Whim is played like nim, except one time, a player can use their whim to decide whether they are playing regular or misère nim.
Many positions have an easy analysis. To play misère nim, just play normal nim, except when it would leave only heaps of 0 and 1, and the number of 1 heaps is even. Instead, make the number odd. So from now on assume no one has used their whim.
Call a position firm if it has at least one heap of 2 or more, otherwise fickle. If you're in a fickle position, and the number of 1 heaps is even or odd, use your whim to play normal of misère nim, respectively. If you're in a firm position with value Grundy value 0, use your whim as a pass move.
The only difficult case is when you're in a firm position with nonzero Grundy value. This probably turns into she-loves-me, she-loves-me-not because there are only three ways to "exit" from this scenario:
- Moving to a position of Grundy value 0
- Using your whim
- Moving to a fickle position
And in each case, the person who exits loses.
Is there a simple strategy to play in this scenario?