Abstract: We model two-player imperfect-information games evolving in time, where one player makes and tests "hypotheses" about the opponent's strategies. We consider algorithms needed for the first player to compute a winning strategy. The main assumptions about the scenario are the following: (1) the hypotheses form a "covering", i.e., each
strategy of the second player satisfies at least one hypothesis; (2) the hypotheses can be enumerated and tested; (3) for each hypothesis, the first player has a strategy that "defeats" all of the opponent's strategies satisfying this hypothesis.

We show, both in "paper-and-pencil" style and using Isabelle/HOL, that under the aforementioned conditions, the first player will win the game.