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The Time Everyone “Corrected” the World’s Smartest Woman (2015)

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Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#51

Post by dllthomas »

jml7c5 wrote: post #20

From reading the problem as posed in the article, the confusion seems similar to the "plane on a treadmill" thing, where people are interpreting the premise of the problem differently. (In plane on a treadmill: "the treadmill moves backwards @ -1 * plane airspeed" vs "the treadmill moves backwards to keep plane airspeed at 0". In this: "the host will open the door at random and in this example it happen to have a goa…

The presentation of the problem included the phrase "the host, who knows what's behind the doors, opens another door", so I think in that case the interpretation that Monty deliberately reveals a goat is more appropriate (in addition, obviously, to being what was intended), although I agree there is wiggle room enough to admit both possibilities and clarity about which case you are discussing is important as it changes the answer.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#52

Post by rsa25519 »

jml7c5 wrote: post #20

From reading the problem as posed in the article, the confusion seems similar to the "plane on a treadmill" thing, where people are interpreting the premise of the problem differently. (In plane on a treadmill: "the treadmill moves backwards @ -1 * plane airspeed" vs "the treadmill moves backwards to keep plane airspeed at 0". In this: "the host will open the door at random and in this example it happen to have a goa…

> In this: "the host will open the door at random and in this example it happen to have a goat" vs "the host will never open a door with a car behind it".)

If the host opens a door with a goat, then it doesn't matter whether or not it was intentional.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#53

Post by kingsuper20 »

crooked-v wrote: post #32
kingsuper20 wrote: post #21

I'm familiar with the problem and my intuition is still wrong. I wonder if you couldn't design a gambling machine that has a variant of the Monty Hall problem built-in favoring the house (naturally).

From what I understand, that would just be overcomplicating the matter, because most modern video gambling machines just use a set number of wins per time interval.

Actually they use a RNG that in the case of slots, has a kind of virtual reel with multiple assignment.

If you like, add a bit of skill that gives the primates the feeling of control (video poker) or when you let loose of the handle or press a button (which simply grabs a number).

Stir in a bit of marketing pizzazz (off-by-one on slots, enormous number of simultaneous smaller bets, low payoff better odds vs. high payoff worse odds) and you can get the mark to stand there for a bit longer.

Networking, recognition and databases on players, etc. add more wrinkles.

In any case, I don't doubt that a Monty Hall bet could be wrappered into the game somehow to give the appearance of better odds than really exist.

(hopefully I got this somewhat right, I've never designed any gaming stuff. I'll bet that a gig at Bally or IGT would be a real eye-opener.)

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#54

Post by inopinatus »

javajosh wrote: post #23

So this is at least in part about the "Monty Hall Problem" and why it's solution not intuitive. The article missed an important angle: when the host opens a door, he's giving you more information , which explains why it's better to switch. If you're the host, you need to know which door the car is behind to do your job 2/3 of the time, to avoid revealing it. It's this quality of unexpected information exchange that I…

I'll suggest we encountered the same class of inadvertent information sharing via a recent post to this forum, The Case of the 50ms request:

https://news.ycombinator.com/item?id=27053941

Having recognised (from crystallized experience) the nature of the problem from the very first hint, I went straight for the jugular at the first opportunity; any residual uncertainty about the diagnosis was extinguished by the wording of the answer prompt, which to my mild disappointment took all the drama out of the reveal.

Sadly, there was no automobile prize on offer. No, not even a goat.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#56

Post by dllthomas »

rsa25519 wrote: post #52
jml7c5 wrote: post #20

From reading the problem as posed in the article, the confusion seems similar to the "plane on a treadmill" thing, where people are interpreting the premise of the problem differently. (In plane on a treadmill: "the treadmill moves backwards @ -1 * plane airspeed" vs "the treadmill moves backwards to keep plane airspeed at 0". In this: "the host will open the door at random and in this example it happen to have a goa…

> In this: "the host will open the door at random and in this example it happen to have a goat" vs "the host will never open a door with a car behind it".) If the host opens a door with a goat, then it doesn't matter whether or not it was intentional.

Yes it does. Or more precisely, it matters whether the host could be counted on to do so reliably; the mechanism for that doesn't matter.

There's a difference here, that our language obscures, between procedure and hypothetical.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#57

Post by shkkmo »

salamanderman wrote: post #26
jim010101020202 wrote: post #11

I may be missing something (not a mathematician, probabilist) but doesn’t the fact that the host would never reveal the car change the calculation? In the table shown in the article game 3 & 6 are nonsensical so with the remaining 4 games the odds are even between switch & stay.

The fact that the host never shows the car is critical to the solution. You choose a door. There's a 2/3rd chance that the car is behind one of the other doors. Monty is kindly going to show which of the other two doors not to choose. ... The other way to think of it is, you choose a door, and then you're asked "would you like to keep what's behind your door, or would you like to have the sum of the other two doors?"

Not at all. Once the door is opened, it doesn't matter if the host knew there was a goat behind it or not.

Edit: The host's knowledge only matter if the host can choose not to open a door.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#59

Post by randyrand »

An intuitive way to think about the problem is from the perspective of the host.

Sometimes the host has 2 goats he can pick from to show, and sometimes he only has 1 goat he can show.

66% of the time the contestant chose a goat, so the host has to reveal the only other goat 66% of the time. So switch.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#60

Post by Spivak »

6gvONxR4sf7o wrote: post #13

There are a number of things I like about the monty hall problem. There's the history, the unintuitiveness, the subtle easy-to-screw-up nature of probability problems, the calculation, the sociology, and the overconfidence of wrong experts. Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness. In fact, it would be much harder to be so widely…

I don’t think you need the 100 or 1,000,000 doors thing.

If you decide before not to switch then your goal is to pick the car which you have a 1/3 chance to do.

If you decide before to switch then your goal is to pick a goat which you have a 2/3 chance to do.

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