#### Only Chess Forum

1. 10 Sep '16 21:33
Assuming rules prescribing draws, wouldn't there be an actual finite number of possible variations of a single chess game? Has this number ever been determined, or is it actually incalculable?
2. 10 Sep '16 21:41
http://www.popsci.com/science/article/2010-12/fyi-how-many-different-ways-can-chess-game-unfold
3. 10 Sep '16 23:37
Originally posted by ParShooter
http://www.popsci.com/science/article/2010-12/fyi-how-many-different-ways-can-chess-game-unfold
Maybe it's a font thing:

'There are only 1015 total hairs on all the human heads in the world, 1023 grains of sand on Earth, and about 1081 atoms in the universe.'

I'm guessing there's a 'to the power of' sign missing there somewhere!
4.  venda
Dave
11 Sep '16 19:56
Originally posted by Jerrard
Assuming rules prescribing draws, wouldn't there be an actual finite number of possible variations of a single chess game? Has this number ever been determined, or is it actually incalculable?
It's probably calculable but you'd need a very powerful computer to do it.
There's 20 possible moves available to white on move 1 and an equal number of replies for black and the number of available moves increases by a lot on move 2 assuming a central pawn or knight move.
Chess has been played for hundreds of years and you still see "this move hasn't been seen before" in Gm game analysis.
5. 11 Sep '16 21:16
Originally posted by aquatabby
Maybe it's a font thing:

'There are only 1015 total hairs on all the human heads in the world, 1023 grains of sand on Earth, and about 1081 atoms in the universe.'

I'm guessing there's a 'to the power of' sign missing there somewhere!
Presumably they should all be "ten to the power of...".

'There are only 10^15 total hairs on all the human heads in the world, 10^23 grains of sand on Earth, and about 10^81 atoms in the universe.'
6. 17 Sep '16 05:41
Originally posted by Jerrard
Assuming rules prescribing draws, wouldn't there be an actual finite number of possible variations of a single chess game? Has this number ever been determined, or is it actually incalculable?
It may be a finite number but it's safe to say it's a really big finite number.
7. 17 Sep '16 12:47
You can get an incredible amount of different positions after 10 moves.
but "Assuming rules prescribing draws." are in progress.

There will be a set number of possible captures (both sides can
only make 15) and a set number of possible pawn moves before they dry up.

A game, in theory, could go, both players move their Knight 49
times, then push a pawn one square. Do the same again

If you stick to the 50 moves a draw rules then the total number of
moves (the last time I looked) was calculated as 5899.
It may have changed since then.
8. 17 Sep '16 13:41
Another take: https://en.wikipedia.org/wiki/Shannon_number
9.  Marinkatomb
wotagr8game
20 Sep '16 14:13 / 2 edits
This Youtube video is a really great explanation of the maths..

10.  moonbus
Uber-Nerd
20 Sep '16 18:50 / 1 edit
Yes, I think there must be a finite number of possible variations of a single game, given that if no pawns are taken after 50 moves, or if a position is thrice repeated, it is a draw. The deeper one goes into a single game, the lower the number of possible variations, since some moves are irreversible (castling, pawn moves, captures, etc.).