I suppose luck Bonus minigames should be kept, the Lottery from MP4, and perhaps the offbeat Battle games that are dependent on luck. (there was one in MP6 or 7, the one where you chose a craft to ride on).
The best luck minigame is probably cardiators... but I'm sure it's going to be awesome if it's a strategy minigame.
Like H-J said, luck minigames is for bonuses only!