Re: [Bug-gnubg] Market window reports

[Joern Thyssen]

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