  Deep Reinforcement Learning combined with Fictitious Play shows impressive
results on many benchmark games, most of which are, however, single-stage. In
contrast, real-world decision making problems may consist of multiple stages,
where the observation spaces and the action spaces can be completely different
across stages. We study a two-stage strategy card game Legends of Code and
Magic and propose an end-to-end policy to address the difficulties that arise
in multi-stage game. We also propose an optimistic smooth fictitious play
algorithm to find the Nash Equilibrium for the two-player game. Our approach
wins double championships of COG2022 competition. Extensive studies verify and
show the advancement of our approach.
