Everybody knows how things ended up for Charles XII of Sweden but what realistic options had been available to him?
1. OTL scenario. The results are well-known. To Charles' defense, it must be said that not only him but pretty much nobody (including the Russian side) in 1700 could anticipate a true scope of the Russian military buildup and it was quite reasonable (especially without a well-developed intelligence service) to assume that a single serious defeat would put them out of business for quite a while. His fundamental mistake was in keeping ignoring the seemingly clear symptoms of this buildup and leaving the Baltic provinces practically undefended allowing Peter's armies to devastate their countryside and to take their cities and fortresses one by one.
2. Diplomatic scenario - breaking the coalition. In 1699/early 1700, after finding out about the "Northern Alliance" (officially formed by the late 1699) Charles makes a pact with Peter ceding him Ingria and Karelia (parts that Peter was going to get by Treaty of Preobrazenskoe) in exchange for breaking with Saxony and Denmark. Options: (a) Narva is included and (b) Narva is not included but Peter is allowed to build a port on Ingria's coast. Highly unlikely, based upon what we know about Charles' personality but, if happens, could keep Russia out of war long enough for Charles to deal with Saxony and Denmark (IMO, at that time none of them was considering Russia as a critical military factor). While dealing with Saxony, Charles can compensate himself for a territorial loss by annexing Courland. Objectively speaking, the only place of a non-zero value for Sweden except for Narva, a port through which Russian imports/exports were coming (and Sweden was getting the custom dues).
3. Denmark - Riga - Narva. After kicking Denmark out of war, Charles goes to Riga (much closer than Narva and a much more important port), which is being besieged by the Saxons.
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After siege of Riga is lifted, the Saxons are retreating leaving Courland to Charles (as in OTL). Not sure if an absence of the Russian corps of 10,000 would make Saxon situation much worse: it seems that only 400 Russians had been actively participating in the OTL operation. Remaining Saxon troops (approximately 10,000) are retreating into neutral Prussia (as in OTL). Charles has approximately 14,000 so it is unlikely that he is going to invade Prussia without getting significant reinforcements.
He still has to do something about Narva, which is besieged by the Russians. There are 2 main options: 1st, he goes there with all his force (as he did in OTL before Riga) and 2nd, after finding that Russian performance at the siege is quite pathetic and considering Saxons as the main opponent, he is just sending by the sea reinforcements and supplies to Narva's garrison (as he did try during the 2nd siege) while concentrating on defeating August.
If he considers August as his 1st priority (which was the case in OTL for few next years), then the 2nd option and the following OTL-like chance is more probable. While the entertainment is going on, Charles is probably losing the Baltic provinces (as in OTL).
OTOH, if he gives a priority to protecting his possessions in Livonia and Estonia than he arrives to Narva personally (with how it was going, the siege would either be still dragging on or completely abandoned) and defeats the Russian army (if it is still besieging Narva). Invasion deep into Russian territory with the forces he had was impractical and, anyway, the goal at that point was anything but clear (in OTL he was hoping to regain the lost Baltic territories by defeating Peter in Ukraine, which was a questionable strategy, to put it mildly). Even capture of Pskov and Novgorod did not make too much practical sense because Sweden already owned everything of a value on the Eastern Baltic coast (in OTL Sweden was holding Novgorod during the Time of Troubles but gave it away rather easily: the only economically valuable thing was possession of the coastline).
What's important is to prevent the Russian invasion into the Baltic provinces, so he is strengthening Swedish military presence there (unlike OTL where Schlippenbach was left with a pathetic force) and starts works for upgrading the existing fortifications including Narva (part of its fortifications had been quite old) and Noteburg (which is controlling access to Neva from Ladoga Lake). Perhaps even bothers with creation of a small flotilla on Ladoga and improves rudimentary fortifications of Nyenschantz (site of the future St-Petersburg). Of course, they could be used as the bargaining chip during the eventual peace talks.
This could be a prolonged conflict more or less along the lines of the previous Russian-Swedish wars with a possible (worst case scenario) result of a Swedish loss of Ingria but Estonia and Livonia remaining in the Swedish hands and so are the revenues from the Lithuanian exports. Presumably, soon after Narva Peter was trying to negotiate a peace deal with Charles in 1701 but was ignored. With war going nowhere (unlike OTL where the 1st victories in the Baltic provinces had been achieved in the early 1701), he would probably be tempted to make a peace offer as well and it is up to Charles to accept or decline (I would not completely reject possibility of acceptance).
This of course, leaves August more or less off the hook but he failed in achieving his main goal, conquest of Estonia and Livonia. If Charles is completely ignoring neutrality of the PLC, he can try to take Danzig, which seems to be more practical than chasing Ausgust all over the PLC. Anyway, occupation of Courland already expands the Swedish possessions of the Baltic coast.
Some other options?
1. OTL scenario. The results are well-known. To Charles' defense, it must be said that not only him but pretty much nobody (including the Russian side) in 1700 could anticipate a true scope of the Russian military buildup and it was quite reasonable (especially without a well-developed intelligence service) to assume that a single serious defeat would put them out of business for quite a while. His fundamental mistake was in keeping ignoring the seemingly clear symptoms of this buildup and leaving the Baltic provinces practically undefended allowing Peter's armies to devastate their countryside and to take their cities and fortresses one by one.
2. Diplomatic scenario - breaking the coalition. In 1699/early 1700, after finding out about the "Northern Alliance" (officially formed by the late 1699) Charles makes a pact with Peter ceding him Ingria and Karelia (parts that Peter was going to get by Treaty of Preobrazenskoe) in exchange for breaking with Saxony and Denmark. Options: (a) Narva is included and (b) Narva is not included but Peter is allowed to build a port on Ingria's coast. Highly unlikely, based upon what we know about Charles' personality but, if happens, could keep Russia out of war long enough for Charles to deal with Saxony and Denmark (IMO, at that time none of them was considering Russia as a critical military factor). While dealing with Saxony, Charles can compensate himself for a territorial loss by annexing Courland. Objectively speaking, the only place of a non-zero value for Sweden except for Narva, a port through which Russian imports/exports were coming (and Sweden was getting the custom dues).
3. Denmark - Riga - Narva. After kicking Denmark out of war, Charles goes to Riga (much closer than Narva and a much more important port), which is being besieged by the Saxons.
`
After siege of Riga is lifted, the Saxons are retreating leaving Courland to Charles (as in OTL). Not sure if an absence of the Russian corps of 10,000 would make Saxon situation much worse: it seems that only 400 Russians had been actively participating in the OTL operation. Remaining Saxon troops (approximately 10,000) are retreating into neutral Prussia (as in OTL). Charles has approximately 14,000 so it is unlikely that he is going to invade Prussia without getting significant reinforcements.
He still has to do something about Narva, which is besieged by the Russians. There are 2 main options: 1st, he goes there with all his force (as he did in OTL before Riga) and 2nd, after finding that Russian performance at the siege is quite pathetic and considering Saxons as the main opponent, he is just sending by the sea reinforcements and supplies to Narva's garrison (as he did try during the 2nd siege) while concentrating on defeating August.
If he considers August as his 1st priority (which was the case in OTL for few next years), then the 2nd option and the following OTL-like chance is more probable. While the entertainment is going on, Charles is probably losing the Baltic provinces (as in OTL).
OTOH, if he gives a priority to protecting his possessions in Livonia and Estonia than he arrives to Narva personally (with how it was going, the siege would either be still dragging on or completely abandoned) and defeats the Russian army (if it is still besieging Narva). Invasion deep into Russian territory with the forces he had was impractical and, anyway, the goal at that point was anything but clear (in OTL he was hoping to regain the lost Baltic territories by defeating Peter in Ukraine, which was a questionable strategy, to put it mildly). Even capture of Pskov and Novgorod did not make too much practical sense because Sweden already owned everything of a value on the Eastern Baltic coast (in OTL Sweden was holding Novgorod during the Time of Troubles but gave it away rather easily: the only economically valuable thing was possession of the coastline).
What's important is to prevent the Russian invasion into the Baltic provinces, so he is strengthening Swedish military presence there (unlike OTL where Schlippenbach was left with a pathetic force) and starts works for upgrading the existing fortifications including Narva (part of its fortifications had been quite old) and Noteburg (which is controlling access to Neva from Ladoga Lake). Perhaps even bothers with creation of a small flotilla on Ladoga and improves rudimentary fortifications of Nyenschantz (site of the future St-Petersburg). Of course, they could be used as the bargaining chip during the eventual peace talks.
This could be a prolonged conflict more or less along the lines of the previous Russian-Swedish wars with a possible (worst case scenario) result of a Swedish loss of Ingria but Estonia and Livonia remaining in the Swedish hands and so are the revenues from the Lithuanian exports. Presumably, soon after Narva Peter was trying to negotiate a peace deal with Charles in 1701 but was ignored. With war going nowhere (unlike OTL where the 1st victories in the Baltic provinces had been achieved in the early 1701), he would probably be tempted to make a peace offer as well and it is up to Charles to accept or decline (I would not completely reject possibility of acceptance).
This of course, leaves August more or less off the hook but he failed in achieving his main goal, conquest of Estonia and Livonia. If Charles is completely ignoring neutrality of the PLC, he can try to take Danzig, which seems to be more practical than chasing Ausgust all over the PLC. Anyway, occupation of Courland already expands the Swedish possessions of the Baltic coast.
Some other options?