Discuss with Other Hangover Victims (World of Warcraft, any MMORPG)
A hangover day is better suited for “trash-talking” than almost any other. Creative language is stimulated, the inhibitions are lowered, and everything seems a bit funnier. The best time to create quirky conversations with others.
In MMORPGs like World of Warcraft, you usually have public or private chats available in which you can globally communicate with others. The probability on January 1st is high that others share your condition here.
So just head to the nearest city and start philosophical discussions about everything. Hangover philosophy is sometimes the best philosophy. And it also brings a few laughs.
Just be careful not to become offensive. A hangover is no excuse for insults, and nobody wants to get kicked from the chat.

