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BACKGAMMON BY THE BAY Problem #8 solution		Match to 11 Blue 1, White 0
		Blue to play 61 Candidate plays: 24/18 7/6 24/18 6/5 24/18 3/2 21/14 21/15 7/6 21/15 6/5 7/1 6/5

RK:
First question: Should Blue run with one of his back checkers or stay back? If he runs a checker, it's exposed to a double shot no matter where he puts it. Nonetheless, it's clear to run. Blue is well behind in the race, but has a solid five-prime to contain any checkers he's lucky enough to hit. Therefore he has to challenge White in the outfield. Getting hit costs Blue little, while if he can hit back, he gains tremendously. Staying back has these other drawbacks:

• The checker can be pointed on with several numbers, making it easier for White to get home.
• Blue breaks his five-prime, reducing his winning chances if he hits a shot.
• He might be forced to break his board further if he can't escape a checker next time.

Assuming Blue does run a checker, should he play 24/18 or 21/15? This isn't so clear.

If Blue plays 24/18 (with 6/5, which of course is better than 7/6), White won't be anxious to hit, since she'll often be subject to several return shots. Blue might even be able to make the 18 point, which would hinder White further. On the other hand, it doesn't challenge White's blot directly, so it results in fewer total shots and wins than 21/15.

If Blue plays 21/15, he directly challenges White's blot, forcing her to hit, safety, or be hit. Therefore, Blue is more likely to get hit with this play (and gammoned). He's also more likely to hit White and win.

If he plays 21/15, what's the best 1? In situations like this, it's often right to stay on the 15 point, because if White hits there, Blue may get some return shots from the bar (16, 36, 46), while if Blue gets hit on the 14 point, there are no return shots from the bar. However, there are other considerations. After 21/14, there are several numbers (66, 63, 61, 43, 33) where White must leave a direct shot somewhere. After 21/15 6/5, the only numbers where White must leave an exposed outfield blot are 54, 52 and 41, but 54 and 41 allow her to point on the 1 point. So White has very few immediate bad numbers (the key here is that advancing 15/14 duplicates White's 5s).

Conclusion: the plays are close, but 21/14 results in the most wins, and loses slightly fewer gammons than 21/15 6/5.

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Pip counts:          Blue   143                     White  103

                     Blue                           White              
Candidate Plays      Equity   Win    G/BG    BG     Win    G/BG    BG  
21/14                -0.479   32.7%   4.8%   0.1%   67.3%  17.7%   0.5%
24/18 6/5            -0.499   29.5%   4.1%   0.1%   70.5%  12.8%   0.3%
21/15 6/5            -0.514   32.0%   4.8%   0.1%   68.0%  19.7%   0.6%
24/18 7/6            -0.540   27.5%   3.8%   0.1%   72.5%  12.7%   0.3%
21/15 7/6            -0.572   30.3%   5.2%   0.2%   69.7%  22.5%   0.8%
24/18 3/2            -0.578   27.4%   3.8%   0.1%   72.6%  16.0%   0.4%
7/1 6/5              -0.604   26.4%   3.9%   0.1%   73.6%  16.7%   0.4%

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