One of the last mini-games I posted about was for shopping. And, in play, it didn't work that well, most of what it did was make what you wanted to buy harder to get- it wasn't available or the wrong size, or too expensive. It wasn't fun. (I have a different solution I'm fleshing out). But what surprised me in looking back at that post was how I had players choose which dice to apply to which column. I had no recollection of using that mechanic whatsoever. And looking at it now, that seems like the coolest part of that whole idea.
What other uses could we have for a roll all the dice table which let players choose which dice should apply to which column? I'm at work, a bit under-caffienated, but it seems like the general principles are: higher is better, but smaller columns are less important. So, for example if you roll a "1" on your d20 you really want to sacrifice a result lower on the table to bump up that d20 column's result, like moving a "6" on you d6 column up and taking the "1" on the d6 column.
So, one idea that springs to mind is a wild magic mini-game. It would be just a matter of fleshing out the columns. I'm thinking of something along these lines, though that was more designed for completely random effects. Players would want to have a bit more control over being able to cause damage in combat etc.
What other possibles uses? Maybe monster breeding where you select for traits. Maybe an abstracted NPC conversation mini-game where it lets you choose what you learn from them and what you have to reveal in turn. Maybe potion making where you are trying to get the best balance of ingredients that have side effects.