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BACKGAMMON BY THE BAY
Problem #21 solution
  		Match to 11
Blue 1, White 6

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0123456bar789101112
     Blue to play 66

Candidate plays:

  1. 16/4* 9/3(2)*
  2. 16/4* 9/3* 8/2
  3. 16/10 9/3(2)* 8/2
  4. 13/7(2) 9/3* 8/2
  5. 13/7 9/3(2)* 8/2
  6. 9/3(3)* 8/2
  7. 9/3(2)* 8/2(2)

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RK:
A great number for Blue, who has to choose four moves from the following options:

Making a five-prime is always appealing. However, its main virtue is to prevent the opponent from escaping, while allowing the possibility of rolling the prime forward smoothly. But here, Blue has already escaped her back checkers and secured a racing lead, so blocking is not of key importance. And how would Blue play the other two 6s? The "purest" play would be 16/4*, but that would allow White 2s and 4s to hit back and 3s to anchor. Pointing on the 3 point would give up the 9 point and leave a blot there, while still leaving 2s to hit and 3s to anchor. So the best play is to cover the 2 point and hit loose on the 3 point, keeping the 9 point.

But if that pseudo-blitz is the best play after making the prime, why not attack all the way? Blue has to move forward anyway, and White's board is at its weakest, so Blue should go for the gusto and try to win a gammon. The best play is simply to cover the 2 point and point on the 3 point, giving a four-point board. White must pray for a 4 to anchor, otherwise he's in serious gammon danger. Even if White anchors, Blue is in good position to breeze home safely. Then after 9/3(2)* 8/2, the obvious fourth 6 is 16/10; 13/7 is unnecessarily loose.

(Another idea is to go all out to deny White an anchor with 16/4* 9/3* 8/2, but this leaves a double shot in return. In a blitz, if you have a choice between making a new home board point and hitting a blot, making the point is usually best.) 

Pip counts:          Blue   123                     White  139

                     Blue                           White              
Candidate Plays      Equity   Win    G/BG    BG     Win    G/BG    BG  
16/10 9/3(2)* 8/2    +1.093   83.8%  42.2%   1.1%   16.2%   1.5%   0.0%
13/7 9/3(2)* 8/2     +1.064   82.2%  43.2%   1.2%   17.8%   2.3%   0.1%
16/4* 9/3* 8/2       +1.047   79.7%  47.3%   1.5%   20.3%   3.5%   0.1%
16/4* 9/3(2)*        +1.016   79.0%  46.1%   1.5%   21.0%   3.8%   0.1%
9/3(3)* 8/2          +0.970   80.7%  37.0%   0.9%   19.3%   2.3%   0.0%
9/3(2)* 8/2(2)       +0.960   78.7%  40.9%   1.1%   21.3%   3.4%   0.1%
13/7(2) 9/3* 8/2     +0.894   79.0%  33.8%   1.1%   21.0%   3.3%   0.1%




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