Being new to D&D and planning to do some DM'ing in the near future, I found myself struggling with "Surprise" in combat. To educate myself on this topic, I first want to understand the surprise mechanic rules as written.
Let us consider the following scenario:
4 PCs are attempting to sneak up on 3 monsters who are behind a hedge
PCs have rolled stealth rolls of (21, 13, 9). The last PC is not attempting to be stealthy at all.
Monster passive perceptions are (18,11,15). Only the 15 is actively on guard duty, but the other two are awake and aware.
In the above scenario, how do I determine if the PCs are successfully stealthy and if the surprise mechanic is used?
Good answers will include consideration of stealth, passive perception, whether or not a creature can be surprised at all, the differences between group vs individual stealth, and anything else I may have missed.