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

[Don Dailey <drd@xxxxxxx>]

> What is a probability of winning?

Probability that a given position is a game theoretic win.  I assumed
that the context of the discussion (evaluation function confidence)
made this clear.

- Don






   Date: Wed, 19 Jan 2005 15:41:28 +0200
   From: Antti Huima <antti.huima@xxxxxxxxxxxxxxxxx>
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   Don Dailey wrote:

   >   Usually at this point somebody will suggest that evaluations should be 
   >   of the form "score + confidence estimate", i.e. that evaluations should 
   >   consist of two numbers, evaluation score, and some form of evaluation of 
   >   the confidence in the score. A generalization would be to let 
   >   evaluations be probability distributions of evaluation scores.
   >
   >If you view evaluation more as the probability of winning (where 0.5 == draw)
   >then evaluation which you have little confidence in could be pushed in the
   >direction of a draw, reflecting your lack of confidence in the reliability of
   >the score.    
   >
   >  
   >
   What is a probability of winning?

   Probability that the playing algorithm will win against a hypothetical, 
   fixed opponent mechanism---which is circular, because the evaluation 
   function affects this probability? And what is the opponent model?

   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'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
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   fax: +358 10 286 6309 
   http://www.conformiq.com/

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