Whee! First post! 
Anyway, here’s something I’ve been wondering about. I have absolutely no desire to dredge up the Monty Hall Problem again, and only bring it up as it relates to something else.
There’s a game on The Price is Right called Barker’s Markers. The contestant is shown three prizes, and a board with four prices. Three are the prices of three of the prizes, one is a “dummy price” with no match. The contestant is given three Markers, and is asked to mark the three prices (s)he thinks match up to the three prizes; it’s not necessary to know which specific price matches up to which prize.
After the Markers are placed, Bob reveals the prices on two of the prizes, since obviously, no matter what, two are matched up. Then Bob offers the contestant the opportunity to switch the third Marker. If the contestant matches all three correctly, (s)he wins all three prizes.
I don’t know whether Bob knows which three prices are correct; assumably he does. So, given that you don’t know anything about the relative prices of the three prizes, is this situation the same as the Monty Hall Problem, and you should thus switch the third Marker? Why or why not?
Thanks!
If you’re just guessing, you should switch. When you guessed, you had 3/4 chance of including the “bad” price in your guesses. By switching you get a 3-to-1 advantage.
P.S. It doesn’t matter if he knows the prices or not, since he can still only reveal correct prices. That’s where the added information comes from.
Yeah, that’s right; if it’s all a complete guess, then 1/4 of the time you’ll win if you stay, while 3/4 of the time you’ll win by switching.
However, this game is definitely distinct from the Monty Hall problem (three closed doors which give you no information), since the items and prices themselves give information. If you have a good idea of how much the prizes are worth to begin with, and use that knowledge in picking the prices, you’ve already increased your chances of winning above the 1/4 predicted by chance.
Interestingly, the price you think is most likely to be one of the correct prices is the one you should NOT choose initially. After Bob shows two of the prices, then you can switch to that price.
Good point, ZenBeam! I’ll remember that the next time I have Bob over 
Yes, Barker’s Markers is a variant on the Monty Hall problem, only you have more information to work with. With a bit of deduction, you should be able to win it virtually every time, using ZenBeam’s strategy (or 75% of the time by blind guessing).
My game show question is this: What the heck is the point of (the old '60s game show) “What’s My Line”? I mean, you have a panel of celebrities, who are presumably already getting paid to appear, and you have a ‘celebrity’ guest for whom the same is likely true, and you have the host, and that’s it. Oh, and every time they get a question wrong, an extra $5 goes up on the tally board, but it’s not exactly clear where the money is going. To the poor cash-starved celebrity panel? To the poor cash-starved celebrity guest? Is that the amount the host gets? It’s like a game show without a game. Or am I missing something?
Mr Death, yes, I’m afraid you are missing something.
Last month’s American Heritage Mag featured a story by the son of a 1950’s WML contestant. The author’s dad was no celebrity (though admittedly, there was one “celebrity” game per show – that’s when the panelists donned those utterly absurd blindfolds). He was a male wedding planner – quite the oddity way back when I suppose. When he stumped the panel to the tune of $50 it was his to keep. And to quote the author’s old man, “Fifty bucks was a lot of money back then.”