Two topological games are strategically dual provided that either player has a winning strategy in the first game if and only if the other player has a winning strategy in the second game. With \(\mathcal{O}\) the collection of open covers of a space \(X\) and \(\mathcal{O}^{\text{gp}}\) the collection of groupable open covers it is shown that the games \(\mathcal{O}^{\text{gp}}\)-\(PO(X)\) and \(G_1(\mathcal{O},\mathcal{O}^{\text{gp}})\) are strategically dual, where \(\mathcal{O}^{\text{gp}}\)-\(PO(X)\) is the game played according to the following rules: for each \(n\in\omega\) the first player picks \(x_n\in X\) then the second chooses open \(U_n\subset X\) with \(x_n\in U_n\), and the first player wins if \(\{U_n\mid n\in\omega\}\) is a groupable cover, otherwise the second player wins. Other results relating winning strategies for games are presented as well as preservation of winning strategies when a game played on a particular space is transferred by a continuous function to the same game played on the image space.