Complete Surprise* is both a term and a concept in OD&D.
As a term, it first appears in the 1976 Supplement (III), Eldritch Wizardry. Page 6 tells us "Complete surprise is basically a die of 2 when checking. Surprise is basically a die 1 when checking, or a die 2 in those cases where the creature in question is difficult to surprise and has only a 1 in 6 chance of being surprised." This note occurs at the bottom of the new and highly complex round segment table, and includes the additional information that complete surprise results in an initiative benefit in that system.
Oddly enough, the term "Complete Surprise" made its way into AD&D too, again without explanation. It is mentioned in the description of the 4th level Illusionist spell Phantasmal Killer and again in description of the Crossbow of Speed. The most prominent mention however is in the description of the Catoblepas in the (1977) Monster Manual. Herein we are told only, "Complete surprise (a 2 on a six sided die) means one of the party encountering the monster has met its gaze," p13. The gaze of a Catoblepas is a death ray.
What all these mentions lack in detail they at least make up in consistency. When a 2 is rolled on a surprise check it indicates a condition of Complete Surprise, resulting in the greatest disadvantage including, in the case of the Catoblepas at least, being subject to an immediate attack.
Now you are probably already thinking that what we have learned about the term Complete Surprise sounds suspiciously similar to the concept discussed in my last post, wherein the distance of 10 to 20 feet was shown to be the immediate strike zone.
Now, the savy reader will be thinking:
"Hold on, surprise distance is 1"-3" by the book, so that's 1d3 right? That's quite seperate from rolling a 2 on a d6 for Surprise"
So lets think about that. Nowhere in the 3lbb's are we actually told to roll a separate die for the surprise distance. I think it is a common and reasonable assumption to do so, but it is not a specific instruction. Consider that it doesn't particularly make sense when dealing with a group, to specify a position of exactly 10, 20, or 30 feet. If there are 5 of you, let's say, who exactly is standing at the 20 foot mark, for example. Is it the person in the lead; in the middle, or what? And what if there is just one of you - like the lone Hero in the Strategic Review example, and your 1d3 die roll determines he is at exactly the 20 foot mark. Is he in or out of the immediate 10-20 foot strike zone?
It does make perfect sense however to say the surprised person(s) is/are either between 20 to 30 feet or between 10 and 20 feet, and for that you only need two numbers, a 1 or a 2.
There is no reason whatever to be more specific than that in OD&D combat. Following CHAINMAIL and the D&D FAQ,each man sized character controls a 10 foot area for combat purposes, so being within 20 feet of each other is the same thing as being right next to each other as far as the game mechanics are concerned.
So here is what I'm saying: a roll for surprise resulting in a 1 or 2 already tells you encounter distance and no additional distance roll is needed. A result of 1 equals a distance of between 20 to 30 feet; a result of 2 indicates Complete Surprise and is at a distance of 10 to 20 feet, where one is at the most disadvantage.
I know this all sounds rather nice and neat, but the skeptics will say I'm back engineering stuff into the 3lbb's that isn't there. I agree, the term complete surprise is never used, nor is it specified in a rule that a 1 or 2 on a surprise die gives you different surprise distances. However, we do see something just like this practiced in the example of surprise given on p 9 of U&WA:
"a Wyvern surprises a party of four characters when they round a corner into a large open area. It attacks as it is within striking distance as indicated by the surprise distance determination which was a 2, indicating distance between them was but 10 feet."
Note that that the "surprise distance determination" was a 2. If surprise were determined by some kind of 1d3 roll, then a result of 2 would surely equal 20 feet, instead we are told a result of 2 "was but 10 feet". It is perfectly possible to consider 1,2 as 10 feet, 3,4 as 20 feet and 5.6 as 30 feet, but it is equally possible to simply read the "2" as being the result of the surprise roll. I don't claim to know exactly which reading was intended here.
*Special thanks to Stormcrow for pointing out the term and discovering the EW & AD&D references.