Re: [Bug-gnubg] Bug: Double/Beaver

[Christopher D. Yep]

At 11:21 AM 8/22/2003 +0000, Jørn wrote:

> gnubg will take any cube position into account, but the forward pruning
> at the intermediate plies will be performed with the original cube value
> and cube position.
>
> This may give problems in positions where the gammon price changes
> dramatically upon turning the cube. Examples, are initial doubles in
> money game with Jacoby rule, and many match scores.

I think I understand everything else you wrote in the rest of the e-mail , 
but I'm still unclear about the above paragraphs.  By the first sentence do 
you mean that if the original cube position is, for example, a centered 
cube then all checker plays will be chosen based on a centered cube even if 
the cube gets turned for some (later) dice sequences in the lookahead?

If so, is this the case for both N-ply evaluations and the "no-double" 
branch of a cube decision rollout (checker plays always based on a centered 
cube even though the cube will almost always be turned at least once during 
each rollout game).

If yes, then I assume the "double/take" branch of the cube decision rollout 
is similar but starts with the opponent owning the cube (and all future 
checker plays are chosen based on the opponent owning the cube, even if the 
cube gets turned later within the rollout).

The above is a reasonable way to do it, I just want to make sure I 
understand it.

> >
> > For every N-ply evaluation and every rollout, if some of the nodes of the
> > lookahead end in double/pass before N-plies are reached, for the 
> purpose of
> > the win/gammon/backgammon breakdown, gnubg uses the final
> > win/gammon/backgammon estimate for these nodes rather than continuing all
> > the way to N-ply, correct?
>
> Rollouts: yes (the rollout is implicitly truncated at double pass)
> Evaluations: no (the evaluation is *not* truncated)

Thanks for the clarification.  I now see that this is the case for 
evaluations by looking at 2-ply, 4-ply, and 6-ply numbers.  The cubeless 
equity changes from -0.038 to -0.045 to -0.047 (although the game always 
ends within 1-ply since player1 will cash the game if player0 doesn't roll 
6-x, while player0 will cash the game at the next opportunity if his first 
roll is 6-x).  I understand how gnubg works for evaluations now, thanks.

> > If so, gnubg can be marginally improved by using
> > minimax as you note,
>
> I'm not sure if the improvement is "marginally". In your original
> example the equity change is from -0.107 to -0.118, or around 10%, when
> we choose another cube value/cube position for the forward pruning.

Careful how you define improvement.  gnubg improved by 0.011 in this rare 
position.  If the equity instead had changed from -0.001 to -0.012 I would 
still say it improved by 0.011 rather than by 1100%.  If the improvement is 
from 0 to -0.011, it's not an infinite improvement.  If you want, you could 
call it about a 1.1% improvement.  :-)

> I've made a few notes available from
>
> <URL:http://www.gnubg.org/win32/gnubg/gnubg.html#Cubeful%20equities>
>
> It would be great if you could expand the chapter. I can provide the
> texi source for the chapter if you want to work on it.

Thanks, I just read through this material and will try to read it a second 
time later today.  Can you send me the texi source?  I promise to work on 
it in the next week or so.  Thanks.

Chris