Both the Player’s Handbook and Dungeon Masters Guide make reference to a condition known as complete surprise. Unfortunately, to my knowledge, it isn’t explained. Let’s look at examples. On page 168 of the DMG under crossbow of speed:
In surprise situations it is of no help, but on complete surprise situations the held crossbow will enable its user to fire in the 2nd segment portion.
So what the heck does complete surprise mean? Could it be that regular surprise is a result of 1 on 1d6, whereas complete surprise is a result of 2?
To make things even more confusing, however, take a look at page 23 of Dungeon Module G1-2-3 Against the Giants. When describing wererats encountered in the secret room on level 2:
They always attack either by surprise (1-3) or complete surprise (4-6).
So is complete surprise is actually anything more than 3 segments? Page 51 of the PHB, in the description of the 6th level cleric spell, aerial servant:
The aerial servant will always attack by complete surprise when sent on a mission, and gain the benefit of 4 free melee rounds unless the creature is able to detect invisible objects, in which case a six-sided die is rolled, and 1 = 1 free round, 2 = 2 free rounds, 3 = 3 free rounds, 4 = 4 free rounds, and 5 or 6 = 0 free rounds (the opponent is not surprised at all).
The only reasonable conclusion, I believe, is that 4+ is complete surprise. As a side note, on page 6 of OD&D’s Eldritch Wizardry supplement:
*Complete surprise is basically a die of 2 when checking