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.

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