[Bug-gnubg] Closeout ignorance

[Albert Silver]

GNU Backgammon  Position ID: AAAAt61NQoAAAA
                 Match ID  : AQFgAWAACAAA
 +12-11-10--9--8--7-------6--5--4--3--2--1-+     O: Owes (Cube: 2)
 |       O     O    |   | O  O  O  O  O  O |     6 points
 |                  |   | O  O     O  O  O |     On roll
 |                  |   |                  |     
 |                  |   |                  |     
 |                  |   |                  |    
^|                  |BAR|                  |     11 point match
 |                  |   |                  | XX 
 |                  |   |                  | XX  
 |                  | X |                  | XX  
 |                  | X |                  | XXX 
 |    O             | X |          O       | XXX 1 point
 +13-14-15-16-17-18------19-20-21-22-23-24-+     X: Exes


Cube analysis
2-ply cubeless equity  +0.582 (Money:  +0.582)
   79.2%   0.0%   0.0% -  20.8%   0.2%   0.1%
Cubeful equities:
1. No double            +0.790
2. Double, pass         +1.000  ( +0.210)
3. Double, take         +0.716  ( -0.074)
Proper cube action: No redouble, take (26.2%)


Here is what Walter Trice says in an article at Gammon Village:

If he can only close out one man he will still be a big (5 to 1)
underdog but if he gets them both he'll be a solid (2 to 1) favourite.
-------------------------------------

As to 3 checkers, according to Douglas Zare, as posted at GOL:

"the actual value is 5-6% according to rollouts, and possibly just under
5% with more accurate play. That makes it a huge market loser, even at
this score. 

There are a lot of hits from the bar (6.5% according to the Sconyers
database when there are spares on the 654 and the only goal is safety;
10.5% with no spares), but they don't all win, whereas almost any hit
saves the gammon if you have a closed board. Also, there are two more
crossovers and perhaps 17 more pips needed to race home rather than to
save the gammon. The race is something like 75-42 to start, so boxcars
don't come close to making it an even race."