  We present a simple primal-dual algorithm for computing approximate
Nash-equilibria in two-person zero-sum sequential games with incomplete
information and perfect recall (like Texas Hold'em Poker). Our algorithm is
numerically stable, performs only basic iterations (i.e matvec multiplications,
clipping, etc., and no calls to external first-order oracles, no matrix
inversions, etc.), and is applicable to a broad class of two-person zero-sum
games including simultaneous games and sequential games with incomplete
information and perfect recall. The applicability to the latter kind of games
is thanks to the sequence-form representation which allows us to encode any
such game as a matrix game with convex polytopial strategy profiles. We prove
that the number of iterations needed to produce a Nash-equilibrium with a given
precision is inversely proportional to the precision. As proof-of-concept, we
present experimental results on matrix games on simplexes and Kuhn Poker.
