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BACKGAMMON BY THE BAY
Problem #19 solution
  		Match to 11
Blue 1, White 6

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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:
At first glance, Blue might not appear to have a big lead in this position. She has one checker trapped back on the 24 point, and White, though not having made any home board points yet, has a large mass of checkers on his side of the board ready to do something with. Also, the race is quite close.

On the other hand, Blue has made the valuable 5 point, and she's shooting at a blot in White's home board. If she hits the blot, good things could happen. The question is, are they good enough to warrant a double now? After all, if White anchors or hits back, Blue won't exactly be able to claim. And if Blue doesn't hit or escape, White may be able to turn the game around quickly.

So how good are Blue's good sequences? Quite good. Any hit/fan sequence is a big market loser, because of the other blot that is then vulnerable as well. (In addition to the 3s that hit, Blue has 61 and 51 to pick and pass, plus 65, 33, 55 and 66 to make the 3 point, and 44 and 22 aren't too shabby either.) These big market losers are enough to justify turning the cube, even for money. The rollouts show that Blue's equity with White owning the cube (.309), doubled, is more than the "cube centered" equity of .561, so a double gains.

At this match score, the double is even clearer. When you're behind in a match, you can't afford to tread too cautiously. If you're going to win, you must get lucky at some point, so it's more important than usual to take advantage of those potential market losers. This doesn't mean you should double frivolously, but when you have solid chances, it's usually worth going for. Another factor favoring a double is that White will be less inclined than usual to rewhip, since Blue would then have the ability to turn the cube to 8.

For money, this position is a very easy take. Rollouts show that, even though he gets gammoned 22% of the time, cube ownership allows him to win close to half the time (45%).

How about at this match score (5-away 10-away)? White needs to be a bit conservative, but not enough to drop here. As mentioned, White will be reluctant to redouble, but even assuming that the game were always played to the end, the cubeless figures show a comfortable take for White. White's raw take point isn't much different than for money, and while gammons hurt a little more than usual, it's not enough to change the decision.

JF:   Double / Accept (level 7 evaluation) 

Pip counts:          Blue   131                     White  128

                     Blue                           White              
Level 7 Evaluation   Equity   Win    G/BG    BG     Win    G/BG    BG  
Cubeless             +0.393   63.1%  19.8%   0.4%   36.9%   7.0%   0.1%

Level 5 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
Cube centered        +0.561   76.4%   4.2%   0.1%   23.6%   1.0%   0.0%
Blue owns cube       +0.636   82.2%   4.4%   0.1%   17.8%   5.0%   0.2%
White owns cube      +0.309   55.1%  21.8%   0.6%   44.9%   1.6%   0.1%
Cubeless             +0.423   63.5%  23.0%   0.6%   36.5%   7.9%   0.4%

Level 6 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
Cubeless             +0.430   64.0%  22.5%   0.6%   36.0%   7.8%   0.4%




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