RE: [Bug-gnubg] Market window reports

[Ian Shaw]

> On Mon, Jan 06, 2003 at 09:39:13PM -0000, ershaw wrote
> >     GNU Backgammon  Position ID: xm7gAwjmdsADBA
> >                     Match ID   : cIl1AAAAAAAA
> >     +24-23-22-21-20-19------18-17-16-15-14-13-+  O: Opponent
> >     |    O     X  O  O |   | O              X |  0 points
> >     |    O        O  O |   | O              X |  
> >     |                O |   |                X |  
> >     |                  |   |                X |  
> >     |                  |   |                  |  
> >     |                  |BAR|                  |v 3 point 
> match (Cube: 1)
> >     |                  |   |                O |  
> >     |                  |   |                O |  
> >     |          X     X |   |                O |  
> >     |    X     X  X  X |   |                O |  Rolled 35
> >     |    X  O  X  X  X |   |                O |  0 points
> >     +-1--2--3--4--5--6-------7--8--9-10-11-12-+  X: ian
> > 
> > 
> > 
> > The market window table reports my Too Good Point as 
> 68.612%. (There is no Copy function on this window, BTW)
> > The 2-ply cube analysis reports the proper cube action as 
> Double/Pass, even though I am over the Too Good point. This 
> seems inconsistent to me.
> > 
> > Cube analysis
> > 2-ply cubeless equity  +0.742 (Money:  +0.630)
> >   0.705 0.288 0.004 - 0.295 0.069 0.003
> > 1. Double, pass         +1.000
> > 2. Double, take         +1.292  ( +0.292)
> > 3. No double            +0.857  ( -0.143)
> > Proper cube action: Double, pass
> 
> First, gnubg uses a 0-ply evaluation for the market window. 
> Second, the
> 68.6% you report is for a fully live cube, whereas the too 
> good point is
> 82.758% for a dead cube.
> 
> 0-ply reports:
> 
> Win   W(g)  W(bg) L(g)  L(bg)   Mwc
> 0.692 0.282 0.003 0.072 0.002   57.01%
> 
> Double, pass        :  60.00%
> Double, take        :  61.85%   ( +1.85%)
> No double           :  59.12%   ( -0.88%)
> 
> Correct cube action: Double, pass
> 
> 
> Since 69.2% > 68.6% you're in the good too window. Now, gnubg
> extrapolates your mwc between (68.6%,60%) (you cash one point) and
> (100%,66.22%) (you win the game with the current gammon ratios). 
> 
> WIth p = 69.2% you get: 60.11% which is your equity with a fully live
> cube.
> 
> Your dead cube equity is 57.01%. 
> 
> Your final equity is: 0.32 * 57.01% + 0.68 * 60.11 = 59.12% which is
> what gnubg reports above as the equity for not doubling.
> 
> As 59.12% is lower than the equity for doubling the position is a
> double.
> 
> Of course, 2-ply is more complicated since it's an average over many
> positions and cube values and ownerships.
> 
> Jørn
> 

Whoa! That's a pretty tricky explanation. I'll have to study it more if I'm 
going to understand it completely. I think the gist of it is that I was looking 
at the Live Cube number and not realising that it represents 100% cube 
efficiency. Since 100% cube efficiency is rare, I need to extrapolate between 
the dead & live cube numbers.

--Ian