More than the number of atoms in the universe. Stick that in your pipe and smoke it.
How many possible games of chess are there?
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Yes, I've read that too, though without finding out where this idea was first published and what evidence has been produced in favour of it. Anyone have a citation for it?
honestly i dont think it really matters....a good deal of the possible games wouldn't be worth seeing.
Of course they wouldn't but this isn't a question about the quality of those games.
Thanks SudhanshuN. And urk, that's the observable universe.
46.4 x 10 raised to a quadrillion; that means 4.8 followed by roughly 1 quadrillion zeroes.
Apparently the number of possible positions has been worked out to +850Billion. In no way answers your question but it's a really big number.
So it is more than 200, right?
Hundreds, literally hundreds.
knig22 wrote:
chessking1976 schreef:
Apparently the number of possible positions has been worked out to +850Billion. In no way answers your question but it's a really big number.
the number of possible games is greater then the number of possible positions
If it wasn't for the 50 move tie rule... the number of possible games would literally be infinite. Hell, a game could go infinitely long.
Karpark wrote:
Yes, I've read that too, though without finding out where this idea was first published and what evidence has been produced in favour of it. Anyone have a citation for it?
If we allow for ridiculously long games, then it should be pretty safe to make a basic observation like:
Average 60 moves in a game = 120 individual moves.
Average 20 legal moves for each player's turn
So already we have 20^120 unique games
Which is much (MUCH) larger than the figure 10^123 for atoms in observable universe.
"Average 60 moves in a game = 120 individual moves."
I believe that the great, great majority of possible games would be much longer than that, given the apparent (to a real player) lack of cogency or interest in forcing mate in the great, great majority of these, making the figure you think way too small to be even way too smaller (if you know what I mean), 011001101101000. Many of these games would have numbers of moves in the thousands and tens of thousands, even with the limitations discussed above that bring games to a conclusion. Let the collective mind here boggle on.
knig22 wrote:
at least 10^120
If this number isn't big enough then you can increase the number of games by adding more pieces and with more ways to move. For example this board has 8 new types of pieces (archbishops, chancellors, guards, etc). Should be good enough to stump the computers too!
dannyhume wrote:
Are you crazy? 2,3 dozens tops.
Hundreds, literally hundreds.
Karpark wrote:
I suggest you work them all out on your chessboard and come back to us when you're done.
I don't expect anyone visiting this thread to be able to answer this question. I certain can't. I am sure, however, that the number of possible games is greater than 'a couple of hundred' which was offered as an almost throwaway answer on another thread. The reason, I guess, for why people might think that this number is less than it really is (though for most of us more than 200!) is, I think, because most people only consider those games which are relatively 'rational', meaning that they represent attempts (even though most are 'patzer attempts') to produce relatively cogent checkmates. Opening theory is perhaps another contributing factor insofar as many games at the higher levels repeat earlier games by other players for as much as twenty moves. The apparent familiarity of such games or opening sequences, however, disguises just how large this number really is, especially when one comes also to consider the number of 'irrational' but entirely legal games.
What I am most interested in here is less the answer itself to the question posed in the thread's title than those factors which demonstrate what a vastly huge number this must be.
First I must say that I believe this number to be finite because there is a significant limiting factor. This is that pawns must inevitably move forward and are inevitably promoted. Without a capture or a pawn move in 50 moves, the game is drawn. Since pawns cannot move backwards or remain pawns and since games without pawn moves come to an end, the number of possible games must be finite at some point.
Now for just a couple of the reasons that may not have occurred to you why the number of possible games must be so huge. (You are invited to suggest others.)
(1) Just think about the number of possible games in which only the knights move. Even after four moves by both players the number of possible sequences is already mind-boggling. After more moves even more so, as these knights enable repeat positions (up to three time) of all of possible positions, as they move around variously to all the squares, in some instances capturing all the other pieces sitting on their home squares. And these are only the games in which the four knights have moved.
(2) For each sequence leading up to a pawn promotion (and the number of these alone is eye-watering), the pawn in question can become a queen, a rook, a knight or a bishop, these possibilities further multiplying the number of continuations. From some of these promotions we have a staggering number of possible continuations that produce positions where, say, black may have three, four, five, six, seven, eight, nine or ten knights.
Yep. Did exactly that after Christmas dinner.
The Shannon number has it as at LEAST 20 different games.... AT LEAST! No, but it's 10 to the 120 which is MASSIVE.
Tell people that there are more positions in a 40 move game of chess than there are atoms in the universe and they look at you like you're crazy but the math is actually very simple, assuming you accept the Shannon Number of 10 to the 120th power as correct.
Number of atoms in typical sun =10 to the 58th power.
Number stars in the typical galaxy = 10 to th 11th power.
Number of galaxies we believe exist from observation=10 to the 11th.
Multiply those all together and you get 10 to the 80th power atoms.
I don't expect anyone visiting this thread to be able to answer this question. I certain can't. I am sure, however, that the number of possible games is greater than 'a couple of hundred' which was offered as an almost throwaway answer on another thread. The reason, I guess, for why people might think that this number is less than it really is (though for most of us more than 200!) is, I think, because most people only consider those games which are relatively 'rational', meaning that they represent attempts (even though most are 'patzer attempts') to produce relatively cogent checkmates. Opening theory is perhaps another contributing factor insofar as many games at the higher levels repeat earlier games by other players for as much as twenty moves. The apparent familiarity of such games or opening sequences, however, disguises just how large this number really is, especially when one comes also to consider the number of 'irrational' but entirely legal games.
What I am most interested in here is less the answer itself to the question posed in the thread's title than those factors which demonstrate what a vastly huge number this must be.
First I must say that I believe this number to be finite because there is a significant limiting factor. This is that pawns must inevitably move forward and are inevitably promoted. Without a capture or a pawn move in 50 moves, the game is drawn. Since pawns cannot move backwards or remain pawns and since games without pawn moves come to an end, the number of possible games must be finite at some point.
Now for just a couple of the reasons that may not have occurred to you why the number of possible games must be so huge. (You are invited to suggest others.)
(1) Just think about the number of possible games in which only the knights move. Even after four moves by both players the number of possible sequences is already mind-boggling. After more moves even more so, as these knights enable repeat positions (up to three time) of all of possible positions, as they move around variously to all the squares, in some instances capturing all the other pieces sitting on their home squares. And these are only the games in which the four knights have moved.
(2) For each sequence leading up to a pawn promotion (and the number of these alone is eye-watering), the pawn in question can become a queen, a rook, a knight or a bishop, these possibilities further multiplying the number of continuations. From some of these promotions we have a staggering number of possible continuations that produce positions where, say, black may have three, four, five, six, seven, eight, nine or ten knights.