> It seems to be surprisingly difficult to outperform the step function > when it comes to mc scoring. I know that many surprises await the mc > adventurer, but completely discarding the final margin of victory > just can't be optimal. ... > an mc program, holding on to a half point victory in the endgame, is > a thing of beauty and terror. But in the opening, where the scoring > leaves are 300 moves away from the root, surely a putative half point > win doesn't translate to a significant advantage, where as a 100 > point win would.
I had a breakthrough in my understanding of why it is "surprisingly difficult to outperform the step function" when analyzing some 9x9 games with Mogo and ManyFaces. Let's see if I can extract that insight into words... I observed that in many situations I could map the winning percentage to the final score. E.g. 50-55%: 0.5pt 55-60%: 1.5pt 60-65%: 2.5pt etc. It wasn't as clear cut as that. In fact what I was actually noticing was if I made a 1pt error the winning percentage for the opponent often jumped by, say, 5%. Thinking about why... In a given board position moves can be grouped into sets: the set of correct moves, the set of 1pt mistakes, 2pt mistakes, etc. Let's assume each side has roughly the same number of moves each in each of these groupings. If black is winning by 0.5pt with perfect play, then mistakes by each side balance out and we get a winning percentage of just over 50%. If he is winning by 1.5pt then he has breathing space and can make an extra mistake. Or in other words, at a certain move he can play any of the moves in the "correct moves" set, or any of the moves in the "1pt mistakes" set, and still win. So he wins more of the playouts. Say 55%. If he is winning by 2.5pts then he can make one 2pt mistakes or two 1pt mistakes (more than the opponent) and still win, so he wins more playouts, 60% perhaps. And so on. My conclusion was that the winning percentage is more than just an estimate of how likely the player is to win. It is in fact a crude estimator of the final score. Going back to your original comment, when choosing between move A that leads to a 0.5pt win, and move B that leads to a 100pt win, you should be seeing move B has a higher winning percentage. Darren -- Darren Cook, Software Researcher/Developer http://dcook.org/gobet/ (Shodan Go Bet - who will win?) http://dcook.org/mlsn/ (Multilingual open source semantic network) http://dcook.org/work/ (About me and my work) http://dcook.org/blogs.html (My blogs and articles) _______________________________________________ computer-go mailing list [email protected] http://www.computer-go.org/mailman/listinfo/computer-go/
