 Being identified with its extensive form, a strategy for player \(\mathbf{X}\) in \(\mathcal{D}(\varphi)\) is the fragment \(S_{x}\) of \(\mathfrak{E}_{\varphi}\) such that each path in \(S_{x}\) represents a play resulting from the \(\mathbf{X}\) strategy. In other words: (i) for every node \(t\) in \(\mathfrak{E}_{\varphi}\) labelled with an \(\mathbf{X}\) move, every successor of \(t\) in \(\mathfrak{E}_{\varphi}\) appears in \(S_{x}\) whenever \(t\) is in \(S_{x}\); and (ii) for every node \(t\) in \(\mathfrak{E}_{\varphi}\) labelled with a \(\mathbf{Y}\) move, if there is at least a successor for \(t\) in \(\mathfrak{E}_{\varphi}\) then there is a unique \(t'\) labelled with an \(\mathbf{X}\) move such that \(t'\) is the successor of \(t\) in \(S_{x}\) and \(t'\) is the move prescribed by the strategy. Thus, in an \(\mathbf{X}\) strategy the ramifications corresponding to \(\mathbf{X}\) having multiple choices are not kept (since a given strategy selects one \(\mathbf{X}\) move) but the ones corresponding to \(\mathbf{Y}\)’s choices are kept (since the strategy must consider all possible moves of \(\mathbf{Y}\)).