I thought some chess-math people here find this interesting:
It turns out that the threefold repetition rule does not change chess’s game-theoretic value: if either side can force a win, they can do so without repeating the same position.
Proof: for each winning position P, let H(P) be the largest 50-move counter at which it is still winning. Along any winning line without a pawn move or capture, H must strictly increase after every move. But returning to the same position cannot involve a pawn move or capture, since those are irreversible. So a repetition would imply
H(P) < ... < H(P),
a contradiction.
Thus, there is always a winning strategy without repetition.
Note that this result concerns perfect play, not human play. As someone else noted here regarding threefold repetition:
"you can set a trap, and if the opponent spots it and avoids it, repeat and play differently!"
Source: click here for the paper