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

[Don Dailey <drd@xxxxxxx>]

>  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/

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