Well, that's not really my goal. I just want things that should be uncertain to be uncertain.
The reaction to the trap really isn't the best one. Again, I'm not talking about all or even most skill checks; I'm talking about ones where a skill is used to determine if a character "knows" something, but where in real life "know" really means "believes". And that there are consequences to being wrong.
But let's still look at the trap thing one more time. So let's say the DM says "click" and the player quickly responds, "I drop prone!"
There are, I think, exactly two possibilities here:
1) The DM has already decided how the trap works, and how the player responds will affect the subsequent die rolls. This is totally fine and fun and I probably wouldn't change this, but I'll point out that the player's choice is effectively completely random (unless he's using 'metagame' familiarity with his DM's habits) and has nothing to do with his character's skill and experience.
2) The DM has not decided what the trap is, and is waiting for the player's roll. If the roll succeeds the DM will say, "It was a scything blade and it passes over you" and the roll fails he will say "A pit trap opens before you even hit the floor. Laterz." In this case I'll point out that the player's decision doesn't actually matter; the only purpose of the mechanic is to draw out narrative. If the player understands the rules he knows that it doesn't matter what he says, just that he has to say something. Which is also perfectly fine.
Other options, such as "make a skill roll to see if it was the right thing to do, and that outcome will affect the saving throw" are really just variants of #2.
When you point out that there's more than one option, you still need to choose whether it's version #1 or #2. If it's #1 then more choices just means more chances the player will make the wrong random choice. If it's #2 then it just means the player has more options to tell a good story, and that none of it affects the outcome.
What I'm looking for is both at once: I want the player to worry about choosing the right option AND I want the probability of that choice being the right one to be linked to the character's skills. With a single die roll, whether the player makes it or the DM does, I believe it's not possible to have both at once. I believe that is only possible by combining one public and one secret roll.
I think you're mistaken in your conclusion.
The resolution isn't binary.
While the characters choice appears random, it's based on the player's judgment of their circumstances and reliance on their experiences. (It helps if the DM keeps the design on theme, so where you're in drow-town, you reasonably can expect poison arrows, etc). But we still have the possibilities for automatic success, automatic failure, and "Idk, let's roll." That 3rd option engages with the character's master-roguery. The declared action, whatever it is, determines what's next. And there is tension there prior to the roll.
Scenario 2 is one I avoid, generally. (Except in DW or AW where "DM invents a consequence" is embedded into the rule of a move). But you're right, outside of that, it's narrative-monkeying.
You want the player to worry about the right choice AND the probability of that choice tied to the character's skills. Isn't it already? That's what the ability modifier, proficiency, and expertise are designed to do - represent improvement or skill that directly impacts their odds of succeeding at something.
What about omitting DCs? Set those secretly, don't say what they are, and a player can feel confident (but not certain) of a high roll. Or set a variable DC by making all checks "opposed" rolls. Even if a character rolls very high, they still need to beat an X factor. ... which ... now I see where your secret failure roll idea comes from.
Hm.
It's not different than an opposed roll, really. It's just a sliding fail% that diminishes as you level. For simplicity, and for satisfaction, I think I would do it as an opposed roll. Mostly bc if I rolled high and you rolled higher, then I just got beat fair and square. But if I rolled high and you rolled the fail die in a way that caused me to fail, I'd feel gypped of success. And on balance, I'd prefer to be beaten fairly than robbed.
-Brad