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Interesting...I suppose I can believe that's a weakness, though I'd imagine it's quite a small one. The difference of giving this disadvantage to every piece in your army must be worth substantially less than the privilege for a player to make null moves--I wonder if anyone has made a reasonable estimate of that value?

Is that a disadvantage specifically of switching pieces, though, or are they just the most extreme case on a sliding scale based on the length of the shortest odd cycle the piece can make? It seems intuitive that a hypothetical piece that takes, say, 9 moves to return to its starting square is much less likely to be able to lose a tempo in practice than a piece that can do it in 3 moves (though I could be wrong).

That would also be interesting because it suggests pieces that capture and move in different patterns should be affected if and only if their non-capturing move is switching, regardless of their capture pattern.