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

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0123456bar789101112
     Blue to play.
Cube action?

Candidate plays:

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

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RK:
Blue has a clear positional advantage here. He's got a more advanced anchor than White, and has five blocking points in front of White to only three for White. He also has a spare on his midpoint to play with, which usually allows him to keep his position for at least another roll, while White's next 6 forces her to break the midpoint or bar point. Blue must double now: it's not clear that White will take, and even if so Blue could certainly lose his market if he fails to double (by making the full prime with 66 or 33, or hitting a shot).

Now for the take decision: White has the 2-point anchor, so worst case she'll have some chances to hit a shot as Blue is bearing off. Her timing for the 2-point game may not be great, but there are always some chances to win. And with only two checkers back, the chances of being gammoned aren't too great.

In addition, as long as Blue hasn't made his bar point, there's always some chance for White to win going forward. Blue isn't guaranteed to get his back checkers home safely. At some point he'll have to run from the 21 point; if White hasn't been forced to crunch her board too badly, she may be able to attack Blue, then escape her back checkers and win. (White has to be careful, though, because if something goes wrong while she's escaping her back checkers, she could end up getting gammoned.)

On level 7, Jellyfish evaluates the position as a clear take (.501 cubeless equity). The rollouts show White doing worse (.566 cubeless) but indicate that White still has enough equity to take (.476 for "White owns cube", compared to .500 for a minimum drop).

JF:   Double / Take (level 7 evaluation) 

Pip counts:          Blue   133                     White  129

                     Blue                           White              
Level 7 Evaluation   Equity   Win    G/BG    BG     Win    G/BG    BG  
Cubeless             +0.501   70.7%  13.9%   0.4%   29.3%   5.4%   0.1%

Level 5 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
Cube centered        +0.781   88.8%   1.1%   0.1%   11.2%   0.5%   0.0%
Blue owns cube       +0.820   91.5%   1.2%   0.1%    8.5%   2.1%   0.0%
White owns cube      +0.476   67.3%  14.0%   0.6%   32.7%   1.4%   0.0%
Cubeless             +0.566   73.1%  14.5%   0.6%   26.9%   4.6%   0.1%

Level 6 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
Cubeless             +0.562   72.8%  15.1%   0.7%   27.2%   5.0%   0.2%




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