Re: [computer-go] An [open] question on game tree search theory

[Don Dailey <drd@xxxxxxx>]

And I made some mistakes here too, which I am sure you won't fail to
notice.

Anyway, the general idea is that higher scores actually mean positions
that are more likely to be wins, and lower scores mean positions that
are more likely to be theoretical losses.  I don't think you can
nitpick that.

And that's not really how most go programs do evaluation.  Most
measure influence and use this directly.  This is different, although
somewhat correlated to winning chances.  (Winning chances is a term
used in the real world too even if it's not tersely defined.)

- Don



   Date: Wed, 19 Jan 2005 16:32:02 -0500
   From: Don Dailey <drd@xxxxxxxxxxxxxxxxx>

   >  Or probability that the game tree node is a game-theoretic win? What 
   >  does this mean? One game node is either win or not, so there is no 
   >  stochastic experiment. You need to have a repeated experiment or a 
   >  population larger than one object to be able to speak of probabilities.

   I think you probably realize that I meant the probability that the
   evaluation function is correct.  This of course has to be estimated somehow.
   Let's not get into that.

   To make this work, a score has to be transformed mathematically.  A
   score less than 0.5 is considered to be a loss, and a score greater
   than 0.5 is considered to be a win.  We have to convert scores greater
   than 0.5 to estimated probablity that the scoring function is correct in
   it's assesment of a win and likewise for losses and score below 0.5.

   If our evaluation always returned 0.5, then we might say it is always
   wrong (or it is always right 0% of the time!)

   Of course we would likely want to tranform our probabilistic score
   mathematically so that negative numbers represented losses with some
   probability and positive numbers represented win belief with some
   probability based on the magnitudes of the number.

   - Don










   1.0/(1.0+exp(-(ev)))

   probably has critial parent?



      I'm not being rude. I think this is one of the key points. "Probability 
      of winning" is often mentioned, but what does it mean? Every node is a 
      game-theoretic win or not, so no probability here. Results from actual 
      game play, with our imperfect algorithms, depend on the opponents. Is 
      there an opponent model implied? Against a perfect opponent, all 
      algorithms that can make mistakes should evaluate the probability of 
      winning to zero!

      Please shew light on this!

      Yours Truly,

      -- 
      Antti Huima (Mr.)
      Director, Conformiq Tools
      mobile: +358 40 528 8667
      email: antti.huima@xxxxxxxxxxxxxxxxx

      Conformiq Software Ltd.
      Stella Terra, Lars Sonckin kaari 16
      FIN-02600 Espoo, Finland
      tel: +358 10 286 6300
      fax: +358 10 286 6309 
      http://www.conformiq.com/

   _______________________________________________
   computer-go mailing list
   computer-go@xxxxxxxxxxxxxxxxx
   http://www.computer-go.org/mailman/listinfo/computer-go/

_______________________________________________
computer-go mailing list
computer-go@xxxxxxxxxxxxxxxxx
http://www.computer-go.org/mailman/listinfo/computer-go/