  We focus on the problem of finding an optimal strategy for a team of two
players that faces an opponent in an imperfect-information zero-sum
extensive-form game. Team members are not allowed to communicate during play
but can coordinate before the game. In that setting, it is known that the best
the team can do is sample a profile of potentially randomized strategies (one
per player) from a joint (a.k.a. correlated) probability distribution at the
beginning of the game. In this paper, we first provide new modeling results
about computing such an optimal distribution by drawing a connection to a
different literature on extensive-form correlation. Second, we provide an
algorithm that computes such an optimal distribution by only using profiles
where only one of the team members gets to randomize in each profile. We can
also cap the number of such profiles we allow in the solution. This begets an
anytime algorithm by increasing the cap. We find that often a handful of
well-chosen such profiles suffices to reach optimal utility for the team. This
enables team members to reach coordination through a relatively simple and
understandable plan. Finally, inspired by this observation and leveraging
theoretical concepts that we introduce, we develop an efficient
column-generation algorithm for finding an optimal distribution for the team.
We evaluate it on a suite of common benchmark games. It is three orders of
magnitude faster than the prior state of the art on games that the latter can
solve and it can also solve several games that were previously unsolvable.
