With just 4 active games, I find that I spend most of my time on Storium trying to figure out where I should play, rather than actually playing.

It'd be great if rather than simply grouping games by "you're the narrator" or "you're a player in" on the homepage, if the homepage list of games were prioritized by how much they need your attention.

For instance:
A game in which you've had the last move would go to the bottom of the list.
A game where you're the narrator and all the challenges have been completed would move towards the top.
A game where you have a revision pending would move towards the top.
A game where you haven't posted a move would move up in proportion to how long since you've moved.

Those are all suggestions based on where I'd personally like to see pressure applied. But the actual presentation would do a lot to drive activity in a particular way, and really constitutes game design.