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Thu Aug 8, 2019, 12:33 AM

Since we're doing Math Games tonight ... how about this ... The Lets Make A Deal quandary!

Last edited Thu Aug 8, 2019, 06:20 PM - Edit history (1)

NO CHEATING AND LOOKING IT UP ON GOOGLE!!!

And try not give too much away in the comments if you KNOW the answer ... just make it sound like a guess til some people have a shot at it

Here's the math problem:

You are a contestant, Dolores, on the old game show, Monty Hall's Let's Make a Deal.

You reach the finale, where 3 doors are presented, and Monty tells you that behind the 3 doors are: A NEW CAR, A Goat, and an IRS Audit.

You're instructed to pick one of the 3 doors, and you do so. Say, it's door #1.

At this point, Monty opens either Door #2, revealing the Goat.

At this point, he says "You know Dolores, I like you. I'm going to give you a chance to change your mind and choose Door #3 ... Would you like to do that?"

Now ... there are two assumptions you should make in solving this problem:
1) Monty KNOWS what's behind each door, and does not want you to win the car, for whatever reason, thus will never reveal immediately that you've already won after your first pick.
2) Monty does not have a choice but to play the game in this fashion, it's just 'how it's done' in the game (which it really wasn't in the actual show, but this is for fun).

Oh, and
3) Winning a car is preferable to an IRS audit

Answer in the poll ... do you change your pick from #1 to #3?

And in the comments, explain why (without too much detail until some people have a chance to play )?


7 votes, 1 pass | Time left: Unlimited
I switch my choice to the other door
6 (86%)
I do NOT switch my choice to the other door
1 (14%)
Doesn't Matter Whether I Change, Odds are the Same
0 (0%)
Show usernames
Disclaimer: This is an Internet poll

16 replies, 308 views

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Response to mr_lebowski (Original post)

Thu Aug 8, 2019, 12:42 AM

1. I have previously read about this one. The suggested way to go does not make sense to me, but

I followed the instructions on how to bet.

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Response to Shrike47 (Reply #1)

Thu Aug 8, 2019, 12:57 AM

2. It's a classic problem, much discussed and dissected ...

In the original form of the published problem from 15 years back or so, the first 2 assumptions I added were not part of the question ... they've since been accepted as 'crucial', that's why I added them.

It's perhaps surprisingly a LOT more vague without those assumptions

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Response to mr_lebowski (Reply #2)

Thu Aug 8, 2019, 05:20 PM

11. Yeah, that's the problem with this puzzle

It's already an interesting counter-intuitive puzzle, but tying it to an actual show and personality just muddles it, since the real Monty Hall had considerable latitude in his behavior.

The always switch answer only works if Monty is a robot that behaves as you stipulated.

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Response to mr_lebowski (Original post)

Thu Aug 8, 2019, 12:57 AM

3. I was lucky enough to read the excellent column

by Marilyn vos Savant (Ask Marilyn) about this very question.

I say lucky because I was in an interview and the person asked me to solve the problem and I explained it just the way she explained it... and then told the interviewer that I had read the column so I already knew the correct answer.

I got the job offer.

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Response to lapfog_1 (Reply #3)

Thu Aug 8, 2019, 01:00 AM

4. That is indeed the source ...

The ensuing discussions over the years hence led me to add the assumptions in my version, as these were not part of her initial 'problem' ... and they should've been.

Still don't want anyone to cheat

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Response to mr_lebowski (Original post)

Thu Aug 8, 2019, 01:00 AM

5. One hint for understanding this problem, Monty's choice of door to open is NOT an independent choice

He has prior knowledge of the system. The fact that he will never open the door with the car behind it when it's his move is key.

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Response to cos dem (Reply #5)


Response to mr_lebowski (Original post)

Thu Aug 8, 2019, 02:20 AM

7. Marilyn vos Savant told me I should pick the

other door on the second guess. She wrote an article about this situation ten or twenty years ago. She was a major league bullshit artist but in this case her reasoning seemed sound.

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Response to comradebillyboy (Reply #7)

Thu Aug 8, 2019, 02:27 AM

8. Yes, as discussed in the small handful of posts above yours, she's the one who 1st posted

this probability problem, and is the source of my bringing it up here.

And the public response to her original article is why I brought up the 'assumptions' to be made in figuring the solution.

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Response to mr_lebowski (Original post)

Thu Aug 8, 2019, 04:43 AM

9. OK, my immediate reaction is that the odds now are 50-50, but...

since this is a trick question the obvious answer is, of course, the wrong one.

Then I notice that two people who have seen this before say "switch". So why switch?

Again, and immediate assumption is that Monty would not give you the option to switch unless your first guess was the right one, now reducing your chances from 100% to 0%. Then I realized that everyone gets that choice.

So, digging round in ancient memories of useless knowledge, I found myself looking up things like Markov chains which reinforces my memories of there being no such thing as "random" that we can initiate, but only pseudo-random. Even a dice roll is influenced by outside forces and not simply probability, as is the roulette ball. Even in an honest game, a slight spin or slip can affect the odds.

Oh, and vos Savant never, ever writes a column mentioning things like Bayesian networks that will put her readers off. She specializes in relatively easy problems that make her readers feel smart once they get the trick.

So, I end up thinking that something in Monty's tone is giving you a huge hint what to do. He is trying to lead you astray and your real job is to figure out just what his "tell" is.

Then I cheat, and realize that increasing your odds from 50% to 66%, even if true, isn't worth worrying about.

BTW, I did lousy in college statistics. Considered changing my major from economics to something about sex. Maybe psychology.

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Response to mr_lebowski (Original post)

Thu Aug 8, 2019, 12:50 PM

10. Dunno if Kicks work on this forum but if they do ...

Kick for the AM crowd...

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Response to mr_lebowski (Original post)

Thu Aug 8, 2019, 05:42 PM

12. Pass because of...

two errors in the description.

KY.........

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Response to KY_EnviroGuy (Reply #12)

Thu Aug 8, 2019, 05:44 PM

13. Where are the two errors?

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Response to mr_lebowski (Reply #13)

Thu Aug 8, 2019, 06:12 PM

14. Maybe my brain is scrambled, so check me but...

no mention of "goat" when you first listed the items behind the doors:
You reach the finale, where 3 doors are presented, and Monty tells you that behind the 3 doors are: A NEW CAR, A Donkey, and an IRS Audit.
----
At this point, Monty opens either Door #2 or Door #3, revealing the Goat.

This may not be an error, but when you said Monty opened either door 2 or three, you didn't say which one (although that could be surmised later):
At this point, Monty opens either Door #2 or Door #3, revealing the Goat.

At this point, he says "You know Dolores, I like you. I'm going to give you a chance to change your mind and choose Door #3

We would therefore surmise that he actually opened Door #2 because he then gave you the choice of opening #3 (and suggesting a bias against opening #1 where the car would then most likely be found).

I am extremely tired so maybe too dense today.........

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Response to KY_EnviroGuy (Reply #14)

Thu Aug 8, 2019, 06:19 PM

15. You're right I mixed up donkey and goat lol will fix ...

But the fact that he opened door #2 in this case revealing the donkey/goat should've been assumable when I said you're given a choice of door #3 ... but i'll fix that too

The assumptions to the problem are: he's biased against you winning (won't reveal you got it right the first time) and that he always conducts the game in this manner (i.e. he must reveal one crap prize, and he doesn't get to choose whether or not to allow you to switch, he always does that).

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Response to mr_lebowski (Reply #15)

Thu Aug 8, 2019, 06:54 PM

16. Thanks, makes sense now.

............

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