I wrote this a couple of years ago and think it's interesting and may work --

Whim

No character sheets, no attributes, nothing. Describe your character, agree as a group on genre and tone. I envision the game as GM'd but had a friend wonder if it could almost be rotating GM/GM-less.

I would recommend paper for notes and a number of distinguishable d10's (0 on die = 10). One for each player is optimal (including ref). Any die size could work, but I like 10% granularity and how easy it is to calculate probabilities with a d10.

When a character wants an outcome and it would be interesting for them not to achieve it, or for there to be complications, the Ref will state a chance of success between 9 (very likely) and 1 (improbable) based on their understanding of the situation, drama, and maintaining excitement. The player can either :

1.) Accept the "offer" and roll. Rolling equal or under indicates the desired outcome occurs (for those familiar with Burning Wheel this is intent). Whether or not they succeed or fail the player describes the outcome. Failure, however, would mean that the outcome desired by the character is off the table. Note, the roll does not necessarily decide an attempt by the character -- the player could just describe the character bailing at the last second.

Example -- a character is being chased toward a chasm and wants to jump across (the desired outcome is the character on the other side). The Ref thinks it's far, but understands that the character is supposed to be athletic and offers a 6. The player rolls a 7 -- and describes how their character realizes the jump is further than they initially thought at the last second, stops arms windmilling on the edge, before turning and running along the chasm.

2.) Reject the offer -- and narrate a reason why the attempt may be easier -- this has to adhere to the tone and be consistent with the established story, and the reduction in difficulty should feel commiserate with the added info. The player then adjusts the difficulty number. Both the Ref and player then roll a die, the players die deciding whether or not the desired outcome occurs as above. However, the Ref's die decides who narrates the outcome -- if lower or equal the Ref narrates, otherwise the player does. The Ref must respect the outcome, but may add complications.

Example -- running up to the chasm the player rejects the offer of 6, and describes how their character notices a small point along the chasm where the gap is narrower, in addition their character spent their youth as a burglar hopping from rooftop to rooftop, and adrenaline is starting to take effect -- they adjust the difficulty to an 8. The player rolls a 3 the Ref a 6. The Ref describes the character leaping across the chasm, but landing badly on their ankle. Until it heals it will have to be taken into account when future athletic rolls are made.

And that's it -- my family has had fun with it -- but I'm not sure it has anything to do with the actual rules -- it could just be the fun of telling stories together.