Author: Graham Laight
Date: 03:09:20 11/21/03
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On November 21, 2003 at 05:23:45, Drexel,Michael wrote: >On November 21, 2003 at 05:07:32, Graham Laight wrote: > >>Everybody knows that as chess computers improve, the proportion of draws in >>their games becomes higher. >> >>The same is true of humans: the following graph suggests that at Elo 3600, all >>games will be drawn: http://math.bu.edu/people/mg/ratings/Draws.jpg . I also >>think that a player who plays at Elo 3600 would be unbeatable - no matter how >>good his opponent was. For a 3600 player, obtaining a draw would, IMO, be almost >>as easy as it would be for me to obtain a draw against Kasparov with only a king >>against a king and a knight. In this situation, Kasparov's extra skill and >>knowledge of the game (and his extra piece) would count for nothing. >> >>If what I'm saying is right (and I personally think that it is), then there's a >>serious problem ahead for the Elo rating system: the system measures chess skill >>by a player's likelihood of beating another player. However - if the computer >>that can see 50 ply ahead is unable to beat the machine that can only see 25 ply >>ahead, then, according to the Elo rating system, it would have the same Elo >>rating! >> >>Is this right, or is this wrong? > >It is clearly wrong. A computer that can only see 25 ply ahead will almost >always lose to a computer that can see 50 ply ahead. >Until the game isn't solved, a computer could always lose a game theoretical. Hmmmmmm. Sometimes, when a visionary looks too far ahead, his reasoning gets rejected out of hand. For example, if Moore's law continues, then supercomputers will match the human brain's computing capacity in less than 20 years from now. This is very easy to demonstrate, if you take 5 minutes to do the arithmetic (I am happy to do it for you if you want to see it - it's not at all difficult). Try telling people this, though, and you'll be dismissed out of hand - and usually by people who should know better! Do you think that money will become obsolete? I do - within 200 years. However - there has never been a time in recorded human history when there was no money - so people cannot conceive this idea, and reject it out of hand without giving it sufficient consideration. Let me see if we can open your mind to the possibility that a 3600 elo player will almost always obtain a draw. I'm sure you'd agree that in some positions, a bad player could get a draw against any opponent, just by sticking to a few simple principles. From here, the leap you have to make is that, with increasing knowlege, the range of positions in which you can obtain a draw increases. In computer chess, depth of ply search substitutes for (or "provides") knowledge. Therefore, the deeper the ply search, the higher the range of positions in which the player can obtain a draw. Also, as the ply search deepens, it becomes increasingly difficult to get the player into a position in which he cannot achieve a draw. If it helps, think of the game of noughts and crosses. This game is known to be drawn, and, although I'm sure that you haven't sat down and crunched out all the possible games, I'm sure that you could obtain a draw against ANY player. You have to realise that, to a computer that can look 25 ply (or whatever depth is needed to achieve an elo rating of 3600) ahead, chess will look like a game of noughts and crosses. >In some seemingly equal positions there might exist a forced mate in 1000 ply or >more. I said "almost always", not "always". You might get an Elo rating of 3600.000001, rather than 3600, for example, if you win one game in a million. Not very exciting. -g >Michael > >> >>If it is right, then the Elo rating system has an upper bound of approximately >>3600. After this, even "solving" chess by computing out all the possible games >>will not give you an improvement in play, because the Elo 3600 will still almost >>always obtain a draw against you. >> >>-g
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