  Counterfactual Regret Minimization (CFR) is an efficient no-regret learning
algorithm for decision problems modeled as extensive games. CFR's regret bounds
depend on the requirement of perfect recall: players always remember
information that was revealed to them and the order in which it was revealed.
In games without perfect recall, however, CFR's guarantees do not apply. In
this paper, we present the first regret bound for CFR when applied to a general
class of games with imperfect recall. In addition, we show that CFR applied to
any abstraction belonging to our general class results in a regret bound not
just for the abstract game, but for the full game as well. We verify our theory
and show how imperfect recall can be used to trade a small increase in regret
for a significant reduction in memory in three domains: die-roll poker, phantom
tic-tac-toe, and Bluff.
