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BACKGAMMON BY THE BAY
Problem #22 solution
  		Match to 11
Blue 1, White 6

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     Blue to play 43

Candidate plays:

  1. 13/6
  2. 8/1
  3. 6/2 8/5
  4. 5/1 6/3

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RK:
Blue is ahead in the race and is simply trying to come home safely. Her best numbers for clearing the midpoint are doubles (other than 11) and 52, which leaves only an indirect shot. In the meantime, a number like this 43 can be played safely from her other spares.

Or should it be? Should Blue consider 13/6, volunteering a shot? The motivation behind a play like that is the fear that she may not be able to clear the midpoint safely anyway, and that a later shot could be more dangerous. For example, check out this scenario: Blue plays 8/1; White makes the 4 point with 42; Blue rolls 62, clearing the 8 point; White makes the 3 point; Blue rolls 63, forcing a double shot. White has more shots and a stronger board than he would have had if Blue had left the shot immediately.

Now, how realistic is that scenario? Not very. Blue will have a few chances to roll doubles or 52, in which case she leaves few or no shots. White's board could get better, but it could also get worse. For example, 6s force White to play deep into his home board, or else break the midpoint, relieving a lot of the pressure on Blue's midpoint. It's worth it for Blue to hold out to hope for one of those events.

Assuming Blue doesn't leave the shot, does it matter much how she plays the 43? Actually, it does matter. Blue's goal is to preserve as much playability as possible; that is, maximize the number of rolls that play safely and flexibly until she can clear the midpoint. To do that, look at how your big numbers (6s, 5s and 4s) play.

Playing 5/1 6/3 (or 5/2 6/2) would be an attempt to "save 6s", by leaving a spare on the 8 point that can play 6s. In some cases this is correct, but here it removes the spares from the 6 and 5 points, which is bad, since Blue can play a 6 (or 5 or 4) from the 8 point, but is then stuck for the other number. It would be right only if you knew Blue was going to roll 61 next time (or possibly 62). But 65, 64 and 63 play much worse.

In this situation, stripping the 8 point is more flexible. (The only numbers that force a shot next time are 61 and 64.) After 8/5, Blue should simply continue 5/1 rather than 6/2. This maximizes Blue's chances of making the ace point, which could be important if there's contact later (i.e. Blue gets hit and hits White back). White isn't about to leave a shot this time, so there's little worry of having the blot on the ace point hit.

Also, playing directly to the 1 point is very efficient when trying to preserve playability. For example, suppose Blue plays 6/2 8/5 instead, and then rolls 54. She technically has nine spare pips but can't play them effectively (she'd have to break the 6 point). 

Pip counts:          Blue    93                     White  128

                     Blue                           White              
Candidate Plays      Equity   Win    G/BG    BG     Win    G/BG    BG  
8/1                  +0.538   75.2%   5.5%   0.1%   24.8%   2.0%   0.0%
6/2 8/5              +0.508   73.7%   5.4%   0.1%   26.3%   2.1%   0.0%
5/1 6/3              +0.460   71.8%   5.1%   0.1%   28.2%   2.6%   0.0%
13/6                 +0.459   70.1%   7.9%   0.2%   29.9%   2.3%   0.1%




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