For example, I'm currently watching The Irresponsible Captain Tylor, a satirical anime poking fun at the heroic space-battleship genre, with a lead character who gets by mainly through blind fortune and refusal to acknowledge the seriousness of any situation.
|By the way, this series is legitimately free to watch on youtube.|
Add a trait called Stupid, Stupid Luck. Every session, it begins with a value equal to 10 minus the character's current level. Yes, "stupid" being stated twice is vital to this mechanic. Vital.
In any given situation or encounter, the character may attempt to roll against their Stupid, Stupid Luck by throwing a d20. if the die lands greater than the current value, luck is against them and things get worse (probably in a non-lethal but embarrassing way) but they get to raise the value by 1d3 points.
If the die lands less than or equal to the current value, luck is on their side and things align in their favor, preferably in a way that is non-violent and paradoxically mundane. The dragon that was about to breathe on them develops a distracting case of hiccups, the sprung trap turns out to have been accidentally loaded with harmlessly pleasant lilac powder, the ogre gang boss turns out to be an old football buddy. However, after the success the value of Stupid, Stupid Luck is halved.
In practice this should lead to a progression where the character depending on luck suffers several indignities only to end up on top at the end, smelling of roses ... or lilacs.
Ways to implement this could be as a character class for whom it's their main ability. Call the class, say, the Blessed Idiot using the Cleric's advancement tables. Or as a communal resource the whole party can make use of. For a truly bonkers game, every character could have Stupid, Stupid Luck, possibly even monster's and NPC's.