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BACKGAMMON BY THE BAY
Problem #20 solution
  		Match to 11
Blue 1, White 6

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0123456bar789101112
     Blue to play 53

Candidate plays:

  1. 24/21*/16
  2. 8/3* 24/21*
  3. 8/3* 6/3

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RK:
Blue already has a better board, having made the 5 point. This roll allows her to put White on the bar, giving good chances to be able to win with the cube next time. So what's the best way to hit?

8/3* 6/3 has the advantage of securing an additional home board point, making it harder for White to enter from the bar. If White fans (25% of the time), he won't be able to take a double.

On the other hand, if White enters, even without hitting back, there are some drawbacks to this play: Blue hasn't gained much in the race; her rear checker is still back on the 24 point; and White could still make the 4 point.

Hitting 24/21* has some big advantages:

  1. It gains a lot of ground in the race.
  2. It reduces White's offense, removing the possibility of his covering the 4 point immediately.
  3. It advances Blue's rear checker to be in better position to escape.

These advantages definitely outweigh the value of making the 3 point.

After hitting, Blue could consider hitting again on the 3 point. This makes it impossible for White to anchor (except with small doubles), leading to the possibility of a blitz. On the other hand, it increases White's return shots from the bar, giving 3s in addition to 2s. Also, if White enters without hitting, Blue won't be strong enough to play for the gammon, but will just claim with the cube. So the extra risk doesn't seem worth it. By simply running with 21/16, Blue escapes her back checker and minimizes return shots. Even if White anchors, Blue is in excellent shape. 

Pip counts:          Blue   131                     White  128

                     Blue                           White              
Candidate Plays      Equity   Win    G/BG    BG     Win    G/BG    BG  
24/21*/16            +0.490   69.2%  16.1%   0.4%   30.8%   5.8%   0.1%
8/3* 24/21*          +0.429   63.3%  24.0%   0.6%   36.7%   8.1%   0.2%
8/3* 6/3             +0.265   57.5%  20.9%   0.5%   42.5%   9.7%   0.3%




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