The Banach–Mazur game is a well-known and studied 2 player mathematical game, invented by S. Mazur between the world wars. It was the first infinite positional game ever studied and in many ways paved the way to modern research of game theory. About 3 decades later, while studying questions in Diophantine approximation theory, Wolfgang Schmidt invented another game, known thereafter as Schmidt's game, which bears a close resemblance to the Banach–Mazur game. Interestingly enough, consequences of this game are strikingly different than the original Banach–Mazur game. In this talk we shall introduce both games and discuss some current questions pertaining to both games. The talk will be self-contained and no prior familiarity with the games will be assumed.

Pizza will be served.

Alice and Bob playing the game