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BACKGAMMON BY THE BAY
Problem #32 solution
  		Match to 11
Blue 7, White 10 (Crawford)

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     Blue to play 61

Candidate plays:

  1. 20/13
  2. 20/14 6/5
  3. 13/7 6/5

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RK:
With this 61, something has to give. Should Blue break her anchor or her midpoint?

Blue is behind in the race and wants to hit a shot. In general terms, it's usually right to retain the furthest back point in order to maximize long-term shots. However, in this position, there are several reasons why breaking the anchor is better.

Since the number plays safely 20/13, Blue leaves no direct shots. White is not anxious to hit loose, and his only crusher is 44. White has no pick-and-pass numbers (other than 11, which is bad with either play); while 53 and 62 play a bit worse, they leave Blue at least one direct return shot. Since White has no points in his own outfield, and no spare on the 6 point, he can't threaten Blue's blot without leaving a direct shot. In effect, leaving a single blot on the 20 point is only slightly worse than having an anchor there.

Breaking the midpoint, on the other hand, exposes Blue to eleven hits, which give White a much easier road to getting home. (In addition, White's gammon chances are increased, although that doesn't matter at this match score.) Some of these numbers, such as 51 and 41, are disasters for White if Blue keeps the midpoint. The only real gain from keeping the anchor is with numbers like 44, 62 and 53. Most other numbers, like 63 or 64, leave the same number of shots either way.

Another consideration is Blue's next roll, if White rolls a stalling number like 32. After 20/13, Blue has an easy time playing the spare from the midpoint, while after 13/7 6/5, she'd probably have to clear the midpoint.

Since gammons don't count for White at this match score, the discrepancies between the plays aren't quite as great as the rollouts show, but nonetheless 20/13 is the clear favorite. 

Pip counts:          Blue   104                     White   63

                     Blue                           White              
Candidate Plays      Equity   Win    G/BG    BG     Win    G/BG    BG  
20/13                -0.356   33.4%   3.5%   0.1%   66.6%   6.0%   0.0%
13/7 6/5             -0.500   29.3%   2.9%   0.1%   70.7%  11.2%   0.2%
20/14 6/5            -0.554   29.2%   3.9%   0.1%   70.8%  17.5%   0.2%




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