  We consider a deterministic game with alternate moves and complete
information, of which the issue is always the victory of one of the two
opponents. We assume that this game is the realization of a random model
enjoying some independence properties. We consider algorithms in the spirit of
Monte-Carlo Tree Search, to estimate at best the minimax value of a given
position: it consists in simulating, successively, $n$ well-chosen matches,
starting from this position. We build an algorithm, which is optimal, step by
step, in some sense: once the $n$ first matches are simulated, the algorithm
decides from the statistics furnished by the $n$ first matches (and the a
priori we have on the game) how to simulate the $(n+1)$-th match in such a way
that the increase of information concerning the minimax value of the position
under study is maximal. This algorithm is remarkably quick. We prove that our
step by step optimal algorithm is not globally optimal and that it always
converges in a finite number of steps, even if the a priori we have on the game
is completely irrelevant. We finally test our algorithm, against MCTS, on
Pearl's game and, with a very simple and universal a priori, on the games
Connect Four and some variants. The numerical results are rather disappointing.
We however exhibit some situations in which our algorithm seems efficient.
