Ah-ha! Wikipedia is our friend. That's what it says:
When neither side has any pawns, the game must be completed within a certain number of moves or it is declared a draw. When a piece is captured the count starts again from scratch only if it is the last piece of one side in the game.
* When neither side has any pawns left, mate must be achieved in 64 moves. The disadvantaged player does the counting, and may at any time choose to stop counting. If the disadvantaged side checkmates the advantage side and did not stop counting, the game is declared a draw.
When the last piece (that is not the King) of the disadvantaged side is captured, the count may be started, or restarted from the aforementioned counting, by the weaker side, and the stronger side now has a maximum number of moves based on the pieces left:
* If there are two rooks left: 8 moves * If there is one rook left: 16 moves * If there are no rooks left, but there are two bishops: 22 moves * If there are no rooks left, but there is one bishop: 44 moves * If there are no rooks or bishops left, but there are two knights: 32 moves * If there are no rooks or bishops left, but there is one knight: 64 moves * If there are no rooks, bishops, or knights, but queens: 64 moves
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