|
|
|
Topic: How many different positions can occur in the game of chess?
| |
|
|
Author
| Message |
|---|
|
|
Thanks for your contributions.
What I mean, tough, is the number of legal positions that can occur in all posible games, and not only in one game.
I'm also talking about the number of different positions - not the number of moves.
Where did you get that information, GileCAR?
|
|
|
| beco wrote: To be more mathematical: the chess game do converge to an end, and cannot be played forever. |
Nope. Draws by repetition and by the fifty-move rule have to be claimed. There's no finite bound on the length of a possible game between two people who decide not to claim the draws they're entitled to.
Anyway, as GileCAR has stated, the number of possible positions is finite, even though the number of possible games is infinite.
|
|
|
Indefinable: http://www.cs.uta.fi/ga/slides/chess_alg.pdf
Though, I've seen 10^43 on other places ...
Richeby: Number of games if finite also. Due to 50 moves rule no game can last longer than 30*50 moves. finite number of positions and finite number of moves must produce finite number of games
|
|
|
| Richerby wrote: Draws by repetition and by the fifty-move rule have to be claimed. |
Oh well... Yes, draws must be claimed... Or else, this simple example is sufficient to show an infinite game:
{Initial position.} 1. Nf3 Nc6 2. Ng1 Nb8 {Initial position repeated for the second time.} 3. Nf3 Nc6 4. Ng1 Nb8 {Initial position repeated for the third time. White can claim the game or keep moving...} 5. Nf3 {Here black can request draw also. This position with Nf3 repeated already 3 times.} Nc6 6. Ng1 Nb8 7. Nf3 Nc6 8. Ng1 Nb8 {And so on...}
But still: if the game has time control, it will be finite (No matter how big! Can be a life-time!)
Cheers,
Beco.
|
|
|
| GileCAR wrote: Number of games if finite also. Due to 50 moves rule no game can last longer than 30*50 moves. |
No. The fifty-move rule is `optional' -- the player must claim the draw and, if he does not, the game continues. Also, even if we assume that the players claim draws as soon as they're allowed to, the maximum length is longer than 30x50 moves, since the players can move pawns as well as have their pieces captured. So the maxiumum is at least 62x50 (every pawn can move at least twice and every piece except the kings is taken).
|
| Previous 1 2 3 4 5 6 7 8 Next |
|
|
|
