“Surprise” or “Surprise!!!”
So surprise rounds. Do I use them often? Usually not.
A lot of the time, it just doesn’t make sense.
In D&D, players are on alert in a dungeon or the wilderness, they won’t be surprised to find enemies behind a door or over the next ridge. They might be surprised at what the enemies are, but that’s a whole other idea.
I do however like to reward players if they use good planning, or can maintain stealth to sneak up on an enemy, however I don’t like to go too overboard.
Sometimes, I just let everyone roll and insert the monster after everyone, sometimes I’ll deduct an amount from the enemy initiative.
I generally just throw an advantage on the scene with FATE. That’s just easier and I don’t have to think about it.
It’s also great for using against players when you do manage to get the drop on them, and everyone has fun with it in my experience.
I’ve debated throwing this rule across to D&D, and just giving the players advantage on their first round, but I haven’t tried it yet.
In Legend of the Five Rings, I’ll give a free boost on Iajutsu, or let players use Kenjutsu or Kyujutsu in it’s place. Stealth has never been a big part of L5R games for me.
Lastly in World of Darkness games, I guess I just give a free action. Honestly, it’s been so long since I’ve thought about it, I’ve no idea.
All of the above might be actual rules, or completely against them, or may have changed with editions of rules I haven’t played yet. Who knows?