.1%   0.2%
13/9 22/21           -0.006   48.9%  12.5%   0.4%   51.1%  11.1%   0.3%
13/9 6/5             -0.035   47.9%  12.7%   0.4%   52.1%  12.0%   0.4%
13/8                 -0.037   47.9%  12.8%   0.4%   52.1%  12.2%   0.4%
6/1*                 -0.081   47.4%  12.6%   0.3%   52.6%  15.2%   0.5%




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