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BACKGAMMON BY THE BAY
Problem #9 solution
  		Match to 11
Blue 0, White 1

0123456bar789101112

0123456bar789101112
     Blue to play.
Cube action?

Candidate plays:

  1. Roll
  2. Double / Accept
  3. Double / Pass

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RK:
If you read the results of problem #8, you've already got a handle on this one. Blue has a clearcut double: a big racing lead, not much difficulty getting home, and some chances to point on White's remaining blot. The tough decision is whether to take. White needs to hit a shot to win, for all practical purposes. His board is strong, even though he did break his 5-prime. After hitting, White will often be able to win with the cube.

Blue has to safety the blot on 16, then she has four points in front of White's anchor to clear. Each of those points represents some chance of being forced to leave a blot and get hit. On the other hand, White's four checkers back represent some chance of getting gammoned, particularly if the loose checker gets pointed on.

Rollouts put the cubeless equity (meaning the game is played to conclusion) at .587 on level 5 and .583 on level 6 (which gives a hint that the level 5 figures are fairly accurate). Does this number indicate a take or a pass?

Certainly dropping couldn't be much of an error if at all. But it's conceivable that a cubeless equity of .587 could be a take. You need to look at the figure for "White owns cube"; this figure takes into account the fact that White can win more games by virtue of cube ownership. In this case, Blue's equity is .501. Therefore, if White takes, Blue expects to win 1.002 points; while if White passes, Blue wins 1.000 points! This is about as close a decision as you can ever get.

So why include this problem, since White can't really be wrong no matter what he does? Well, it's actually quite useful to see positions that are right on the borderline. Make White's position any better (e.g. assume he made one of the recommended plays in problem #8) and it's a clear take. Make Blue's position better (say the blot on 16 is safely on the 8 point) and it's a clear drop. And at other match scores this could be a clear take or a clear drop (here the match score doesn't give significantly different odds than money play).

JF:   Double / Pass (level 7 evaluation) 

Pip counts:          Blue   103                     White  136

                     Blue                           White              
Level 7 Evaluation   Equity   Win    G/BG    BG     Win    G/BG    BG  
Cubeless             +0.595   73.7%  15.4%   0.4%   26.3%   3.5%   0.1%

Level 5 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
Cube centered        +0.878   93.1%   1.8%   0.0%    6.9%   0.2%   0.0%
Blue owns cube       +0.900   94.7%   1.9%   0.0%    5.3%   1.2%   0.0%
White owns cube      +0.501   67.4%  15.8%   0.3%   32.6%   0.9%   0.0%
Cubeless             +0.587   72.8%  16.6%   0.3%   27.2%   3.7%   0.1%

Level 6 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
Cubeless             +0.583   72.7%  16.6%   0.2%   27.3%   3.8%   0.2%




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