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BACKGAMMON BY THE BAY
Problem #33 solution
  		Match to 11
Blue 8, White 10

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     Blue to play 41

Candidate plays:

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

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RK:
The obvious 1 is to cover the 5 point, but then Blue has to leave a blot somewhere. Or she can avoid leaving a blot by making the 4 point instead. How to decide?

Blue is ahead in the race, and mostly wants to get home safely, which argues for making the 4 point. Making the points in strict order is not crucial in this position, since Blue isn't going to form a prime and is unlikely to carry out an attack.

On the other hand, after making the 4 point, Blue's position is a bit inflexible, so there's a good chance of leaving a shot next time. In addition, White has 2 blots in his board, which will be covered soon. This argues for taking a risk now to try for a better position.

If Blue decides to make the 5 point, which is the correct 4?

At this match score, a gammon is especially valuable to Blue, so one might consider attacking aggressively with 6/2*: if White hits back, Blue might pick up one or more of White's other blots. However, the play is anti-positional, and leaves Blue only 6s to cover a point she doesn't really want to make yet. And it's not very likely to result in a successful blitz, since Blue doesn't have enough ammunition in place. Therefore, a more positional play is warranted.

Slotting the 4 point seems logical, since it's the point that Blue wants to make next. However, there are some drawbacks. First, there are some awkward rolls next time that not only don't cover but force an additional blot (61, 65). More importantly, White gets to hit with his spare back checker and keep his anchor.

On the other hand, after 13/9, if White wants to hit he's likely to have to break his anchor, leaving a wide-open position with greater gammon risk (particularly dangerous at this score). Also, Blue's next turn plays well, with many numbers to cover the 9 point or make an inner board point, and no numbers that force a double shot. 

Pip counts:          Blue   134                     White  151

                     Blue                           White              
Candidate Plays      Equity   Win    G/BG    BG     Win    G/BG    BG  
13/9 6/5             +0.260   61.3%  10.6%   0.4%   38.7%   7.5%   0.1%
8/4 5/4              +0.239   61.5%   7.5%   0.1%   38.5%   6.6%   0.1%
8/4 6/5              +0.155   58.0%   8.3%   0.2%   42.0%   8.7%   0.1%
6/2* 6/5             +0.098   55.9%   8.5%   0.2%   44.1%   10.4   0.2%




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