A lot
I need a math genius to explain how many Chess positions there are.
Sort:
Upper bound: 1.9605348*10^71.
how this number is calculated: 13^64
13 possible square states (6 for both black and white, and one blank state)
64 for the number of squares on the board
Eniamar wrote:
There's a better page on wikipedia that explains it a bit better, however:
http://en.wikipedia.org/wiki/Chess#Mathematics_and_computers
So between 10^43 and 10^50 positions, given that nobody else is smart enough to figure out how to account for all the special cases and arrive at an exact number.
People are smart enough, just the ones that ARE smart enough don't really care enough to do it
Chat gpt says:
The number of possible chess positions is incredibly vast. Estimates suggest there are about \(10^{40}\) to \(10^{50}\) legal positions in chess. This estimate comes from considering the various combinations of pieces, the rules of the game (like castling and en passant), and the typical number of moves.
To break it down:
1. **Game Complexity**: Chess has a branching factor of about 35, meaning each player has approximately 35 possible moves at each turn.
2. **Game Length**: A typical game lasts around 40 moves, but some games can go significantly longer.
3. **Position Calculation**: The Shannon number, proposed by Claude Shannon, estimates that there are about \(10^{120}\) possible game variations, but this includes sequences of moves rather than just unique positions.
In summary, while the exact number of legal positions is hard to pin down, it's clear that chess offers a virtually infinite landscape of potential configurations!
The number of possible chess positions is incredibly vast. Estimates suggest there are about \(10^{40}\) to \(10^{50}\) legal positions in chess. This estimate comes from considering the various combinations of pieces, the rules of the game (like castling and en passant), and the typical number of moves.
To break it down:
1. **Game Complexity**: Chess has a branching factor of about 35, meaning each player has approximately 35 possible moves at each turn.
2. **Game Length**: A typical game lasts around 40 moves, but some games can go significantly longer.
3. **Position Calculation**: The Shannon number, proposed by Claude Shannon, estimates that there are about \(10^{120}\) possible game variations, but this includes sequences of moves rather than just unique positions.
In summary, while the exact number of legal positions is hard to pin down, it's clear that chess offers a virtually infinite landscape of potential configurations!
Shannon's number
Koh-i-noor wrote:
Shannon's number
Does not address the number of positions, but rather sequences of moves. The numbers are different.
lihi2303 wrote:
Chat gpt says:
The number of possible chess positions is incredibly vast. Estimates suggest there are about \(10^{40}\) to \(10^{50}\) legal positions in chess. This estimate comes from considering the various combinations of pieces, the rules of the game (like castling and en passant), and the typical number of moves.
To break it down:
1. **Game Complexity**: Chess has a branching factor of about 35, meaning each player has approximately 35 possible moves at each turn.
2. **Game Length**: A typical game lasts around 40 moves, but some games can go significantly longer.
3. **Position Calculation**: The Shannon number, proposed by Claude Shannon, estimates that there are about \(10^{120}\) possible game variations, but this includes sequences of moves rather than just unique positions.
In summary, while the exact number of legal positions is hard to pin down, it's clear that chess offers a virtually infinite landscape of potential configurations!
The number of possible chess positions is incredibly vast. Estimates suggest there are about \(10^{40}\) to \(10^{50}\) legal positions in chess. This estimate comes from considering the various combinations of pieces, the rules of the game (like castling and en passant), and the typical number of moves.
To break it down:
1. **Game Complexity**: Chess has a branching factor of about 35, meaning each player has approximately 35 possible moves at each turn.
2. **Game Length**: A typical game lasts around 40 moves, but some games can go significantly longer.
3. **Position Calculation**: The Shannon number, proposed by Claude Shannon, estimates that there are about \(10^{120}\) possible game variations, but this includes sequences of moves rather than just unique positions.
In summary, while the exact number of legal positions is hard to pin down, it's clear that chess offers a virtually infinite landscape of potential configurations!
1 and 2 have to do with move sequences, not positions.
You realize this includes pawn (under)promotions, calling rights, en passant ing rights?
I’m a math smart person,maybe not genius yet, but I don’t think I can do that.
I’m a math smart person,maybe not genius yet, but I don’t think I can do that.
Here's a question for y'all: Are there more possible chess positions or more stars?
My opinion is that we can't know because we can only observe a portion of the universe, so we can't even estimate. So maybe a better question is... are there more in the OBSERVABLE universe?
There are way more chess positions, because there's only one Star - myself! 
There are around 100 billionish stars in just our galaxy. If we assume our galaxy to be about average and there are around 2 trillion galaxies in the OBSERVABLE universe then 100 billion x 2 trillion equals a ginormous gargantuan number.
DreamscapeHorizons wrote:
Here's a question for y'all: Are there more possible chess positions or more stars?
My opinion is that we can't know because we can only observe a portion of the universe, so we can't even estimate. So maybe a better question is... are there more in the OBSERVABLE universe?
More stars and that’s just what we can see. The confusion comes, as evident on every page in this thread, in the confusion between possible chess games (Shannon’s number) and possible positions (the OP’s query). A math genius may be needed to answer the question, but simple literacy is enough to dismiss most attempts (that are answering a different question).
DreamscapeHorizons wrote:
Here's a question for y'all: Are there more possible chess positions or more stars?
My opinion is that we can't know because we can only observe a portion of the universe, so we can't even estimate. So maybe a better question is... are there more in the OBSERVABLE universe?
I bet there are more possible Chess games than atoms in the entire universe, observable or not
Enough to circle the planet earth several times over!!!