It's also about trial/error and character knowledge, not about meta-gaming because a person has come across it before in their previous PC adventures.
I think it touches on both. Some characters might simply know how to kill a troll, others might be smart enough to figure it out on the spot. If none of those apply, savvy players will simply "help out" their characters by conjuring up a situation where the monster's weakness becomes apparent (or, more blunt, will just go ahead and burn it). What I mentioned in the last sentence is what I call meta-gaming, as it's about knowing how to play this kind of game. As such, asking the DM whether your character may roll a check to see if his character has heard that a troll is vulnerable to fire and acid is also by that loose definition meta-gaming. But in this case, if you abide by the outcome of the roll, you aren't using your player knowledge to help out your character. Any player could have asked to roll if his character knows about any weaknesses that monster might have.
I think there is a big difference, but maybe I don't understand what you mean by consistently allocating character resources and behaving like your character.
Simple example:
[sblock]Room 1 of the dungeon has the following scrawled on the wall:
"To reach your goal you must pass through the wilderness. Follow the stag."
The walls of Room 3 are covered in different frescoes: a city, a saint, and a forest scene with a stag. The stag is looking at a specific branch. Pushing on the branch opens a secret door.
In one game, the players have to figure out that they have to manipulate the branch.
In another game, the players have to allocate enough character resources to their "Find Secret Doors" or "Understand Clues" skill and roll high enough.
These are fundamentally different choices the players are making. I don't think that you can say that the difference doesn't matter.[/sblock]
Anyway, that should clear up my point of view. I'd be interested in hearing you expand on your point above.
My idea of a P&P RPG is that the players take on the roles of the characters rather than their own.
They do that by coming up with a character concept and making that concept viable within whatever system is played by allocating resources, which might or might not work so well, depending on how well your concept is transferable and how balanced the system is. That's what you do during character creation.
The other part, what you do during actual play, is behaving like the character you have made up would, and maybe gradually evolving as the character grows in experience and power. What I mean by consistent is that you play your character roughly the same way across sessions, and that you continue to use the game resources you gain to simulate your concept within the rules framework.
So, in your riddle example, players with no clue rely on the die roll to see if their characters figure it out (the DM doesn't have to give it all away, he can give clues to the players because come on, riddle solving with a check isn't fun).
Those players who have figured it out by themselves...also rely on the die roll, IF a roll is even called for. If the first player to figure it out plays a sufficiently perceptive character, he cracks the riddle and the story can continue, but if he plays a certified idiot, he has to roll at any rate. Otherwise, where's the balance? I'd dump all mental stats and put the points into strength, because that's where I can't substitute for my character.
I don't know if that's any clearer. One important thing is that I don't think everything should be relegated to rolls. As the DM, you should keep an eye on the ideas put forward by the players. If you believe that those ideas could have come from the respective characters, you allow them, and if there are any other factors that introduce a reasonable chance of failure, you call for a roll.
Because it's the player who is able actually to enjoy playing a game.
I know what you mean, but as you put it's not really an answer, since you can enjoy a game where your choices and ideas
as a player matter, or one where you try slip under the skin of a fictitious character. You are referring to the former.