You're playing rock, paper, scissors.

It's your first throw and your opponent says "I'm going to throw scissors."

You have no history with your opponent, and have no way of knowing whether they're lying or not.

What do you throw, and why?

I see no reason to deviate from the Nash equilibrium at this point. 33% of each until otherwise indicated.

If your opponent says the truth with probability P not 1/3, your opponent will be exploitable. Hence, if he plays GTO, what he says doesnt matter

OP asked me to move it here.

As an overall strategy, I'd have to opt for throwing Rock, Paper, and Scissors each 1/3 of the time at random intervals, until I could spot some kind of pattern for opponent...

The very first throw, hmmm... I'd guess, that if there's even a nickel at stake, I would expect villain to SAY that he's going to throw scissors only to play head games or whatever, moreso than telling the truth. So, I'd expect him to expect me maybe to believe that he's going to throw scissors.
Based on that, he might think that I think he'll throw scissors, so he might think that I'll throw rock, which beats scissors. So then, he might throw paper instead... I'd throw scissors as a first throw. This would undermine him if he's just trying to be tricky by telling me that he'll throw scissors but throws paper instead (thinking I'll throw rock). But if it ends up that he in fact does throw scissors, then I guess we'll tie. However, if he throws rock then I guess I'd lose.

Interesting question, though. I just quickly came up with an answer, so I didn't explore the possibility that there's a definite solution that math will solve.

Scissors.

When he's telling the truth you tie.

When he's lying, then probably he's hoping you'll believe him and throw a rock.

The option that he's lying and hoping you'll level yourself into throwing paper is the least likely.

this should prob be moved again to poker theory or smp

But the opponent, now having read your comment, is most limey the throw paper. Or, having independently decided that your analysis above is the most likely analysis that the average person will make, he determines that he should most likely throw paper.

How could you possibly know that "the option that he's lying and hoping you'll level yourself into throwing paper is the least likely" without performing experiments? Actually, I just thought of some...

We could have people say "I will throw scissors," have them play one round with another person (only once), and see what percentages of people choose what. If there is a significant pattern in either, this may say something about the level the average person is likely to be thinking in, and thus answer the original question. (Having the opponent be a computer (that says "I will throw scissors) and seeing how that changes the outcomes of human responses might also be interesting.)

Actually, I remember hearing about a conceptually similar experiment, except that it was a multiplayer game. I think it was something like everybody chooses a cash amount between $0 and $10 and whoever chooses the lowest amount gets that amount. Anybody know what I'm talking about?

Dynamite

You'd end up with nothing but GTO nerds who'll just say to randomize your throws with equal probability.

I don't know. It's my best educated guess.

If your guess is different that's fine, i won't be offended.

If it's not based on experience or an argument, how is your guess "educated"?

Came here to post this