[Bug-gnubg] Bearoff dB position, few questions

[Massimiliano Maini]

Hi all,

on a forum I've found this: same position
(in 2-sided bearoff dB)
in money play and match play (3aw-3aw)
shows different cubeless
equities. I tried to explain it but
I run into some confusion.

That's money play:

    GNU Backgammon  Position
ID: 6AUAADoDAAAAAA
         
          Match ID   : UQkAAAAAAAAA
    +24-23-22-21-20-19------18-17-16-15-14-13-+
 O: gnubg
 OO |        
 O  O  O |   |            
     |  0 points
 OO |        
    O    |   |          
       |  
 OO |        
    O    |   |          
       |  
 OO |        
    O    |   |          
       |  
  O |        
         |   |        
         |  
    |      
           |BAR|        
         |v 
  X |        
         |   |        
         |  
 XX |        
         |   |        
         |  
 XX |        
 X       |   |          
       |  
 XX |        
 X     X |   |            
     |  On roll
 XX |       X  X
    X |   |              
   |  0 points
    +-1--2--3--4--5--6-------7--8--9-10-11-12-+
 X: MaX (Cube: 2)

Hint shows this:

Cube analysis
2-ply cubeless equity  +0.4971
  0.7485 0.0000 0.0000 - 0.2515
0.0000 0.0000
Cubeful equities:
1. Double, take      
  +0.9158
2. Double, pass      
  +1.0000  ( +0.0842)
3. No double        
   +0.7661  ( -0.1496)
Proper cube action: Redouble, take

From eval (ctrl+E) I see (uninteresting
parts removed):

Position ID:        6AUAADoDAAAAAA
Match ID:        UQlgAAAAAAAA

Evaluator:        
Bearoff2

         
   Player       Opponent
Position        
 880           912

        Win  
  W(g)    W(bg)   L(g)    L(bg)   Equity
   Cubeful  
static: 0.7485  0.0000  0.0000
 0.0000  0.0000   +0.4971   +0.7661  
 1 ply: 0.7485  0.0000  0.0000
 0.0000  0.0000   +0.4971   +0.7661  
 2 ply: 0.7485  0.0000  0.0000
 0.0000  0.0000   +0.4971   +0.7661  

Static, 1ply and 2ply figures are identical,
which makes me think they all
come from the 2s bearoff dB (eval output
is a bit confusing here).

That's the same for match:

    GNU Backgammon  Position
ID: 6AUAADoDAAAAAA
         
          Match ID   : UQlgAAAAAAAA
    +24-23-22-21-20-19------18-17-16-15-14-13-+
 O: gnubg
 OO |        
 O  O  O |   |            
     |  0 points
 OO |        
    O    |   |          
       |  
 OO |        
    O    |   |          
       |  
 OO |        
    O    |   |          
       |  
  O |        
         |   |        
         |  
    |      
           |BAR|        
         |v 3 point match
  X |        
         |   |        
         |  
 XX |        
         |   |        
         |  
 XX |        
 X       |   |          
       |  
 XX |        
 X     X |   |            
     |  On roll
 XX |       X  X
    X |   |              
   |  0 points
    +-1--2--3--4--5--6-------7--8--9-10-11-12-+
 X: MaX (Cube: 2)

Cube analysis
2-ply cubeless equity  +0.4797
(Money:  +0.4797)
  0.7399 0.0000 0.0000 - 0.2601
0.0000 0.0000
Cubeful equities:
1. Double, take      
  +0.9565
2. Double, pass      
  +1.0000  ( +0.0435)
3. No double        
   +0.7841  ( -0.1724)
Proper cube action: Redouble, take

        Win  
  W(g)    W(bg)   L(g)    L(bg)   Equity
   Cubeful  
static: 0.7485  0.0000  0.0000
 0.0000  0.0000   +0.4971   +0.8543  
 1 ply: 0.7399  0.0000  0.0000
 0.0000  0.0000   +0.4797   +0.8308  
 2 ply: 0.7399  0.0000  0.0000
 0.0000  0.0000   +0.4797   +0.7841  

The original question was: why the
2-ply cubeless GWC are different
between money and match ?
First answer was: it's using bearoff
dB from money and not for match.
Objection was that gnubg could/should
use the dB even for match, at
least for the cubeless GWC figures.

Here I tried to explain that cubefull
figures from the dB can only be
used in money play, but what about
cubeless ? Are cubeless figures from
the dB used as a base for cubefull
eval in match play ?

Looking at the figures I would say
yes: the static cubeless GWC for match
are exactly the ones you have in money.
But they diverge at 1 and 2 ply.

Am I right if I say that doing 2ply
eval in match, gnubg needs to compute
a lot of 0ply cubeless evals and it
takes them from the dB. The figures
are converted into 0ply cubeful (Janowski
formula) and then "backpropagated"
to get 2ply cubeful. 2ply cubeless
is computed by inversing the Janowski
formula on 2ply cubeful figures.

If all the above is true, I do see
the objection coming: it's true that what
matter are cubeful figures (and these
cannot be taken from the dB in match),
but why gnubg isn't showing the "right"
cubeless GWC (the ones from the dB)
in match ?

Side question: I tried to use bearoffdump.
I manage to get the info putting
in the position ID:

D:\Documents\gnubg>bearoffdump.exe
-p 6AUAADoDAAAAAA gnubg_ts0.bd
Bearoff database: gnubg_ts0.bd
Position ID     : 6AUAADoDAAAAAA

Information about database:

 * On disk 2-sided bearoff database
evaluator
   - generated by GNU Backgammon
   - up to 6 chequers on
6 points (924 positions) per player
   - database includes both
cubeful and cubeless equities
   - number of reads: 0


Dump of position ID: 6AUAADoDAAAAAA

         
   Player       Opponent
Position        
 880           912

Cubeless equity      
        : +0.4971
Owned cube        
           : +0.7661
Centered cube      
          : +0.7451
Opponent owns cube      
     : +0.4579

But I had no success in using the -n
option (enter directly the
position indexes, 880 and 921): how
is this supposed to work ?

MaX.