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H. G. Muller wrote on 2011-01-21 UTC
I agree that longer repeat cycles are quite rare. Although they would get more frequent when you allow them, but not 4-ply cycles, because the losing player would start to especially seek them in order to dodge the 4-ply rule. I tested in engine games, and between an engine that knows the rule, and one that doesn't, about 13% of the games end in a perpetual chase. (when both know about perpetual checking. If one of them does not know that rule, he would lose almost every game by doing it.)

The point is of course that it becomes progressively more difficult to keep chasing the piece for a longer number of moves. But this would typically occur when the chased side does not know that chasing is illegal, and desparately tries to escape it. (E.g. a passed Pawn chased by a Rook along files, running back and forth over the full width of the board.)

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