Demonstration in numbers why chess is in practice infinite • page 1/1 • General Chess Discussion • lichess.org

jose1122 edited

Chess is literally infinite without FIDE rules, many games would be literally infinite when King x King, I think I should mention this before everything.

But considering the FIDE rules, there should be a limit, let's see some numbers:
I will start with the Shannon's Number because this is the most common number to describe the limits on chess.

Claude Shannon, a mathematician developed the Shannon's Number to describe aproximately how many chess games it is possible, he analyzed many games and got the conclusion that in general, games long 40 moves each (80 then) and in each position players normally have 30 moves available. Then we got 30^80 games, or 10^120 (I don't know how to convert, I just trust because this is the official number)

How big is 10^120? ( number 10 with 120 zeros)

Just to compare, scientists often say that the observable universe contains 10^80 atoms, so 10^120 is insanely huge, but let's also remember that 10^81 is bigger than 10^80 + 10^79 + 10^78 ...
For example: 5^5 = 3125, now 5^4 (625) + 5^3 (125) + 5^2 (25) + 5^1 (5) + 5^0 (1) = 781
I'm saying this because 80 to 120 doesn't look great thing but it is actually monstruous, each new number destroys all the others left behind by far. Another example is:

10^3 = 1 thousand, 10^6 = 1 million, 10^9, 1 billion... just 3 zeros and you get millionaire, 3 more and you get billionaire, each zero counts a lot, a single zero makes the new number incomparable.

So, only with the Shannon's Number we would have trillions and trillions of games to each atom of our universe and it would not be enough.
But the Shannon's Number is only a simple approximation, now let's come back to the FIDE rules. Considering the 50 moves to draw, 3 repetitions and insufficient material, the longest possible chess game discovered until today have 8848 moves, it means instead of 30^80, we should do 30^8848 actually, and the base is 30 not 10 so it gets even higher.
The probabilistic model called Monte Carlo (don't know much of this) says chess can reach 10^29241 games which I think it is just the converted number base 30 to 10.

This is simply unreachable, unthinkable, we can't even describe what number 10^29241 is, this exceeds anything inside our universe multiple times.

Now, another way to see how chess is near infinite. When analyzed backwards, chess was completely solved in all positions up to 7 pieces on the board (the result of this method is called tablebase, the most common tablebase is called Syzygy), and computers are now trying to solve chess with 8 pieces in all legal possibilities, it will take some years to be complete.
(fun fact, the longest known forced checkmate with 7 pieces has 549 moves in sequence).

The estimative to store the entire 8 pieces tablebase data is 2 petabytes, being 1 petabyte = more than 2 million gigabytes (1 petabyte = 1024 terabytes, 1 terabyte = 1024 gigabytes).
Many people like Garry Kasparov say that 8 pieces will be the limit for computers to do, even the time to finish a 9 pieces tablebase would take more than a full millenium when estimated... and chess have 32 pieces.

We could also consider new possibilities, like growing the 50 moves rule to 75 as some people want, or ideas like the chess of Capablanca, where the table is 10x10 squares, with 2 Kings and a brand new piece, or even if we consider the 960 Fischer random chess, things get even crazier.

Chess is in practice infinite.

Chess is literally infinite without FIDE rules, many games would be literally infinite when King x King, I think I should mention this before everything. But considering the FIDE rules, there should be a limit, let's see some numbers: I will start with the Shannon's Number because this is the most common number to describe the limits on chess. Claude Shannon, a mathematician developed the Shannon's Number to describe aproximately how many chess games it is possible, he analyzed many games and got the conclusion that in general, games long 40 moves each (80 then) and in each position players normally have 30 moves available. Then we got 30^80 games, or 10^120 (I don't know how to convert, I just trust because this is the official number) How big is 10^120? ( number 10 with 120 zeros) Just to compare, scientists often say that the observable universe contains 10^80 atoms, so 10^120 is insanely huge, but let's also remember that 10^81 is bigger than 10^80 + 10^79 + 10^78 ... For example: 5^5 = 3125, now 5^4 (625) + 5^3 (125) + 5^2 (25) + 5^1 (5) + 5^0 (1) = 781 I'm saying this because 80 to 120 doesn't look great thing but it is actually monstruous, each new number destroys all the others left behind by far. Another example is: 10^3 = 1 thousand, 10^6 = 1 million, 10^9, 1 billion... just 3 zeros and you get millionaire, 3 more and you get billionaire, each zero counts a lot, a single zero makes the new number incomparable. So, only with the Shannon's Number we would have trillions and trillions of games to each atom of our universe and it would not be enough. But the Shannon's Number is only a simple approximation, now let's come back to the FIDE rules. Considering the 50 moves to draw, 3 repetitions and insufficient material, the longest possible chess game discovered until today have 8848 moves, it means instead of 30^80, we should do 30^8848 actually, and the base is 30 not 10 so it gets even higher. The probabilistic model called Monte Carlo (don't know much of this) says chess can reach 10^29241 games which I think it is just the converted number base 30 to 10. This is simply unreachable, unthinkable, we can't even describe what number 10^29241 is, this exceeds anything inside our universe multiple times. Now, another way to see how chess is near infinite. When analyzed backwards, chess was completely solved in all positions up to 7 pieces on the board (the result of this method is called tablebase, the most common tablebase is called Syzygy), and computers are now trying to solve chess with 8 pieces in all legal possibilities, it will take some years to be complete. (fun fact, the longest known forced checkmate with 7 pieces has 549 moves in sequence). The estimative to store the entire 8 pieces tablebase data is 2 petabytes, being 1 petabyte = more than 2 million gigabytes (1 petabyte = 1024 terabytes, 1 terabyte = 1024 gigabytes). Many people like Garry Kasparov say that 8 pieces will be the limit for computers to do, even the time to finish a 9 pieces tablebase would take more than a full millenium when estimated... and chess have 32 pieces. We could also consider new possibilities, like growing the 50 moves rule to 75 as some people want, or ideas like the chess of Capablanca, where the table is 10x10 squares, with 2 Kings and a brand new piece, or even if we consider the 960 Fischer random chess, things get even crazier. Chess is in practice infinite.