  We propose and analyse a 2-parameter family of 2-player games on two heaps of
tokens, and present a strategy based on a class of sequences. The strategy
looks easy, but is actually hard. A class of exotic numeration systems is then
used, which enables us to decide whether the family has an efficient strategy
or not. We introduce yet another class of sequences, and demonstrate its
equivalence with the class of sequences defined for the strategy of our games.
