  Monte Carlo Tree Search (MCTS) has recently been successfully used to create
strategies for playing imperfect-information games. Despite its popularity,
there are no theoretic results that guarantee its convergence to a well-defined
solution, such as Nash equilibrium, in these games. We partially fill this gap
by analysing MCTS in the class of zero-sum extensive-form games with
simultaneous moves but otherwise perfect information. The lack of information
about the opponent's concurrent moves already causes that optimal strategies
may require randomization. We present theoretic as well as empirical
investigation of the speed and quality of convergence of these algorithms to
the Nash equilibria. Primarily, we show that after minor technical
modifications, MCTS based on any (approximately) Hannan consistent selection
function always converges to an (approximate) subgame perfect Nash equilibrium.
Without these modifications, Hannan consistency is not sufficient to ensure
such convergence and the selection function must satisfy additional properties,
which empirically hold for the most common Hannan consistent algorithms.
