Monty Hall problem on MythBusters

[Irishman]

@Telemark

The section you quoted was actually about a different version of the problem. We’re all in agreement about the 2/3 in the random case, we’d moved on to the case where Monty makes sure that a black card is always shown and his methods of selecting that card/side to display.

Ok, thanks.

If you pull the cards at random from the bag, and if a white face shows up you put all the cards back in the bag and try again then your odds are 2/3.

But, if you flip all three cards, and have Monty look in the bag and always pull out the closest card with a black face your odds change to 3/4. It’s an interesting variation. My initial analysis was wrong, I thought it stayed at 2/3.

At least I think I’ve summarized the variant correctly.

Yes, I agree, if you pull the card randomly, you might end up with a white card.

If Monty selects the first Black he sees, then there are 3 black sides and 1 white side in play.

Your Montyless descriptions sound accurate.

[SlackerInc]

It should.

[filmore]

The Buzzr network shows old game shows, one of which is “Let’s Make a Deal”. I’ve been watching it for a while and I have yet to see the situation described in this problem:

• A player selects one of three unknowns
• Monty reveals what’s behind one of the unselected unknowns
• The player is given the opportunity to switch to the other unknown

Did that situation ever really happen on the show? It may be getting confused with the final showcase. The final showcase has 3 doors, but two people play and each one picks a door. He initially shows what’s behind the unpicked door, but there’s not another door for someone to trade to.

The other thing I’ve noticed is that Monty is like a carnival barker and is controlling the flow of the game. Trading one hidden prize for another hidden prize is common on the show, but Monty sometimes makes it more or less enticing to switch. He may offer the player more and more money to switch. He may give hints about one prize or the other to perhaps fool the player or encourage the player into switching. He seems to guide the play to more wins if there have been a few losses or if he likes the player. It’s not just about statistical probability. The game is a bit like poker where it’s not just the stats that control the game–the players themselves are a factor.

The discussions in this thread of the OP are for the pure statistics problem. But if you were actually a contestant on the show, you would need to be able to figure out Monty’s motivations in order to know when it’s best to hold or switch.

[ftg]

This is why it is vital to make the rules crystal clear. The TV show isn’t like the problem. The presumption that Monty might be trying to trick you to switching away from the big prize isn’t a consideration.

It has to be clearly explained that this deal will be made regardless of what door you initially pick.

Note that Marilyn didn’t state the problem clearly, hence there was more than one correct answer hence there was no need to mock those who gave other answers.

[STELLARWIND]

If the simplest solution is usually the correct one, and if brevity is the soul of wit. Then THAT reply was Occam’s Wit.
I’ve always gotten the math. But, putting it that way, so simply and succinctly and CORRECTLY…well, the 50/50ers are gonna have a hard time with this analogy.
#"Switchmen"FTW

Note: this “Problem” makes people go. CRAZY. I almost went actual fisticuffs over this shit.
People think they’re SOOOOOOOO right. And…sometimes we’re ALL wrong. Open-mindedness is key. That, and a basic understanding of 5th-7th grade mathematics. Marilyn Vos Savant (highest IQ ever-recorded lady–yeah, her) got ABUSED by multiple Ivy League professors. Saying she was WRONG to switch. They called her an EMBARRASSMENT to MENSA/IQ-testing, herself, her column, etc. They were… Brutal.

Then. They “checked their work” I suppose.
And fucking APOLOGIZED. Dicks. Bet it destroyed them to be “out - MATHED” by a CELEBRITY (not “real”) INTELLECTUAL who’s a WRITER, not a mathemafuckingtician.

What sweet, sweet ineffable vindication.
And still, people fight this math. Like it’s SUBJECTIVE! Math is ANYTHING but. That’s what makes it beautiful. The answer is NOT open to interpretation. No more than the cubed-root of, say, 27. It’s not 9. Or 18. Or 5.2. It’s (well, you guys know.)
And it’ll ALWAYS be 3. Math–at least, THIS BRANCH, is not open to interpretation. Sorry to be so loquacious. I’ve spent HOOOUUURRSS arguing against 50/50ers who called me RETARDED. And I’m a Mensan. Doesn’t make me right, but being right DOES.

Whew. That was therapeutic. Thanks, Doc. Same time next week?

@Little_Nemo

Okay, another way to visualize it for
those having problems seeing the logic.

Standard set-up of one prize and three doors. You pick a door at random. But Monty’s lazy in this game and doesn’t feel like opening doors. He just offers you a choice - you can keep the door you have or you can switch and take both of the other doors.

Now do you stay with the one door you have or do you switch and take two doors?

Mathematically this game is identical to the standard game.

[SlackerInc]

People often complain about revival of zombie threads, but I really enjoyed this random invitation to walk down memory lane. And some of the best parts of the “walk” were from 2015, when it was revived after a longer (three year) interval, by a not-especially-helpful post that somehow led to some really interesting discussion.

[TimeWinder]

@STELLARWIND

If the simplest solution is usually the correct one, and if brevity is the soul of wit. Then THAT reply was Occam’s Wit.
I’ve always gotten the math. But, putting it that way, so simply and succinctly and CORRECTLY…well, the 50/50ers are gonna have a hard time with this analogy.
#"Switchmen"FTW

How’s that TimeCube coming?