 Simply put, a strategy for player \(\mathbf{X}\) in a dialogical game is a complete conditional plan of action. It is conditional in the sense that the strategy informs how \(\mathbf{X}\) plays depending on the moves of the adversary. It is complete in the sense that it must inform how \(\mathbf{X}\) plays for every possible choice of move by the adversary. Given a formula \(\varphi\), a strategy for \(\mathbf{X}\) in the game for \(\varphi\) can be described as a function that assigns an \(\mathbf{X}\)-move \(M\) to every non-terminal play \(\Delta\) ending with a \(\mathbf{Y}\)-move such that extending \(\Delta\) with \(M\) results in a play for \(\varphi\). Such a strategy is winning if all terminal plays resulting from it are \(\mathbf{X}\)-terminal (i.e., won by \(\mathbf{X}\)). In other words, a winning strategy for a player is a complete conditional plan of action leading to the player’s victory no matter how the adversary plays.