DENMARK
Denmark is one of the most challenging and interesting positions in the game. It has quality troops, starts with a decent navy and colonial prospects, and rich mineral resources. But it is hampered by geography as it is split between Norway and the European mainland. (sample GUI empire file)
The Economy
Denmark has some of the richest mineral resources in the game: two ore and one gold mine in Norway. It also has numerous coordinates with improved sheep breeding, horse breeding, and improved foodstuff, although the latter are vulnerable to attack. There are abundant forest and mountain terrain for lumbercamps and quarries, and several coordinates with large populations for factories, mints and weaving mills. Denmark's capital Trade City, Copenhagen, is located on the mainland and gives it merchant fleet access to Karlskrona and St. Petersburg. Danish baggage trains have a good location for trade in central Europe. Demark starts with a quality position in the Caribbean including the Trade City Martinique, a small fleet, and some troops. It has two islands capable of producing wine, and can immediately compete for unowned islands and mines. A Danish merchant fleet can do very well operating in the Caribbean, selling excess wine and trading at the colonial Trade Cities.
The Army
The size of the initial army of 8 European brigades is below average and like the other empires will form the backbone of the Danish army for first few months. Denmark has good troops, especially cheap Riflemen (EF 8, 120 louisdore) and King's Garde cuirrassiers. Denmark can also add battalions of elite Carabiniers to existing brigades; these unique cavalry do well both as shock troops and skirmishers. The colonial army begins the game in the Caribbean and is available for immediate action.
The Navy
The navy totals 13 warships and 664 cannon, including three Class 4 Cruisers. Like other small nations with some colonial holdings, battle fleet is not large enough to think of challenging the larger colonial powers like Spain or Great Britain, but is sufficient to maintain a presence in India, and to build upon.
Strategy
Mainland Denmark is the nation's breadbasket and economic center, but is vulnerable to attack from Holland, Rhine and Prussia. Denmarks main army lies in Copenhagen, whereas its most dangerous potential enemy shares is the immediate neighbor to Norway. Denmark's relationship with Sweden is critical. A long-term treaty will allow Denmark to hold onto the mainland and concentrate on the Caribbean. Poor, or uncertain, relations with Sweden means Denmark will have to defend Norway - meaning that Copenhagen can only be defended by active diplomacy. A war with evenly matched Sweden would most likely be long and costly, and probably result in the lost of Denmark proper and Copenhagan, espeically if the Garde cavalry is transported to fight the Swedes. The fortress at 34,17 and associated mathematical battles can be used as a key bottleneck to delay early invasions of mainland Denmark, but fortifying this with a garrison can be accomlished only at the expense of defending the mines in Norway. Denmark's relationship with Russia, e.g. a Russia that will invade Sweden, can be key to controlling its fate.
Conclusion
Because it is split between the European mainland and Norway, Denmark is a challenging position to play in Austerlitz. Its relationship with Sweden is key. Denmark needs time to develop its economy and military and has the potential to become a colonial power. Even more so than other Austerlitz positions, skillful diplomacy is required for Denmark to succeed.