"The recent extensions of the European Union brought a priori measures of voting power (power measures or power indices) in the spotlight. Originating from game theory these measures serve as indicators of the voting powers of players in a given voting situation. However, a priori measures of voting power are no more than statistical expectations of power as a result of random voting and therefore power indices lack the game theoretical features attributed to them. We rebuild these game theoretical foundations by introducing strategic power indices: we expand the model by allowing players to reject particular coalitions and thereby possibly increase their power. We characterise strategic power indices and apply them to real-life voting situations, such as the European Union’s Council of Ministers. We discuss implications to values, in particular the Shapley value. Further, we extend these models to farsighted players, players with preferences, such as for games on convex geometries and for games on networks. We also consider a modification of strategic power indices where players can renegotiate blocked coalitions and in these negotiations different credits can be given to critical/pivotal players in the same coalition. Finally, we develop a model to calculate the “true” power of a winning coalition in a parliamentary voting situation, where the power of a particular coalition belongs to the interval [0,1] to reflect the margin by which it is winning/losing."