I think the metagaming problem with rolling for stealth is fairly well-known: once the player rolls for stealth at the start of their sneaking, they know how high they rolled and might, consciously or not, adjust their later course of action based on their knowledge of the stealth roll. There are various ways to partially mitigate this, such as delaying the stealth roll until the first time it is needed. However, I wonder whether it is possible to implement a way to resolve "rolling stealth vs. passive perception" situations without the player ever rolling any dice, while at the same time being mathematically equivalent (thus preserving game balance). Conceptually, it seems like one could define a "passive stealth" and then have enemies roll perception against that. However, the naive implementation of this changes the math. For example, if you have one rogue trying to sneak past 3 guards, the conventional way would have the rogue roll once against 3 passive perception scores, while the "passive stealth" approach would have three perception rolls, which obviously changes the probability of at least one guard noticing the rogue. And you also have things like advantage/disadvantage and Reliable Talent that can affect the stealth roll, which would need to be handled somehow.
So, to bring it all together with a single example, suppose we have a rogue with +8 to stealth and Reliable Talent trying to sneak past 3 elite guards who all have a +10 to perception (i.e. 20 passive perception), and furthermore the rogue has disadvantage on their stealth check because they're trying to sneak out while carrying the prized Bell of Loud Tolling that they've just stolen. Is it possible to resolve this by having the DM roll for the guards' perception instead of the player rolling for stealth, while at the same time giving the same probabilities of success and failure as if the player was rolling against the guards' passive perception?
- I know it's rare in practice for guards to have a higher perception modifier than the rogue's stealth modifier, but if I don't set it up this way then Reliable Talent gives the rogue a 100% chance of success, and that would defeat the point of asking about probabilities.
- I realize that having the DM roll the PC's stealth check in secret is one possible solution, but it would be preferable to have an equivalent solution in which the DM only rolls for NPCs. I've suggested the start of the obvious solution, in which one simply swaps the passive and "active" sides of a contested check, but I've also pointed out that this alone isn't a full solution. If you have another way of resolving things that achieves the stated objectives (i.e. DM rolls for NPCs instead of player rolling for PC, while preserving original success probabilities), feel free to suggest it.