Will our grandchildren see over 9000 strength play?

[Ajedrecista]

Hello Robert:

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.

Where do you get a meaningless number like 9000? HAL 9000? The way you are going about it is wrong.
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.

I want to point out some things:

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.

[Terry McCracken]

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.

Where do you get a meaningless number like 9000? HAL 9000? The way you are going about it is wrong.
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.

Fortunately, most moves are just noise, even legal moves. So you don't need the entire game tree to find the best moves but it will be hard to separate the wheat from the chaff. How do you find all best lines over 100 plies even with a Zettaflop computer 20 or more years from now?

I don't know?

[Uri Blass]

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.

400 elo difference does not mean that the stongest player always beat the weaker player and I also think that rating is not something that is well defined because it is dependent on the pool of players that you test.

I believe that at some level that is not close to perfect chess white will never lose games.
suppose A never lose with White and A has rating of X elo(X may be
CCRL rating of 4000 for the discussion.

No program B is going to get more than 75% against A so the best B can do based on a match against A is rating of 4200 elo
but it is possible that if B does not play directly with A it is going to get rating of 4600 and the process is going to be the following:

A1 beat A in part of the cases with white and get a rating of 4100
A2 beat A1 in part of the cases with white and get a rating of 4200
A3 beat A2 in part of the cases with white and get a rating of 4300
A4 beat A3 in part of the cases with white and get a rating of 4400
A5 beat A4 in part of the cases with white and get a rating of 4500
B beat A5 in part of the cases with white and get a rating of 4600

In other word it is going to be unclear what is the rating of B and if it is 4600 or 4200.

[Terry McCracken]

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.

400 elo difference does not mean that the stongest player always beat the weaker player and I also think that rating is not something that is well defined because it is dependent on the pool of players that you test.

I believe that at some level that is not close to perfect chess white will never lose games.
suppose A never lose with White and A has rating of X elo(X may be
CCRL rating of 4000 for the discussion.

No program B is going to get more than 75% against A so the best B can do based on a match against A is rating of 4200 elo
but it is possible that if B does not play directly with A it is going to get rating of 4600 and the process is going to be the following:

A1 beat A in part of the cases with white and get a rating of 4100
A2 beat A1 in part of the cases with white and get a rating of 4200
A3 beat A2 in part of the cases with white and get a rating of 4300
A4 beat A3 in part of the cases with white and get a rating of 4400
A5 beat A4 in part of the cases with white and get a rating of 4500
B beat A5 in part of the cases with white and get a rating of 4600

In other word it is going to be unclear what is the rating of B and if it is 4600 or 4200.

I think these numbers are meaningless. Chess has a limit and elo is an estimate in playing strength. What's happening here is inflated numbers.

The elo system wasn't meant to deal with huge ratings.

If you're going to start with arbitrary numbers at least bring it down 1000 elo.

[Ajedrecista]

Hello:

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.

400 elo difference does not mean that the stongest player always beat the weaker player and I also think that rating is not something that is well defined because it is dependent on the pool of players that you test.

I believe that at some level that is not close to perfect chess white will never lose games.
suppose A never lose with White and A has rating of X elo(X may be
CCRL rating of 4000 for the discussion.

No program B is going to get more than 75% against A so the best B can do based on a match against A is rating of 4200 elo
but it is possible that if B does not play directly with A it is going to get rating of 4600 and the process is going to be the following:

A1 beat A in part of the cases with white and get a rating of 4100
A2 beat A1 in part of the cases with white and get a rating of 4200
A3 beat A2 in part of the cases with white and get a rating of 4300
A4 beat A3 in part of the cases with white and get a rating of 4400
A5 beat A4 in part of the cases with white and get a rating of 4500
B beat A5 in part of the cases with white and get a rating of 4600

In other word it is going to be unclear what is the rating of B and if it is 4600 or 4200.

I think these numbers are meaningless. Chess has a limit and elo is an estimate in playing strength. What's happening here is inflated numbers.

The elo system wasn't meant to deal with huge ratings.

I fully agree with Uri and Terry. The most important thing about Elo rating system is not the number itself but the difference between the rankings of two players (higher rated player has difference d > 0 while the lower rated player has d < 0), and this difference measures the expected win probability of each player (it could be done with more than two players). There also exists an error because of the number of games played, and it is proportional to 1/sqrt(n) if we called n at the number of games played (please correct me if I am wrong), so the true interval should be ]d - K/sqrt(n), d + K/sqrt(n)[, with K > 0 (that depends on the winning score, the draw ratio...).

More info about Elo rating system could be found at Wikipedia and Chess Programming Wikispace, for example. When |d| = 400, the higher ranked player has probability 10/11 (~ 90.9%) of score in a game, while the lower rated player has probability 1/11 (~ 9.1%); scoring 100% (or 0%) in n games (with n enough big) implies that |d| tends to infinity. An score of 75% - 25% means |d|~ 191 ± K/sqrt(n). My explanation will be surely poor (and I hope it is not wrong), so any comments or corrections are welcome.

The best examples of the meaningless fact of the numbers themselves are the different rating lists: SWCR, IPON and Clemens-Keck rate Houdini 1.5a x64 1 core at roughly 3000+, while CEGT (in different time controls), CCRL (also in different time controls) and Sedat (for example) rate it at 3300+.

Regards from Spain.

Ajedrecista.

[S.Taylor]

maybe i will see this, when im 93 years

In the past 5 years the elo rating has been quite fluid. Increasing a bit more than the previous 5 years. You may not have to wait that long.

.

I am surprised that you are prepared to go along with any fantasies like these. I thought you were one of the wiser experts at chess in this forum.

[muxecoid]

No program B is going to get more than 75% against A

Suppose we have the same (or at least same strength) engine running on two different processors. The second processor is 64 times faster than the first. Do you really believe that A will not lose as white?

[Robert Flesher]

Hello Robert:

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.

Where do you get a meaningless number like 9000? HAL 9000? The way you are going about it is wrong.
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.

I want to point out some things:

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.

Thanks for the corrected numbers! As I stated I was not sure of the accuracy, but they are amusing.

[Don]

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.

I personally believe that 9000 ELO is impossible even with perfect play. The upper limit is probably less than 5000 but that is just my own opinion with nothing too solid to back it up. It may be as low as 4000. There are ways to estimate it but it's hard to say how close we can get to the correct values. There is also a lot of trouble with transitivity which has a lot to do with playing style at those levels so a precise ELO max is impossible to come by. Another way to say this is that the ELO formula give you an approximation of chess skill but it's not a completely accurate model of it.

Your statement that 400 ELO means you never lose is not correct. There is a linear version of the ELO formula that would predict that, but of course it's only very accurate when players ratings are fairly close. But even 600 ELO gives you about a 3% chance of scoring.

[Uri Blass]

No program B is going to get more than 75% against A

Suppose we have the same (or at least same strength) engine running on two different processors. The second processor is 64 times faster than the first. Do you really believe that A will not lose as white?

Not today because programs are not strong enough but sometimes in the future(in theory even today if you use time control that is 1,000,000 times slower than tournament time control but we cannot practically test it without having hardware that is million times faster than the hardware of today)

I suspect that with hardware that is million times faster than the hardware of today at least one top program never lose with white at 3 minutes per move inspite of losing with black in part of the games and it is obvious that we cannot test my theory today because hardware is not fast enough.