As for suggesting actual board/card games, how about Citadels?
http://boardgamegeek.com/boardgame/478/citadels
There is certainly a factor of randomness (it's a card game, after all), but that is mitigated well enough by the bluffing aspect of the game. Turns are generally short and are not determined by where you are sitting; they are determined by what card you choose at the beginning of each round.
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"Filthy lawbreaker, unhand that vending machine!" - Casey Jones