  Counterfactual Regret Minimization (CFR) and its variants are the best
algorithms so far for solving large-scale incomplete information games.
However, we believe that there are two problems with CFR: First, matrix
multiplication is required in CFR iteration, and the time complexity of one
iteration is too high; Secondly, the game characteristics in the real world are
different. Just using one CFR algorithm will not be perfectly suitable for all
game problems.
  For these two problems, this paper proposes a new algorithm called Pure CFR
(PCFR) based on CFR. PCFR can be seen as a combination of CFR and Fictitious
Play (FP), inheriting the concept of counterfactual regret (value) from CFR,
and using the best response strategy instead of the regret matching strategy
for the next iteration. This algorithm has three advantages. First, PCFR can be
combined with any CFR variant. The resulting Pure MCCFR (PMCCFR) can
significantly reduce the time and space complexity of one iteration. Secondly,
our experiments show that the convergence speed of the PMCCFR is 2$\sim$3 times
that of the MCCFR. Finally, there is a type of game that is very suitable for
PCFR. We call this type of game clear-game, which is characterized by a high
proportion of dominated strategies. Experiments show that in clear-game, the
convergence rate of PMCCFR is two orders of magnitude higher than that of
MCCFR.
