On Tue, Oct 26, 2010 at 9:50 AM, Matthew Woodcraft <[email protected]>wrote:
> Olivier Teytaud wrote: > > I've been told recently that there are some works measuring how deep > > a game is as follows: > > - consider a fixed 0.5 < p < 1; > > - consider how many categories of people you can find such that the > > category number n wins with probability p against the catégory number > > n-1. > > > > Clearly, this is not so well defined - but it's interesting (at least > > to me :-) ). > > I think a difficulty with getting anything useful out of this idea is > that it's sensitive to the length of the game. > > For example, if you consider a three-game Go match to be a game in > itself, it obviously turns out to be much 'deeper' than Go. But it's > surely not deeper in any very interesting sense. > That's an interesting point and it's correct. However, I think the length of the game is in most cases highly correlated to the "depth" of the game and this might still work as a general approximation. One could also adjust for game length I suppose to get some kind of measure of the difficulty of a single move of the game in question. If you were using my idea of ELO range you might simply adjust in linear fashion for the average length of the game in the 2 games being compared. I'm not sure if the appropriate adjustment should be linear but it would probably be a little more accurate. Each move of any 2 player game gives the players an additional chance to exercise his superiority, or demonstrate his inferiority over his opponent. It's probably going way too far to consider each move a separate game when making the adjustment calculation but adjusting linearly is probably not enough. Don > > -M- > _______________________________________________ > Computer-go mailing list > [email protected] > http://dvandva.org/cgi-bin/mailman/listinfo/computer-go >
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