Mike suggested in another thread using the actual game of poker as a mechanic. I myself have been thinking about this a lot lately.
The way I see it, it would work like this:
Chips = scene framing
Cards = resolution
Each chip colour represents a different thing, (maybe, red is physical force, blue is your contacts, and white is your mental stability; each colour is a different way of overcoming a problem)
Everyone puts in one chip ante at the start of a scene. They then define one fact about the conflict in the scene, based on the colour chip they put in. (red = a potentially violent external problem, blue = a non-violent external problem, white = an internal problem). At the same time, each participant has the option of declaring who's in the scene; their own character, NPCs, whatever. You cannot place another player's character in a scene.

The GM always starts the bidding. Basically, when you throw in chips to bid, you state how the conflict is escalating. The GM has a limitless supply of chips, (in theory).
Each time you throw in a chip(s), (GM or player), you state a fact relating to the colour of the chip.

Other than that, it's standard five-card draw. The final show is the end of the scene. If you lose red chips, you're hurt. If you lost blue chips, you lose contacts (which could very well be friends and loved ones). If you lose white chips, you start getting mental problems.
You know that bit where you draw new cards? (I'm not up on my terminology...) That is always a turn around in the scene, a twist. The last person who called in the first bidding round defines the nature of the twist.
Folding represents getting out a scene without losing anything more.

I intended this for a Burke-esque game.
I imagine Burke as a player with lots of blue chips, (contacts), and quite a few white chips, (patience, mental hardness), but not a lot of red. He plays it safe, folding more often than not; conservative with his chips.

What I like is that you don't have to write anything down; your character is shown by the chips in front of you. At the start of each session, you decide where your character's at, and divide your twenty chips (or whatever) amongst the appropiate colours (each colour is the same bid value).

What I don't like is that only one player can win in a scene. Only one player can overcome their problem; everyone else is going to lose all their chips in the pot.
I guess that's to be expected when you use a game as a narrativist mechanic.
Maybe it'd be better as a gamist mechanic?

Perhaps when a player folds, it doesn't have to mean their character leaves; they can stick around, they just can't influence events.

For instance, in the novel 'Flood', Burke and Flood are in a number of scenes together. However, after a brief bit of arguing at the start, one usually becomes dominant in a scene and leads the events, the other following meekly.

Oh, and when you're out of chips, you're out of the game; prison, death, retirement, citizenship, whatever.