What was Denmark hoping to get out of the war anyway? I'm always a bit puzzled, because the 17th century strikes me as very much a history of Sweden trying to expand.
I honestly don't get, what he was after.
But it's important to remember that Denmark had never been stronger than it was between 1611-1625, the army and navy was strong, the royal coffer full, the entire country thrieved, and it had humiliated Sweden in 1611. The problem was that Denmark had structural problems, the coffin was full because a Swedish ransom for getting Elfborg (Göteborg) back, the army strength build on small elite corps of mercenaries and the royal prestige, the country thrieved because of the collapse of German exports and their need for imports. The navy was the only thing which wasn't build on a weak fundament. But these things are easy to see today, in the day Denmark looked like a major deal, while Sweden didn't.
So he may very well have thought he was able to beat the emperor and set himself up as defender of Protestantism and overlord of the German protestants. If he had succes he could very well have been able become heritable Oberst (colonel) of Lower Saxon Circle, which would have good chance to extent his possesions in Germany.
Faeelin
Denmark was in a similar position at the time, both in terms of rivarly with Sweden and looking to expand. Also Christian sought to make himself into a leader of the Protestant powers in response to the counter attack the Hapsburg's were involved in at the time. With Sweden still involved in war in the Baltic Denmark had a relatively free hand to make gains.
The thing is Denmark had Christian, who I think turned into a bit of a drunkard after Lutter destroyed his army and Sweden had Gustav Adolphus.
Steve
He was always a drunk, through he was also a workaholic, the war just turned him into a mean drunk.
But it's important to remember that Danish prestige before the 30YW was much greater, Denmark was richer, had a greater population, a bigger army, it had more or less forced concessions out of Sweden in every war since the Swedish independence. But after the Swedish defeat in the Kalmar War, Sweden had reformed their army, while the Danish army still was based on the traditional mercenary pattern and a native office corps of nobles, Sweden adopted limited conscription and a office corps based on both burghers and knights, which forced them to create a standardlised officer training, while Denmark office corps was ad hoc trained.