If Carl decides to march to Moscow it doesn't matter how bad Russian army is. Distance alone would deteat him.
True.
As much as I'm enjoying the spirited discussion of who would get Poland and how Russia would turn out, I'm wondering if we aren't getting bogged down a little in what's going on in Russia (before the POD) and how this will affect a war with Sweden. Hence I'm positing a new scenario. Basically, we still get a Wettin Poland (for lack of any real better option that everyone can agree on).
August the Strong gets elected king of Poland (like
@Vitruvius pointed out, August basically carried things forward by sheer bravado at his election), but his brother had died leaving an infant son. The regency was supposed to go to August, but on his conversion to Catholicism, it was decided that a Catholic "foreign" regent would hardly act in a Protestant princedom's best interests, and so August was forced to resign the Saxonian regency in favour of his cousin, Johann Adolf I, duke of Saxe-Weißenfels on behalf of the infant prince. However, Johann Adolf dies later that year (1697) and Saxony undergoes a squabble over the regency between Johann Adolf's eldest son (Johann Georg) and his brother (Heinrich of Saxe-Weißenfels-Barby).
This is where it gets interesting. Because Johann Georg of Saxe-Weißenfels himself is underage (briefly) and August the Strong became regent for him as well. Not only this, but Johann Georg of Weißenfels made his duchy an important centre of commerce and the arts in Germany,
plus he was interested in building a fleet (I was unaware that Saxony had sea-access which one would need to build a fleet, but hey, the last king of Württemberg was also ship-crazy so I guess it's not unthinkable).
Heinrich, OTOH, is ruling a county that Johann Adolf regarded as rightfully his (so there's likely to be some bad blood between brothers), and objected to his dad (August of Weißenfels) partitioning his lands among his sons. However, much like his nephew in Weißenfels, Heinrich's rule was known for it's economic and cultural importance for Barby. In addition to this, Heinz was also a soldier of some renown from his time fighting the Turks in Hungary. However, he runs into the same problem as August in that he converted - from Lutheranism to Calvinism in 1688. Which means he might be of the mind that he's the senior Protestant Wettin male but the other male Wettins are saying "no, bub".
Which brings us to the next senior Wettin male - Johann Georg and Heinrich's half brother, Friedrich Erdmann (b.1673). He was a military man and was resident in Dresden from the 1680s, he later became a lieutenant general, so once August gets entangled in this whole war with Sweden thing, I could see Saxony jumping in (if Friedrich Erdmann's regent)
I figure that August being elected means that things are going to go more or less as OTL for most of Europe - for a while at least. Maybe when August the Strong gets deposed in the early 1700s, he heads back to Dresden in the hopes that he can lasso Saxony into helping him get his Polish throne back. The Saxonian estates are probably gonna say "nope" (unless Friedrich Erdmann is regent - and even then, it'd depend on how the young elector feels about his uncle most likely)