Poker is an interesting multiplayer game.
The most straight forward would be to simply pick up no limit texas hold'hem (the question is : are the rule too complicated for a google ai challenge ?)
it is probably possible to simplify this game quite a bit while retaining the important characteristics. Simplifying would make the game more unique (and impossible to use already existing heuristics)
Players start with the same number of chips. After a fixed number of turns players are sorted according to the number of chip they possess.