  In this paper we investigate the Follow the Regularized Leader dynamics in
sequential imperfect information games (IIG). We generalize existing results of
Poincar\'e recurrence from normal-form games to zero-sum two-player imperfect
information games and other sequential game settings. We then investigate how
adapting the reward (by adding a regularization term) of the game can give
strong convergence guarantees in monotone games. We continue by showing how
this reward adaptation technique can be leveraged to build algorithms that
converge exactly to the Nash equilibrium. Finally, we show how these insights
can be directly used to build state-of-the-art model-free algorithms for
zero-sum two-player Imperfect Information Games (IIG).
