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BACKGAMMON BY THE BAY
Problem #14 solution
  		Match to 11
Blue 2, 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 certainly has the edge here. A 21-pip racing lead, a three-point board to White's one-point board, only two checkers back to White's three. Clearly a double is called for, since Blue's position could easily get overwhelming between now and the next roll (with a roll such as 33, or even just hitting loose on the 4 point followed by White dancing). And White has no threats to turn the game around any time soon.

The tougher question is: Should White take? White appears to have nothing going in this position. No offensive points made, and no anchor to defend against Blue's attack. And Blue's stronger board represents a higher than usual gammon risk. However, what White does have is: Potential.

First, there's the potential to anchor. White's three blots represent three slotted points. White has 2s and 3s to make the 21 point, while if Blue attacks there, White may hit back or make the 23 or 24 points. Blue doesn't have enough ammunition in place to make a closeout likely, so the odds are that White will, at worst, end up with some kind of anchor game.

Second, White has the potential to trap one or both of Blue's back checkers. Even though she's made no new points yet, there is always a chance of rolling some point-making numbers. Blue has to escape the checkers, and this isn't always an easy task. White can often attack those checkers, and she may develop some kind of prime. Of course, attacking is also risky, since getting more checkers sent back against a stronger board increases the gammon risk.

So, is this potential enough to let White take? Jellyfish's level 7 evaluation says not quite, but the rollouts show White getting enough leverage from cube ownership to take fairly easily. They show White actually turning the game around 41.5% of the time, although losing 25.5% gammons. (The level 6 cubeless rollouts show White doing a bit worse, but close enough that the take still seems right.)

JF:   Double / Drop (level 7 evaluation) 

Pip counts:          Blue   148                     White  169

                     Blue                           White              
Level 7 Evaluation   Equity   Win    G/BG    BG     Win    G/BG    BG  
Cubeless             +0.585   68.6%  26.5%   1.4%   31.4%   6.5%   0.2%

Level 5 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
Cube centered        +0.735   84.8%   4.1%   0.2%   15.2%   0.5%   0.0%
Blue owns cube       +0.782   88.6%   4.2%   0.3%   11.4%   3.4%   0.2%
White owns cube      +0.433   58.5%  25.5%   1.7%   41.5%   1.0%   0.0%
Cubeless             +0.537   66.4%  26.7%   1.8%   33.6%   7.3%   0.3%

Level 6 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
Cubeless             +0.559   67.3%  27.2%   1.8%   32.7%   7.3%   0.4%




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