Bernadotte stays loyal to Napoloen

IMO Sweden can bring little strength to France's side. The last war (against Russia) was lost and no on will pay war subsidies.

If the Swedish estates accept going to war against all French allies, expect to lose Sweden some and gain nothing. IOW, Hither Pomerania goes to Prussia without compensation, Russia might try to gain the island Gotland and Denmark surely will not lose Norway (that alone is a biggie).
When the dust settles, Bernadotte will be deposed (and perhaps shot). No idea who the next king of Sweden might be, but the Congress of Vienna will find someone unexpected. Perhaps some Lutheran prince the bigger fish in the German pond will want to remove - the Duke of Oldenburg or the Duke of Mechlenburg-Schwerin or ...
 
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