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'The cycle is over after the last undefined piece has been defined by a
player and then simultaneously all the pieces fall back into their
undefined initial state and a new cycle begins.'

this could be interpreted a couple different ways as well - EITHER player
finishes defining, or BOTH players finish defining... it reads more like 
the latter, right?  although i can see nothing wrong with the former,
which would make things interesting - you could tactically end a cycle
quickly before your opponent did something.

whichever one is correct, if all the pieces are on the board, then it will
actually be the second-to-last piece to be defined which will finish the
cycle, because then the last is automatically known.