(no subject)

[plonq]

I made the mistake of bringing up the "Monty Hall" theorem yesterday.  That entailed 30-minutes of diagrams and explanation to convince a co-worker of the answer.  At one point I actually ran some simulation software for him to illustrate the odds in practise.

He still didn't get it.  "It's 50/50 I tell you!"

I finally drew a multi-coloured grid to represent the three doors in all three states, and it finally clicked for him.  He grudgingly admitted that, as counter-intuitive as the answer is, he could see that it worked.  I'll have to keep this diagram in mind the next time I feel masochistic enough to bring this one up again.

Comments

[funos.livejournal.com]

That theorem *is* hard to grok. I didn't completely get it until I saw a tree diagram of the probabilities. It is very non-intuitive if one thinks that the first and second choices are not connected, which they are. That's the core concept to get through to them first.

Still, you have such patience (or stubborness) :)

[plonq.livejournal.com]

My next step was going to involve hiding a little square of paper under one of three pennies, and then have him select the one that he thought the paper was under. I'd have him keep a tally to see what his winning percentage was over a long enough time to establish a pattern.

I had quite an argument about this with a guy on a mailing list once. At one point he fell on the defense that "odds and probabilities have no bearing on reality". Apparently he was quoting his math teacher.

I tersely suggested that he should play the lottery then, because if odds didn't apply to him then he was a sure winner every time. I wouldn't say that I won the argument, but I surely ended it.

[furahi.livejournal.com]

Could that be TLK-L when someone (you?) posted the example with Rafiki as the host?

[plonq.livejournal.com]

Yes, that would have been TLK-L, with Rafiki playing a shell game with a couple of cubs.

[furahi.livejournal.com]

I was one of the 50/50 ones at first, but your explanations (and I think Greg Ludwick's) convinced me I was wrong, I couldnt beleive it, especially having taken a probability and statistics class the semester before =P

[leopanthera.livejournal.com]

It would be 50/50 if the game show host picked a door at random. But he doesn't, he can't, he knows which is the "bad" door and cannot choose that one.

It's easier to understand once you realise that fact.

[plonq.livejournal.com]

Yes - thank you! That is the key to the answer.

The game host is not random.

I thought that I was going to go horse from repeating that phrase yesterday. Oy. Ultimately I saved a thousand more words by drawing a picture. ;)

[plonq.livejournal.com]

Er, make that "hoarse".

[mwalimu.livejournal.com]

The basic reasoning becomes much clearer if instead of three doors, with Monty opening one, you change it to have a hundred doors, with Monty opening ninety-eight.

[plonq.livejournal.com]

Ah, I've employed that argument too, but it always comes back to the same counter-argument.

"But once it's down to two doors, it's 50/50...!!!"

(The three exclamations are the staccato sound of my head thumping the desk.)

[tzisorey.livejournal.com]

Technically that's correct.... once it's down to 2 doors it's 50/50. But that's when you're already half-way through the game.

[dakhun.livejournal.com]

Well, you have a 2/3 chance that you didn't pick the right door to begin with, and nothing else that happens changes that. The opening of one of the other doors basically means you get a choice between your one door, or BOTH the other two doors.

But the REAL question is can you mathematically prove what you should do if you switch doors, but Monty offers you a choice of what's behind that door, or... what's in the box?

[kfops.livejournal.com]

Never go for the box! There's a 50% chance it contains a duck dressed as a goat with a life-time supply if brillo pads!

[plonq.livejournal.com]

If the duck could sing, then one could still squeeze lemonade out of that prize. (At risk of mixing metaphors or something.)

[atara.livejournal.com]

I thought we'd agreeed that you weren't to bring up this subject again?

[neowolf2.livejournal.com]

The way I explain this is to generalize to N doors, and have Monty open N-2 of them. The correct conclusion becomes easier to see.

[dronon.livejournal.com]

Here, this should help.

It's from a book I got last Christmas that I'm putting into our office's fundraiser internal garage sale this year.