On Tue, Oct 26, 2010 at 11:40 AM, Álvaro Begué <alvaro.be...@gmail.com>wrote:
> On Tue, Oct 26, 2010 at 11:34 AM, Don Dailey <dailey....@gmail.com> wrote: > > > > On Tue, Oct 26, 2010 at 11:07 AM, Álvaro Begué <alvaro.be...@gmail.com> > > wrote: > >> > >> A few years ago I had a conversation with John Tromp about this > >> measure of depth, and he pointed out that "who has bigger feet" has as > >> many levels as there are players, but doesn't make for a very > >> interesting game. > > > > That's not as logical as it sounds. If you could measure ELO ratings > with > > infinite precision, you would have as many ratings as people too. We > are > > not interested in how many different foot sizes, but the range of > possible > > values in some context that has real meaning. With ELO we don't care > > about how many different ELO ratings there are, we care about the range > of > > values and the context is how much 1 ELO point is worth in terms of > winning > > probability. > > No, the point is that a player with slightly larger feet than another > player will win with unbelievable consistency, while this is not true > of small ELO differences. > I understand your point now, my take on it was incorrect. ELO range is not a mathematically precise notion of "depth", but I think it might be the only reasonable measure of how "difficult" a game is from a purely human subjective point of view. Branching factor is almost a useless measure of how difficult a game is. I'm sure John Tromp is interested in this question from a more scientific mathematical perspective and thus "ELO range" based on human play is not going to be very interesting to him. Let's just say that we are trying to measure something different. How "difficult" is a given game for a human player? If we define it that way, then we don't have to be concerned about game length - longer games are more difficult to play because they present more opportunities for blunders and missteps and we are interested in ONE complete game, not a match and not a single move. So from my point of view I think it's very interesting to measure the range of skill (as measured approximately by ELO) of the worst to the best human players for the various games. Intuitively, what we really want to know is how difficult it is to beat a perfect player but we cannot measure that (accurately) for most games. Don > > > Even with foot size, if you measure the day to day variation, you could > > probably classify them into just a few types. For example there are > > finite number of shoe sizes and only 6 or 7 different shoe sizes fit 95% > of > > the population (assuming adults only.) > > OK, let's play "who has a higher Social Security Number", then. > _______________________________________________ > Computer-go mailing list > Computer-go@dvandva.org > http://dvandva.org/cgi-bin/mailman/listinfo/computer-go >
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