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BACKGAMMON BY THE BAY
Problem #26 solution
  		Match to 11
Blue 1, White 8

0123456bar789101112

0123456bar789101112
     Blue to play 63

Candidate plays:

  1. 18/9
  2. 18/12 18/15
  3. 18/12 13/10
  4. 18/12 9/6
  5. 18/12 6/3
  6. 13/4
  7. 13/7 18/15
  8. 13/7 9/6
  9. 13/7 6/3
  10. 9/3 18/15
  11. 9/3 13/10

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RK:
The main question here is: Should Blue keep the anchor on White's bar point, or start to clear it?

Blue has a solid front position. Her 5-point prime, with White anchored away from the edge, is practically as good as a 6-prime. It's virtually impossible for White to win going forward, since it requires two 1s and two 6s to escape the back checkers, and White runs a serious risk of being hit and closed out if he attempts it.

In fact, White's main goal should be to avoid getting any additional checkers hit, which would increase his chances of getting gammoned, and just hope for a shot as Blue bears off. The last thing he wants to do is hit Blue now, because that would hurt his timing for the ace-point game and run the risk of getting more checkers hit.

Therefore, there's no danger to Blue in leaving a single checker back on the 18 point. Blue's main worry is being forced to break her prime, which is her main asset. If she keeps the 18 point, then a roll of 44 next time would break the prime. By running at least one checker with 18/12, she avoids that possibility, while still maintaining pressure on White's outfield checkers. White has to play carefully to avoid having another checker sent back.

After 18/12, how should Blue play the 3? She might as well leave one checker back on the 18 point to bother White. Therefore 13/10 keeps the greatest number of builders aiming at the 8 point. 

Pip counts:          Blue   114                     White  135

                     Blue                           White              
Candidate Plays      Equity   Win    G/BG    BG     Win    G/BG    BG  
18/12 13/10          +0.847   86.8%  12.0%   0.6%   13.2%   1.3%   0.0%
18/12 18/15          +0.841   86.6%  11.8%   0.5%   13.4%   1.5%   0.0%
18/9                 +0.829   86.4%  10.9%   0.5%   13.6%   1.2%   0.0%
18/12 9/6            +0.822   85.0%  13.6%   0.7%   15.0%   2.0%   0.1%
18/12 6/3            +0.817   84.8%  13.6%   0.7%   15.2%   2.2%   0.1%
13/7 18/15           +0.798   83.3%  15.5%   0.8%   16.7%   3.1%   0.1%
13/7 9/6             +0.796   84.1%  12.8%   0.6%   15.9%   2.0%   0.1%
13/4                 +0.793   83.7%  13.6%   0.7%   16.3%   2.3%   0.1%
9/3 13/10            +0.790   83.7%  13.4%   0.7%   16.3%   2.4%   0.1%
9/3 18/15            +0.788   82.5%  16.5%   0.9%   17.5%   3.5%   0.1%
13/7 6/3             +0.784   83.6%  12.9%   0.6%   16.4%   2.2%   0.1%




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