Whoa. Wasn’t there a thread awhile back titled “A googol of anything?” I thought I remembered that there wasn’t a googol of anything, not even atoms. Now we know that there’s more than a googol of chess moves.
BTW - What would you call 100,000,000,000,000,000,000?
Hence the “in theory” qualifier. Remember, you’re talking to someone who spends time thinking about transfinite cardinals. Practicality is not a concern. 
That said, it’s definitely possible to dynamically calculate the best next move. Whether it can be done efficiently or not…who knows?
That’s why you would write the move on an electron. I’ll leave it to sharper minds than I to determine how you would write the move on an electron.
Chess moves aren’t tangible objects though, are they.
There is more than a googol of integers; heck, there’s more than a googol of integers divisible by 17.
That is not a stalemate. A draw may be declared by either player, but a draw is not necessarily a stalemate. A stalemate is when a player has no legal move.
The rule that Winkelreid quoted is from the 1997 Fide rules. I’ve heard that it the 50-move rule has been rescinded, at least in part, since then because computers have shown that some winning positions take more than 50 moves to win. I am unable to verify that, but I believe that if a player can establish that fact on the board, which would be a very rare occasion with a B and N (and K) against a K in some rare positions, he can be allowed to play for the win.
I remember reading that a famous GM claimed the repeat position (3 times) in a game, called over the tournament director, and after replaying the game, it was agreed that the position was about to be repeated for the third time, but the first time was many moves ago. It is important to remember that anytime the position is going to be repeated for the third time, you can claim the draw. (That GM had a great recollection of the positions in the game and, obviously, he was in a losing game.)
sorry, my last was in reply to Cisco
And, Mangetout, you would run out of atoms long before you got halfway.
100 Quintillion. Thank you SDSTAFF Dex.
:smack: you’re right ultrafilter 10[sup]75[/sup] is not just over half of 10[sup]120[/sup]
What a stupid mistake that was - you can tell I don’t use this kind of maths every day.
This may be too big a hijack but it seems better to ask here than a new thread.
I’m under the impression that the game Go has chess beat hands down for possible board combinations. Anyone have a clue how many combinations you can potentially get from a Go game?
Of course, it’s still literally true that there isn’t a googol of anything. Theoretically possible chess positions aren’t really a “thing”
Chess is a reasonably simple game; you could take any one of a number of more complex games and come up with even more absurd numbers for “possible moves.” The number of different ways to play a game of Civilization III would be vast beyond comprehension, there being more “pieces,” more possible places to put them, and more things to do. It would be orders of magnitude of orders of magnitude more than chess.
Yes it is…at least to us mere mortals who don’t cogitate on transfinite numbers 
!
10[sup]120[/sup] really is darn big. As you mention in your linked thread we’re talking about a number so large it really is beyond human comprehension except in the abstract.
Besides, for any number you care to mention I can come up with a bigger one. To quote my wife when we’d try to ‘out big’ the other person:
“Plus one to anything you say!” 
The Mathworld page on chess gives a few more numbers than have been thrown out there. Their Go page states the estimate for board positions (not games) at 4.63 * 10[sup]170[/sup].
It’s also important to make clear exactly what numbers are being talked about here. The 10[sup]120[/sup] number is the number of 40-move games (the average length of a game). I would think a fair number of these have repetitive positions; some may even be tournament rule draws. The Mathworld page has an estimate for the total number of games at 10[sup]10[sup]50[/sup][/sup] , which is moderately large, I’d say.
The total number of positions is going to be a lot smaller. There’s probably a good estimate of that somewhere too. I did a very quick estimate, and came up with :
SUM ( k=2, 32) : C(64, k) * 12[sup]k[/sup]
which (again using quick estimates) I don’t think is higher than 64! * 12[sup]32[/sup] / 32!, which is only about 90 digits. And it’s an overestimate.
Going back to numbers of games and similar games, Shogi (a Japanese game in the Chess family) has 10[sup]226[/sup] ‘average games’ (according to this page ). This is partly because the average game is longer, at 57 1/2 moves, and partly because the game itself has more moves (since captured pieces can come back into play).
Mangetout wrote:
Don’t forget that ultrafilter was talking about the theoretical “Ultimate Chess Strategy” (UCS), in which case you could throw out a lot of board positions as “silly.”
For example, let’s say the UCS begins with the same move that Fool’s Mate does. In which case, the UCS Guide could say “if your opponent makes a move which leaves them open to Fool’s Mate and does nothing to prevent Fool’s Mate later on, you can ignore that move.” In other words, you don’t have to write down all 10[sup]10[sup]50[/sup][/sup] board positions in the UCS (especially since the UCS won’t allow many of them), but only a subset of them.
Theoretically, there will be only one first move for the person following the UCS, so that cuts out nearly 1/20th of the possibilities right at the start. And a lot of later moves would be ridiculous, anyway.
If we put a further constraint on the UCS, that it only be used against reasonably competent chess players (master and above?), that would further limit the possibilities. After all, using the UCS against a novice or even a computer which moved randomly would be overkill. If the UCS author can say, for example, “well, only an idiot would make that move,” then the UCS author can avoid having to consider those possibilities. (And perhaps the UCS starts with a “general rule” for picking the closest board position after a non-anticipated move by an opponent.)
So, if a decent opponent would narrow down those 30 or 40 possible moves to, say, 5 rational ones, on average, for each move of the game, then the UCS player needs no more than an equal number of responses. In other words, the UCS player makes fixed moves in response to the opponent, and doesn’t increase the number of possible board positions at all - every position the UCS player creates is determined by the previous move of the opponent. Instead of 30 or 40 squared possibilities for each set of moves, we’re down to 5 (and not 5[sup]2[/sup], just five).
If the UCS player starts as white, he’s got one move, period. His opponent counters with one of 5 (or so). For each one of those, he responds with a single move (each). His opponent will probably do one of 5 (or so) in response to each of those five. So at the end of two moves, the UCS only has 30 board positions written down (5 for after the opponent’s first move, and 25 for after all probable second moves by the opponent).
If we run with these assumptions, then after 40 moves (if a UCS game takes that long), the UCS big book will need to have just over 1.1 x 10[sup]28[/sup] board positions listed. Even if you wanted to keep track of 30 possible opponent choices each move, that’d only be about 1.4 x 10[sup]56[/sup] positions.
I still wouldn’t want to even try to write it, but at least it’s down to fewer moves than there are atoms in the Universe.