RE: [Bug-gnubg] Measuring Complexity

[Michael Depreli]

I should post the positions but I set up three different positions and made the top three plays in each which were close in equity.
I then evaluated the position with the old build and compared the contact net numbers.
As an example for one of the weights (OFF2) (I have no idea what it means) I got these numbers:
Position A 0.275 0.292 0.085
Position B 0.118 0.241 0.062
Position C 0.073 0.074 0.084

Position C both players had escaped all checkers to midpoint and it was soon turning in to a non-contact race so no complexity there as can be seen in the numbers (and all other numbers in the weights.)

Position A involved playing 22 and deciding whether to leave the 18 point anchor and go all the way, part way and build, or leave them and all build.
So to me that's more complex but involves 2.5 decisions as whether to leave the anchor at all.
The weights of the two anchor abandoning plays look a little similar.

Poistion B involved 3 very different plays. Running from an anchor, safetying a checker but burying it on the acepoint, or aggressively slotting the homeboard against a direct hit. So this is the most complex position and this shows in the bigger differences of the weights.

I'm not a mathematician but couldn't the volatility SD or whatever of these numbers somehow be used to judge complexity?

Michael











> From: address@hidden
> Date: Fri, 4 Sep 2009 08:07:13 +1200
> Subject: Re: [Bug-gnubg] Measuring Complexity
> To: address@hidden
> CC: address@hidden
>
> If someone where to put several 10's of positions and remark on the
> complexity we may have a better place to start discussing. I was
> thinking about the moves being different, but it may be that positions
> may work as well. Doubles are especially interesting because of the
> greater number of possible moves.
>
> -Joseph
>
> On Fri, Sep 4, 2009 at 7:59 AM, Michael
> Depreli<address@hidden> wrote:
> > Yes I agree.
> > Doesn't a neural net like a brain take in all the different aspects of a
> > position and weight them and come up
> > with equities and then rank them?
> > So is there a way to extract from the weights of the net a measure of how
> > many different factors make up the overall equity?
> > In the old builds you used to be able to call up the evaluator for the
> > contact net and it would show you all the weightings.
> > Depending say how different these weightings were for plays that were close
> > in equity could determine how complex a position was no?
> > There are 22 different weights displayed when I call up the evaluator. (I
> > hope I've got that techincally correct).
> > Let's just say for simplicity sake for one position there are 2 moves and 20
> > of the weights are identical and only 2 different and in another
> > position 15 are identical and 7 different then that would be more complex.
> >
> > Michael
> >
> >
> >
> >
> >
> >
> >> From: address@hidden
> >> Date: Fri, 4 Sep 2009 07:27:59 +1200
> >> Subject: Re: [Bug-gnubg] Measuring Complexity
> >> To: address@hidden
> >> CC: address@hidden
> >>
> >> I think it is not an easy one. My personal view is that a position is
> >> "complex" if there are several *different* top moves which are very
> >> close in equity. Now it all hangs on what "different" means :)
> >>
> >> -Joseph
> >>
> >> On Thu, Sep 3, 2009 at 11:13 PM, Michael
> >> Depreli<address@hidden> wrote:
> >> > I posted this on BGO:
> >> > Has anyone ever tried to tackle the subject of measuring complexity in
> >> > backgammon? Firstly you could take out moves / cube actions "that are
> >> > completely unimportant". You include opening moves and maybe even
> >> > replies
> >> > amongst those? After that maybe you could use the move filters within BG
> >> > software to assign a value. So let's say using gnubg analysis no plays
> >> > get
> >> > analysed at 2-ply as it's trivial then that move gets discarded. After
> >> > that
> >> > you could assign some kind of values based on how many moves and how big
> >> > an
> >> > equity difference they are away from the best play at 2-ply to reach a
> >> > figure and divide it by the total plays. I'm no mathematician so
> >> > wouldn't
> >> > know how to weight these factors etc. Any thoughts or does no one really
> >> > care?
> >> >
> >> > Michael
> >> >
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> >> >
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