What if Sigismund III intervened in the Thirty Years War?

The Thirty Years War was a war between the Protestant and Catholic states of the Holy Roman Empire. The Polish Lithuanian Commonwealth, being a majority Catholic country, threw it's support behind Holy Roman Emperor Ferdinand II. But Sigismund III wanted to go one step further. He wanted to outright participate in the war.

The PLC's intervention in the war would've taken the form of an invasion and, possibly, an occupation of Transylvania. At the time, Transylvania belonged to the Princes of the Protestant Houses of Bethlen and Rakcozy, who were allied to the Ottoman Empire, who supported the Protestants against the Hapsburgs.

The Sejm refused to support any intervention in the Thirty Years War. They refused to supply the PLC's military for the effort and they even refused to give subsidies to the then-ongoing war with Sweden. Sigismund III eventually realized that intervention in the Thirty Years War would only be extremely detrimental to the PLC's power and stability in the region.

But what if the Sejm was willing to back Sigismund III in invading Transylvania? How would this have impacted the Thirty Years War? How would this have impacted the Polish-Lithuanian Commonwealth?
 
Depending on when they intervene. If the intervention is in 1618, then the Ottomans are just in a succession crisis making an immediate response harder. If it is after 1622, the situation is worse for the Ottomans. Although if Sigismund III invades Transylvania then Osman II has the chance to send the Janissaries away to fight in Transylvania. He avoids the Janissary revolt as wel as Abbas of Persia declaring war again. He might as well create a new force with the absence of the Janissaries.

Ottoman intervention is really likely in the war. And not just OTL version, a more active version. For the better for Swedish intervention in the North.
 
The Thirty Years War was a war between the Protestant and Catholic states of the Holy Roman Empire. The Polish Lithuanian Commonwealth, being a majority Catholic country, threw it's support behind Holy Roman Emperor Ferdinand II. But Sigismund III wanted to go one step further. He wanted to outright participate in the war.

The PLC's intervention in the war would've taken the form of an invasion and, possibly, an occupation of Transylvania. At the time, Transylvania belonged to the Princes of the Protestant Houses of Bethlen and Rakcozy, who were allied to the Ottoman Empire, who supported the Protestants against the Hapsburgs.

The Sejm refused to support any intervention in the Thirty Years War. They refused to supply the PLC's military for the effort and they even refused to give subsidies to the then-ongoing war with Sweden. Sigismund III eventually realized that intervention in the Thirty Years War would only be extremely detrimental to the PLC's power and stability in the region.

But what if the Sejm was willing to back Sigismund III in invading Transylvania? How would this have impacted the Thirty Years War? How would this have impacted the Polish-Lithuanian Commonwealth?

Taking into an account that Transilvania played a noticeable role only on the very first stage of war, the impact of such invasion would be minimal. Not that it would make too much sense from the PLC perspective because from 1617 and till 1629 it was, with the short interruptions, at war with Sweden (in which PLC lost Livonia) plus between 1605 and 1618 and in 1632 - 34 it was at war with Moscow and in 1620 - 21 with the Ottomans. A rather busy schedule for a country without a permanent army.
 
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