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How many different chess positions are there?

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CraigIreland
CraigIreland
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Aug 2, 2022
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#381

All of the serious numbers in this thread are attempts to determine upper bounds because the perfect Chess automaton would drastically restrict the number of possible positions by making them unreachable. The problem of course, is without that elusive algorithm it's very difficult to even guess the size of the set of positions which it would permit. If we take the example of possible pawn structures, it's reasonable to assume that the vast majority of legal pawn structures would be impossible to construct against the perfect Chess algorithm, because they would be too vulnerable to attack during construction.

tygxc
tygxc
Aug 2, 2022
0
#382

#390
"the perfect Chess automaton would drastically restrict the number of possible positions"
++ Yes, that is correct. The vast majority of the 10^44 legal positions or the 10^37 legal positions without promotions to pieces not previously captured are not sensible. The vast majority of the sensible are not reachable in the course of calculation by a perfect automaton. The wast majority of the reachable are not relevant. That leaves 10^17 legal, sensible, reachable, and relevant positions, needed to weakly solve chess.

"without that elusive algorithm it's very difficult to even guess the size of the set of positions"
It is possible without the algorithm. The 10^17 estimate stems from the Gourion paper 10^37 positions without promotions to pieces not previously captured. A sample of 1000 such prositions shows these are not sensible, that leads to an estimated 10^32 sensible positions. Checkers has been weakly solved visiting 10^14 positions and Losing Chess has been weakly solved using 10^9 positions. That leads to an estimated 10^19 reachable positions. Weakly solving only needs a (one) strategy, not all. That leads to 10^17 relevant positions.

dullerthanthou
dullerthanthou
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Aug 9, 2022
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#383

There is only one move in every real chess game. Pretend to look at the board while slyly pulling out a gun under the table and blowing your opponents nuts off... game over!

HotDog300
HotDog300
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Dec 22, 2022
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#384
Fourpointo skrev:

This is a hard one, but I thought about it and it could be a new way to look at chess and/or chess computers. Assuming there is a perfect single move for every position, how many would have to be known to create a theoritical perfect chess computer/player?

To start, there are 7 different possiblilites that can be on a square at one time. A King, Queen, Knight, Bishop, Rook, Pawn, or an empty space. So that means the max possible number of positions would be 7^64 (number of squares) which is somewhere around 1.2 e 54, or 2.4 e54 if you count whose move it is. But then when you start taking out impossible combinations, such as more than 2 king on the board at once, pawns on the back row, more than 10 of a knight, rook, bishop, 9 of a queen, or 8 of a pawn on either side, it gets smaller. And of course there are other board impossibilites, like 8 pawns on the same side lined up vertically, a double knight check, etc.

So has anyone ever heard of someone who has calculated this number? I tried searching for it but it doesn't seem many people have thought as chess this way.


Edit: There would be 13^64 maximum possible positions, because each piece could either be black or white.

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So this means there are 1,219,760,487,635,835,700,138,573,862,562,971,820,755,615,294,131,238,401 different positions in chess. Wow, that's a high number!

 

tygxc
tygxc
Dec 22, 2022
0
#385

@391

Only 10^44 positions are legal.
Even less make sense: 10^37 is a more sensible number.

13^64 is the number of ways monkeys can put part of 64 boxes of chess men on a chess board. That includes and empty board and a board with 64 white kings and everything in between. It has nothing to do with the game of chess.

Unseekedspy
Unseekedspy
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Dec 4, 2023
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#386
Fourpointo wrote:

This is a hard one, but I thought about it and it could be a new way to look at chess and/or chess computers. Assuming there is a perfect single move for every position, how many would have to be known to create a theoritical perfect chess computer/player?
To start, there are 7 different possiblilites that can be on a square at one time. A King, Queen, Knight, Bishop, Rook, Pawn, or an empty space. So that means the max possible number of positions would be 7^64 (number of squares) which is somewhere around 1.2 e 54, or 2.4 e54 if you count whose move it is. But then when you start taking out impossible combinations, such as more than 2 king on the board at once, pawns on the back row, more than 10 of a knight, rook, bishop, 9 of a queen, or 8 of a pawn on either side, it gets smaller. And of course there are other board impossibilites, like 8 pawns on the same side lined up vertically, a double knight check, etc.
So has anyone ever heard of someone who has calculated this number? I tried searching for it but it doesn't seem many people have thought as chess this way.
Edit: There would be 13^64 maximum possible positions, because each piece could either be black or white.

You also have to take into account illegal positions, ex: https://lichess.org/editor/KKKKKKKK/KKKKKKKK/KKKKKKKK/KKKKKKKK/KKKKKKKK/KKKKKKKK/KKK1KKKK/KKKKKKKK_w_-_-_0_1?color=white

Here, if we were to take into account just the white king, we would have to add all 64c64+64c63+64c62+..., I'm not sure, maybe permutations. What I am saying is that it is like subtracting infinities from each other.

albusbluderdore
albusbluderdore
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Dec 4, 2023
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#387
No but there could be DIFFERENT pawns on different squares and stuff right!
Tdale77
Tdale77
Dec 30, 2023
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#388

It's interesting to look at how many opening moves there are, and then how many possible moves there are.

Opening move: Pawns 16 possabilities + Knights 4 possabilities = 20

Next move: Also 20, which equals 400 different positions after two moves.

Third move: Depending on opening move, 27, which equals 10800

Fourth move: Also 27 possible moves = 291600 possible positions.....