TITLE: How long is the longest path in the game tree of chess?
QUESTION [5 upvotes]: I can only think of an upper bound, which consists of all configurations and so has length $5^{64}$. If the true value is intractable, we may give up solving chess. But if it's small, there still could be a fast algorithm to solve chess.
I say give up because I'm still thinking of traversing the game tree. But this may not be required on a second thought. Anyway I think this question is still interesting theoretically.

REPLY [4 votes]: Apparently to avoid perpetual check, a rule was initially set such that a sequence of moves that repeats three times will be declared a draw.
A recent nice video by James Grime and Rune Friborg notes that in the 1920's mathematician and chess grandmaster Max Euwe showed that players can engage to create a set of moves corresponding to the Thue-Morse sequence, such that no sequence of moves will be repeated three times.
For example:

call "white moves a left piece, black moves a left piece" $0$;
call "white moves a right piece, black moves a right piece" $1$;
have the players play a set of moves such as $0110100110010110...$ according to the Thue-Morse sequence.

Thus there would never be a sequence of moves that repeats three times.  Cooperative play would never accidentally lead to a win.  Indeed there might be a position wherein the best move for white is to check black with either a left ($a-d$ file) or right ($e-h$ file) rook, and for black to respond by checking white with either a left or right knight.
However, of course there would be a position that repeats three times, even if players cooperate - hence the the change in the rules.