From the 10,000 word post:
"Complete information can be defined within the game format as all the information that is necessary for a player to make an informed decision ... with the understanding that if harm arises from that decision, it is not because the DM failed to tell the player something the player would certainly know about in that moment."
I recently had a situation come up in which the online party decided to storm the front gates of a castle, in order to stop the lord of that castle from continuing an evil ritual within its walls. The party comprised of a 4th level, a 3rd level and two 1st levels. To obtain control over the castle gates, they had to overcome 12 guards.
How much information was necessary in this circumstance? To begin with, the players are entitled to what they can see, hear, smell and so on - in effect, what their five senses tell them. Said information would be the location of the guards, their general equipment and the kind of activity in which they are employed: where they are, what they have, what they're doing.
The players have, presumably, learned something about what the guards are protecting. And the players may have access to information gained through magical means.
What the players are not entitled to includes what the guards are thinking; nor does it include anything about their motivation, nor does it include anything about how strong or dextrous the guards are, or how many hit points they have, etc.
It was suggested to me (abusively) that as a DM I was duty-bound to provide clues to the strength of the guards. Certainly, if any of these guards is of high level, he or she should be in plate mail. They should carry ornately carved weapons. They should be tough-looking and huge.
Be careful of these kind of tropes. They exist throughout prefabricated RPG literature, and represent two-dimensionalism in writing and game design. There are reasons not to wear plate mail, like mobility and speed; the guard may be multi-classed; the guard may have a temporary skin disease which precludes the wearing of plate. The guard may simply not like plate metal.
Not all persons of strength and power wish to draw attention to themselves with outward expressions of wealth and status, such as carrying weapons of a fabulous nature, or bedecking themselves with jewels, or wearing expensive clothes while carrying forward ordinary mundane duties. Many party players keep the same weapons level after level; some players develop an sentimental affection for the sword they carried through this campaign or which they used to slaughter such-and-such a monster. Nor are all magical weapons necessarily remarkable to look at; there are benefits to having a +4 sword that looks ordinary, with a worn handle.
Not every "tough-looking" soldier is high level; some are simply soldiers who have eaten a lot of poor grub and lived a long twenty years in the service of their lord. Virtually every guardsman is tough-looking. And why should a guard necessarily be "huge"? History isn't filled with short, wiry men who could kick your ass from here to Mars if they wanted?
Players are going to try and trap you into giving them more information than they are entitled to have - through tropes like these, or with questions to which they could not possibly know the answer. Few are the nights where I run a campaign where a player does not ask me something like, "What is the guard want?" As a dungeon master, you're not responsible for conveying what the guard wants; the players are only entitled to what the guard says. The guard's motivations, or background, or hit points or level are not things the players are able to glean with the use of their senses, SO DON'T TELL THEM.
Remember that momentum is always the child of tension, and that tension is always created by what the party does not know. Of course the party will want to know these things; knowledge is power, and the more power the party has, the safer they are. The less they know, on the other hand, the less power they have, and the less they feel safe. Not feeling safe creates a strong, ambiguous feeling in the gut that makes the body uncomfortable and the player anxious. Do not let your party get comfortable. Comfort murders momentum. Terror provides it.
Remember also that the party will learn all they need to know in due time. They will eventually, through fighting the 7th level fighter, that the fighter is 7th level. True, it may be too late for them. It may result in their deaths. But that will only instigate in your player's mind a layer of terror that will be there for you to exploit once they've rolled up a new character and are set to tackle the next instance.
Finally, remember that none of this begins the subject of disinformation, in which what the player's senses betray the player into thinking they are getting information they're actually not getting. Disinformation is a nasty part of the game, and is sure to make your players upset, distrustful, addled and prone to overreaction and extreme cautiousness.
Ain't it fun?