OK, smarty-pants, what's the best move?

[boost]

Depends on whether or not an empty box or goat behind a door or whatever MUST be revealed (as in the classic Monty Hall problem), or it just so happens to be. This is a crucial detail that is often missed by people who know the solution to the MH problem but who don't truly understand it.

I'm not sure I follow. Of course he could reveal the prize, but then of course you'd change your pick, so long as you were allowed to still pick the prize.

[Lukie]

I'm not sure I follow. Of course he could reveal the prize, but then of course you'd change your pick, so long as you were allowed to still pick the prize.

Right. That's the whole point.

I don't watch any game shows anymore but we have all seen enough over the years. There are some really weird ones out there. Spin this, win this, choices, non-choices, call a friend, poll the audience, etc. Like at the end of wheel of fortune you pick a choice and win that prize. There's no game theory problem or whatever involved.

It is disingenuous to present the problem while withholding a key detail. The point of the Monty Hall problem is to point out a counter-intuitive but mathematically correct principle, not to test or assume that someone else would design a game show in the same way.

"Oh, look, we revealed the prize! Would you like to switch? *crowd laughs* haha. Ok, now run over there and spin that wheel!!!........"

Also I'm not really a fan of the answer, "well you should always switch, since it can't hurt you", especially when the whole point of presenting a Monty Hall problem is usually to try to 'catch' someone who has never heard of the problem (and thus isn't familiar with what should and shouldn't be included). So if you present a question like in the OP, if the box is revealed empty but done so randomly, you have a 50/50 shot regardless of whether you switch. Many people argue this and are correct. You can't just say "well you should always switch because it will never hurt". The entire point is arguing over switching gives you a 1/2 or 2/3 chance of winning the prize. Another way to look at it is, you can switch, but we will add $20 to your prize if you stay with the box you first selected. Then whether or not the box was revealed accidentally or not has a material effect on your decision.