The Extraordinary Adventures of Baron Munchausen - the RPG of Drinking, Gambling, and Competitive Lying is back in (virtual) print - as a
The game is incredibly simple, and involves no dice, cards, or other randomizing device, but only your wits and a trusty blade! (Or rock, paper, scissors, if you want to be all safe about it.) You play nobles gathered around a table swapping exaggerated tales of your own devising, with help and bribery from your friends and rivals.
This is a great RPG to play in a public place, preferably a bar or other den of inequity. (I have played it in bars with SCAdians, at Ren Faires with complete strangers, and as a game within a game for a Changeling LARP.)
The winner buys the drinks.
The Auld Grump
*EDIT* The SCAdians and some of the Rennies did solve their conflics with a quick duel or two...
It is the only RPG that I have ever played that actually does have a winner. (I have been that winner more than once, curse the luck - winning can get expensive! While you get to keep the wagers I don't think that they ever covered the tab. (Except at the Changeling LARP - where the drinks were a. free and b. nonalcoholic and the wagers were play money only.) The Changeling LARP was also the only one that didn't have any dueling - the players were more than willing to just share tall tales and complicate each others yarns.