FrogReaver
The most respectful and polite poster ever
Why is this necessarily a GM facing problem? You could space this at the system level with a more socially designed stealth system, tested in scenarios that match the intended level of competence. Off the top of my head, reworking Stealth as a fixed value that's spent down to perform actions seems directionally like a good start.
The impact of iterated probability is obviously very real, but that's as much or more an indictment of the system designer than the situation. That, and it's only a problem if the player is expected to resolve most situations by making action declarations that resolve as rolls with some chance of failure every time.
I’d suggest it’s a bigger problem. I mean at some point you get a feel for your DMs style and so in a sense learn this aspect for your given table. But making tactical/strategic decisions before you’ve ’found the pattern’ makes this nearly impossible. In practice this ‘unknown’ means players are much more conservative when trying things that are likely to rely on skill checks than they might otherwise be.
That said it seems like determining the appropriate level of zoom/granularity for a an action declaration in a narrativist game yields similar results.