Battle of Southern Sweden
18k Swedish v.s. 8k Scottish + 12k Scottish Mercs + 16k English + 14k Danish
18k v.s. 50k = 32/4 = +8
Bonuses: +1 from trenches v.s. -2 from amphibian (only Scots and English, so actually -1.44)
= +5.66 to attackers
Rolls: Defenders 5, attackers 1
RESULT: +1.66 to attackers, attacker victory.
The Swedish retreat from the province.
How was this calculated? Well, the number of troops that can be stationed in a country is 2sqrt(total_development), which is 29k for Sweden, 12k for Scotland, 38k for England, 27k for Denmark, 31k for Austria, and 23k for Brandenburg. A nation can hire as many mercs as its force limit (so a nation that can have 12k regular troops can also have 12k mercenaries).
Size bonus is the actual difference in troops divided by 4k, with other modifiers tossed in. Neither side had a general, so there was no general bonus. Finally, a 1-6 dice is rolled for both sides and that is added to the modifier. In this case, Sweden rolled very well but the other modifiers balanced it heavily.
cnai play as serbia
Serbia does not exist.