Author: Graham Laight
Date: 03:07:44 05/10/01
Given that we cannot formally/mathematically solve chess right now, I think it would be worthwhile to look for ways to take an informed guess at what the solution is. I think that one way we can do this right now is to look for things that seem to correlate well, and extrapolate them forward. This is what I had in mind when I suggested (in another thread) looking for a correlation between depth of search and proportion of hash table hits. The idea was to see whether, as the depth of search increases, the proportion of node positions which are generated which have already been seen before increases. If it did, and especially if it did at a linear rate, then we could make a good estimate as to how deep we'd have to search to pretty well solve chess (IMO). Unfortunately, as Dr Hyatt pointed out, computer program hash tables don't represent repeated chess positions with 100% accuracy. Something I've always wanted to do is to see if there's a linear correlation between strength of players and proportion of draws (or wins for white) in their games against roughly equal opposition. Or maybe plot tournament strength against proportion of draws. If I had a copy of chessbase, I would definitely do this. I would get a spreadsheet (or a piece of paper), and just make a simple graph of player strength against against Elo rating. I would then calculate the correlation of the plotted points. I reckon that after an hour or so of research, I'd have a good idea what the answer is. I feel sure we'll find that, as strength increases, the games are converging towards draws. When we know the shape of the graph, we'll then be able to estimate the maximum possible Elo level. Then, by plotting the Elo levels of computers against time, we'll be able to estimate when computers will be able to play "perfect" chess. -g
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