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BACKGAMMON BY THE BAY
Problem #3 solution
  		Match to 11
Blue 0, White 0

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0123456bar789101112
     Blue to play 51

Candidate plays:

  1. 8/2
  2. 13/8 3/2

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RK:
You'll recognize this as a followup to the previous position. Having broken the 8-point, Blue has to decide whether to re-make it (and leave a blot on the midpoint) or whether to safety the lone checker.

The big drawback of 13/8 3/2 is that it leaves 16 shots (aces, plus 33, 63, and 54). How bad is it to get hit? It costs Blue his racing lead, and then he needs to enter White's strong board. If Blue enters quickly, he has some counterattacking possibilities (since White will be exposing some blots in order to hit). Odds are he'll be able to avoid being closed out, and will retain a bar-point holding game, but he'll still be an underdog.

If White doesn't hit, then Blue is glad to have re-made the 8 point. It's a valuable point here, putting pressure on White's two back checkers, as well as serving as a landing point. And the checker left on the midpoint represents a roll or two of timing before Blue has to break anything else.

A big problem with the safe play is that Blue now has two outfield points that are far from home. Only doubles will move them safely. Blue is out of 6s, and has no spares on his 6 and 5 points. So Blue is likely to have to leave some shots next time, or start dismantling his board. A roll of 63 would be particularly embarrassing, forcing two blots. Is it possible White could have to break first, allowing Blue to hit? 61 is the only number that forces a shot, and some other 1s would be awkward, but most of the time White safely clears the 8 point (he can also play 21/13 with 8s).

Normally in this type of position, it's not correct to leave a shot if you have any alternative, particularly when the opponent's board is strong, as it is here. You can always hope for doubles, or a chance to hit the opponent before he hits you. However, in this position, the safe play makes Blue's next roll awkward, so the decision is close. Nonetheless, the rollouts still show a slight edge for 8/2. 

Pip counts:          Blue   108                     White  125

                     Blue                           White              
Candidate Plays      Equity   Win    G/BG    BG     Win    G/BG    BG  
8/2                  -0.158   46.0%   6.9%   0.2%   54.0%  14.6%   0.3%
13/8 3/2             -0.182   45.1%   6.6%   0.1%   54.9%  14.7%   0.4%




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