[Bug-gnubg] Re: Beaver bug

[Christopher D. Yep]

To answer my own bug report, I forgot that beavers may be dropped.  gnubg 
is actually giving correct interpretations of its 0-ply, 2-ply, and 4-ply 
evaluations.  At 0-ply, 2-ply, and 4-ply, O is actually *too good* to 
beaver since the reported normalized equities for redouble/take (4.297, 
4.237, and 4.107 respectively) are > 2.000.  If O mistakenly beavers, X 
should pass the beaver, giving up only 2 times the original cube value.

Also note that I gave a centered cube in the original diagram, but actually 
I tested it with X owning the cube; I then forgot to change the diagram 
before posting.

I tested gnubg with a variety of extreme positions and found that the 
interpretations of its evaluations always made sense.  Impressive!!

BTW, I'm not bothered that gnubg's evaluations are way off for this 
position since it's an "extreme" position.

Here's the original position (corrected):

    GNU Backgammon  Position ID: Pp8PAAAAAPh8Pg
                    Match ID   : UQkAAAAAAAAA
    +24-23-22-21-20-19------18-17-16-15-14-13-+  O: gnubg
    | X  O  X  O  X  O |   |                  |  0 points
    | X  O  X  O  X  O |   |                  |
    | X  O  X  O  X  O |   |                  |
    | X  O  X  O  X  O |   |                  |
    | X  O  X  O  X  O |   |                  |
    |                  |BAR|                  |v
    |                  |   |                  |
    |                  |   |                  |
    |                  |   |                  |
    |                  |   |                  |  On roll
    |                  |   |                  |  0 points
    +-1--2--3--4--5--6-------7--8--9-10-11-12-+  X: Chris (Cube: 2)
Pip counts: O 60, X 330

Here are the relevant equities mentioned above:


> 0-ply:
>
> Cube analysis
> 0-ply cubeless equity  -2.120
>     7.9%   0.0%   0.0% -  92.1%  87.0%  40.8%
> Cubeful equities:
> 1. No double            -2.093
> 2. Double, pass         +1.000  ( +3.093)
> 3. Double, take         -4.297  ( -2.204)
> Proper cube action: No redouble, take (41.6%)

The above is correct; if X redoubles, O should not beaver since 4.297 > 
2.000.  If O mistakenly beavers, X should drop the beaver, losing only 2 
times the original cube value.

> 2-ply:
>
> Cube analysis
> 2-ply cubeless equity  -2.091
>     7.5%   0.0%   0.0% -  92.5%  86.5%  37.5%
> Cubeful equities:
> 1. No double            -2.066
> 2. Double, pass         +1.000  ( +3.066)
> 3. Double, take         -4.237  ( -2.172)
> Proper cube action: No redouble, take (41.5%)

The above is correct; if X redoubles, O should not beaver since 4.237 > 
2.000.  If O mistakenly beavers, X should drop the beaver, losing only 2 
times the original cube value.

> 4-ply:
>
> Cube analysis
> 4-ply cubeless equity  -2.027
>     6.9%   0.0%   0.0% -  93.1%  85.1%  31.3%
> Cubeful equities:
> 1. No double            -2.004
> 2. Double, pass         +1.000  ( +3.004)
> 3. Double, take         -4.107  ( -2.104)
> Proper cube action: No redouble, take (41.2%)

The above is correct; if X redoubles, O should not beaver since 4.107 > 
2.000.  If O mistakenly beavers, X should drop the beaver, losing only 2 
times the original cube value.

Chris