I want to point out some things:Robert Flesher wrote:Terry McCracken wrote:Where do you get a meaningless number like 9000? HAL 9000? The way you are going about it is wrong.muxecoid wrote:9000 is a popular magic number so I tried to estimate how long it will take to have a computer playing at that strength.

400 ELO difference means higher rated player always beats lower rated, 9000 strength requires 20 such steps.

Computing power nearly doubles every two years and double performance gives around 70 ELO. If we assume that the performance increase will slow down we can assume 20 ELO per year due to better hardware.

Improvements in software give up to 100 ELO per year, depending on engine. Let's take rather optimistic guess and say we get 50 ELO per year due to better software.

Currently best engine on best software plays at about 3400 strength. It means that in (9000-3400)/70=80 years. It means our grandchildren may see chess play rated over 9000.

Perfect chess has a limit. It would be well under a 4000 elo. Machines don't play at 3400 today that's not a scientific measurement.

Perfect chess might be around 3400 elo hypothetically. Programs are beginning to max out on tactics that would exceed 3000 elo but they're weaker at position and incapable of true plans. Perfect chess may be impossible but near perfect chess if work continues might be seen late this century.

Heya Terry, I agree with you regarding 9000 being an arbitray elo number. What I find very interesting are the questions, how is perfect chess defined? Is it define only mathematically? Will there eventually be tablebases that can included every conceivable move ? (not in our lifetime ). However, I believe it still remains clear that computers are no where near maxing out on tactics and eons away from perfect chess as they still suffer from the horizon effect. For sure they are much better than the best humans, but they still miss tactics.

Some points of interest, not sure of the accuracy. But they are amusing!

There are 318,979,564,000 possible ways to play the first four moves of chess.

In addition, America's Foundation for Chess found that there were

169,518,829,100,544,000,000,000,000,00… ways to play the first ten moves of chess.

The Shannon number, 10 to the 120 power, is an estimated lower bound on the game-tree complexity of chess.

As a comparison, the number of atoms in the observable Universe, to which it is often compared, is estimated to be between 4 × 10 to the 79 power and 10 to the 81 power.

There are 400 different positions after each player makes one move apiece.

There are 72,084 positions after two moves apiece.

There are 9+ million positions after three moves apiece.

There are 288+ billion different possible positions after four moves apiece.

The longest chess game theoretically possible is 5,949 moves.

The number of possible ways to play the first eight plies (four by white and four by black) is 84,998,978,956. The number you give is wrong and it is explained in François Labelle's web, at the end of the web. These numbers are known as

*perft*and are used as a debugging tool in the move generators of chess engines. More info could be found at Chess Programming Wikispace, searching Perft and Perft Results. There are more info in Programming and Technical Discussions subforum of TalkChess. Google could be of help for finding even more info, as usual.

For the first ten moves (twenty plies), I also refer to Labelle's web; there is a nice thread here in TalkChess at this link.

The number of different positions after two moves (four plies) is 72,078 and not 72,084. For three moves, it is 9,417,681; and finally, for four moves is 988,187,354. This info has been extracted from this web (third column). These results are the correct ones.

That is all. I hope I have not included typos in this post.

Regards from Spain.

Ajedrecista.