Context is your friend. Here it is again for you.
"One final note: as valuable as this volume is with its wealth of information, some DMs may wisely wish to forbid their players from referring to the MANUAL in the midst of an encounter, since it will be considerably more challenging to confront a monster without an instant rundown of its strengths and weaknesses - and besides, a D & D player’s true mettle (and knowledge) will be put to the test. And as even the most casual D & D player knows, that’s what this fascinating game is all about. . ."
I mean, he is literally saying that keeping the numbers from the players during the encounter makes the game more challenging right before he says that the game is about challenge.
He
literally says that not letting the players look up the book makes the game more challenging. He then comments that not letting them look up the book will put their knowledge to the test. What knowledge is he referring to? To me, those most natural reading is
their knowledge of the contents of book.
This advice seems to me to date from a period where
memorising the Monster Manual, and more generally
remembering monster stats and attributes was part of the environment of skilled play. It's a particular application of a wargame ethos.
There is no implication in what Gygax says that players should be inferring their to hit numbers from the GM's description, or via inference from what rolls by what players for what PCs do and don't miss. There is no implication in what Gygax says that it is
unrealistic for the players to know numerical information about AC, hp etc. In fact the game seems to me to take for granted that players will think in such terms: various armour types are rated by
class, and then other modifications (for DEX, magic etc) are applied to generate equivalent degrees of protection even when a creature/NPC is not wearing armour of that precise class. Spells like Bless and Shield have their effects expressed in related numerical terms. Players are encouraged to think of the risk posed by monsters in terms of their Hit Dice, which are a numerical marker of both their durability, and the threat they pose, in combat. When it comes to rangers' tracking and thieves' special abilities, these are directly expressed to players in terms of % chances of success.
Applying Gygax's model to
@hawkeyefan's examples, the GM would tell the players "You see a troll" or perhaps "You see a nine-and-a-half foot tall, rather gaunt, moss-green humanoid, with long claws and fangs". The players then discuss among themselves: What's its AC? Does anyone remember its immunities? Etc. And the brains trust would put together, via their recall, that it is more than 6 HD, is AC 4, and regenerates unless burned by fire or acid. They might also remembers that it deals rather punishing damage in melee (an average of 20 hp per round, multiplied by the to-hit chance).
And suppose that the players are correct in their recollection. The Gygaxian referee has no reason not to congratulate them on their knowledge. Or suppose that they mis-remember - they recall AC 5, for instance. Well, when they roll a hit against AC 5 and say to the GM, "I reckon I've hit it" nothing stops the Gygaxian referee replying with a taunt - "You memory is off today. It's AC 4!"
This is all about wargaming skill, where memorising opponent stats (eg how many hits does it take to destroy such-and-such a tank?) is part of the skill. It has nothing to do with
realism, or
immersion.
I was talking to
@pemerton who tried to use the game's wargaming roots as the reason to hand out the numbers.
And here is what I actually posted:
Gygax's approach to D&D was a wargame approach, in which some information (from the fiction) that is obvious to the characters (eg how is this mercenary equipped?) is numerically represented in ways that the players are expected to be familiar with - eg a sword does d8 damage, a hauberk is AC 5, etc. Whereas some other information is hidden, and part of the point of play is to try and learn it.
There is no principle in Gygax's work that I am familiar with which states that it is important that the GM not tell the players any stats, because this is not the players' role.
So not only are you,
@Maxperson, wrong about what Gygax
literally said, you are also wrong about what I "tried to" do.