[Myrmornis]

You make your initial guess. What's the probability you're right on your initial guess? 1/3. What's the probability you're wrong? 2/3.

So now, you're presented with your second decision. Do you stick or switch? Well, if you stick, that's going to lead to success if and only if you were right on your first guess. And if you switch, that's going to lead to success if and only if you were wrong on your first guess.

We all agree that you were more likely to be wrong on your first guess. So you should bet on the fact that you were initially wrong. I.e. switch.