Stealth

One possibility might work thus:

Should you run out of Stealth points, you will be noticed. You can lie low for a time to regain Stealth points. However, this not being a videogame, alert guards might not rest easy for hours or even days if they spot a burglar but never catch him, nor see him leave.

Ambushing targets while in Stealth should work quite differently from sneak attacking in combat. Quite simply, a rogue should be outstanding at this. It should require a great amount of preparation, timing, and even luck, but it should be possible to assassinate targets through superiority of Stealth alone.

Randomness can be injected into this system by making small adjustments to the player's Stealth score without his knowledge. He still knows his own score, but it isn't entirely accurate.