Why did Frederick William later change sides from Sweden to Poland and the Habsburg emperor?

Frederick William’s decision to shift his allegiance from Sweden to Poland and the Habsburg emperor during the First Northern War was primarily driven by strategic pragmatism and the pursuit of sovereignty for his territories.1

Initially, Frederick William had been forced to accept Swedish suzerainty and provide military support to King Charles X Gustav of Sweden after Swedish forces overran Poland and threatened East Prussia. However, as Sweden’s military position began to deteriorate, the Elector sought to secure his own long-term interests.1

By negotiating with Poland, he aimed to gain full sovereignty over the Duchy of Prussia, which had previously been held as a Polish fief. Through the Treaty of Wehlau in 1657, he successfully secured this recognition from the Polish king, John Casimir, in exchange for military support against Sweden. This shift allowed him to align with Poland and the Habsburg emperor to drive Swedish forces from western Pomerania. Ultimately, this maneuver, later confirmed by the Treaty of Oliva, solidified his status as a sovereign ruler rather than a vassal.12