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the court houses are all based on faction. there's court of blades, coin, and truth. faction with these houses can be earned either by doing the entry quests in sinking sands (the tents near the docks) or by killing the guards in majdul, collecting coins and turning them into the guys in the tower of the moon.
for instance if you want to build faction with court of truth, you'll do the quests for court of truth, or you can kill the blades or coin guards and hand those tokens into the truth guy in the tower of moon.
some side notes on this <may have changed, someone please double check me> the quest guys run on a timer, an hour between quests i think, and each quest line will give you positive faction for one with negative faction for another. so be careful not to do a quest of a different faction after you start the faction you want. also when killing the guards in majdul, be careful the palace guards dont see you. dont remember the names, but they fly around on carpets, and if they see fighting they will kill you. usually you spot a warning when they are in the area, but i found a few times i never noticed until after i was lying in a mangled heap wondering why i was dead, and realised that i missed the message, hehe. also if you have money to burn and dont want to bother with the guard killing, there are usually plenty of tokens for each faction available on the broker. whether bought or looted, the tokens were the fastest for me to get my faction. hope this helps :)