GNU Backgammon  Position ID: 4PPgAVDMTvABJA                 Match ID   : 
cAkAAAAAAAAA +13-14-15-16-17-18------19-20-21-22-23-24-+     O: gnubg | X       
    O    | O | O        X     X |     0 points | X           O    |   | O       
         |      | X           O    |   | O                |      | X           
O    |   | O                |      | X                |   | O                |  
  v|                  |BAR|                  |     (Cube: 1) |                  
|   |                  |     | O                |   |                  |      | 
O                |   | X                |      | O                |   | X  X    
 X       |     On roll | O           X    |   | X  X     X     O |     0 points 
+12-11-10--9--8--7-------6--5--4--3--2--1-+     X: Stick
 
 
   The cubeless numbers are reasonable each time for 0ply, 1ply, and 2 ply. But 
the cubeful numbers are reasonable only for 0-ply. 
 
Cube analysis0-ply cubeless equity  +0.552870  0.663548 0.288003 0.010951 - 
0.336452 0.070565 0.002616Cubeful equities:1. Double, take         +0.8769532. 
Double, pass         +1.000000  ( +0.123047)3. No double            +0.680082  
( -0.196871)Proper cube action: Double, take
 
 
Cube analysis1-ply cubeless equity  +0.590686  0.679289 0.290100 0.013408 - 
0.320711 0.069290 0.002110Cubeful equities:1. Double, take         +0.0456332. 
Double, pass         +1.000000  ( +0.954367)3. No double            +0.036137  
( -0.009496)Proper cube action: Double, take
 
Cube analysis2-ply cubeless equity  +0.570977  0.668266 0.296238 0.012481 - 
0.331734 0.071660 0.002615Cubeful equities:1. No double            +0.1608762. 
Double, pass         +1.000000  ( +0.839124)3. Double, take         +0.159837  
( -0.001038)Proper cube action: No double, take (0.1%)
 
Bob Koca
 
 
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