@goodguy5 @SirCinnamon @DavidCoffron
well, it having a first turn, even if it must do nothing on it because of the "Surprised" condition that goes away at the end of a creature's turn, means it still took that turn. Thus rolling a higher initiative than the assassin rogue means the assassin rouge doesn't get advantage, nor do they auto-crit. And rolling lower means you get one chance advantage and autocrit
Having a surprise round means the assassin rogue always gets the advantage and autocrit, and then again if they have a higher initiative.