  There has been tremendous recent progress on equilibrium-finding algorithms
for zero-sum imperfect-information extensive-form games, but there has been a
puzzling gap between theory and practice. First-order methods have
significantly better theoretical convergence rates than any
counterfactual-regret minimization (CFR) variant. Despite this, CFR variants
have been favored in practice. Experiments with first-order methods have only
been conducted on small- and medium-sized games because those methods are
complicated to implement in this setting, and because CFR variants have been
enhanced extensively for over a decade they perform well in practice. In this
paper we show that a particular first-order method, a state-of-the-art variant
of the excessive gap technique---instantiated with the dilated entropy distance
function---can efficiently solve large real-world problems competitively with
CFR and its variants. We show this on large endgames encountered by the
Libratus poker AI, which recently beat top human poker specialist professionals
at no-limit Texas hold'em. We show experimental results on our variant of the
excessive gap technique as well as a prior version. We introduce a numerically
friendly implementation of the smoothed best response computation associated
with first-order methods for extensive-form game solving. We present, to our
knowledge, the first GPU implementation of a first-order method for
extensive-form games. We present comparisons of several excessive gap technique
and CFR variants.
