wens

I'll be getting wheels soonish, I need to figure out how soon I can afford them now that I'm supposed to be all the way to being an adult (or something like that).

Flatballer

We discussed the Monty Hall problem at lunch today. Being a nerd is fun.

caloso

I think this week's Car Talk puzzler is a variation on the MH problem, isn't it?

Flatballer

Haven't heard it yet. I listen to Car Talk and Wait Wait Don't Tell me on podcast. I'm way behind on my Car Talk, a couple months I think. I'll go check it out online though.

edit: yeah, sounds like a variation.

I think whichever you pick first you have to give up and pick another one. If that is smaller than the first you pick again, if it's larger you stick with it.

That gives you better odds than just a random first choice.

mattm

wtf is the "Monty Hall" problem?

Flatballer

https://en.wikipedia.org/wiki/Monty_Hall_problem

Famous statistics paradox. The answer is extremely counter-intuitive and takes a while to figure out.

substructure

I'm glad I'm a simpleton.

mattm

No wonder.. I hated stats in college and still do.

So when does that come in handy anyway? (excluding cocktail parties & job interviews)

Flatballer

Well, it shows you that human brains are susceptible to certain errors, and people will stick to their wrong answers until the end. The fact that probability isn't always what it seems at first is pretty important just by itself. Gambling, stock market (same thing really), sports, games, business decisions, etc.

You never know when some obscure piece of information will help you solve a real world problem.

Hida Yanra

headed home... the last few days have been really draining.
time to try to get 2hrs in on the bike.

mike868y

like all the nyc nerds who think bikes should be able to run red lights?

P.S. that was a joke, don't get ape **** on me, but you probably will.

mattm

I agree it's interesting - but that's not the same as useful.

The hard part is taking the simple analogy - 3 doors, one good choice - and expanding it to real life (500+ doors, 50 reasonable choices, some better than others)... if people could do that in their heads they wouldn't continue to make bad bets in the stock market/gambling, business, etc.

Enthalpic

Must have recently seen the movie 21.

roadiejorge 

No but it is used to that effect now. If you haven't ridden in it or are familiar with the street closure rules in order to accommodate joggers and cyclists then I'm not sure how you think it makes sense for you to be so adamant about this. I think they need to readdress traffic laws in parks as it relates to cyclists and take a common sense approach rather than just the blanket rules they have now.

roadiejorge 

best of luck to you psimet. next set of wheels I buy will be from you.

Flatballer

I've been wanting to see that, but no. I don't remember why it came up, actually. I think we were probably talking about Jeopardy, but I'm not sure how we got from there to the MH problem.

mike868y

thinking they need to readress traffic laws in the park is totally different than feeling like you can break them just because you think they are wrong.

Enthalpic

The person can reasonably stick with their first guess –albeit incorrectly- by thinking their chances changed from 1 in 3 to 1 in 2; it's not a refusal to accept change.
+1

roadiejorge 

indeed. in the days NYC was a rougher place it was sink or swim, this is why I find it funny when I hear people who weren't around for the gritty aspect of the city pine for it when they would have headed for the hills if they had to live in it day to day.

Flatballer

I'm not saying that it's unreasonable to stick with their guess. I'm more talking about the 10,000 people who wrote in to Parade Magazine in 1990 when the problem was brought out, including the 1000 people with Ph.Ds, who were all extremely adamant, sometimes even angry, saying that "switching" was the wrong answer.

echappist

alright kid, it seems as if your ass is glued onto your moral high horse. So answer the following questions

-Have you rolled through a stop sign or red light on your bike when you know you won't be subjecting both yourself and anyone else to injury.

-When you are driving, have you done anything you know is against the books but you do anyway because it saves you a ton of time (e.g. making a left just as the light goes from yellow to red or driving 5mph over the speed limit).

If you can't give a straight no to any of the questions, you need to learn the meaning of the word hypocrisy.

mike868y

I've done both. the difference is if I had gotten a ticket for it I wouldn't blame the police.

bostongarden

Fun stuff! I've used it in some of my classes. A non-mathematical way to get the point across is as follows:
1) Suppose that there were 10,000,000 doors (each to a room) that you could select. Behind one door (i.e., in one of these rooms) is a prize -- new bike of your choice (and the door behind which it has been placed was randomly selected).
2) You select a door.
3) We agree that the odds are 1 out of 10,000,000 that you selected the door to the room where the bike is located (assuming that you have no special psychic ability and I don't have a special "tell" which gives it away).
4) At this juncture, do you really believe that you have selected that 1 door (of 10,000,000) which will lead you to the bike? Isn't it tons more likely that the bike is behind one of the other 9,999,999 doors? Just nod your head up and down.
5) Let me ask you something: if I gave you the choice of now sticking with the door you currently have selected, or, collectively choosing all of the other 9,999,999 doors (yes, I'm serious, and, yes, you would get the bike if you chose all 9,999,999 doors and it is behind one of them), what would you prefer? C'mon, seriously, you aren't going to abandon your 1 door to select the other 9,999,999 doors?!! For the moment, I'm just asking.
6) Now, of course, I know where the bike is located. Of the 9,999,999 doors that you did not select (think of these as "my" doors), I proceed to open all but one of them (i.e., 9,999,998 doors -- I have a special button that does this quickly so we aren't waiting around for a lifetime or two to get this done).
7) Think about it a bit (hint: reread #5), do you want to switch? Do you now suddenly think that it is equally likely that the bike is behind the door you selected or the one door (of the "other"/"my" 9,999,999 doors you did not select) that I did not open?

Whether it is 3 doors, 100 doors, or 10,000,000 doors, the approach should be the same; although, I think the example with 10,000,000 helps one "see" the best way to go (and think about making an optimal choice for this problem). In the game on "Let's Make A Deal," Monty Hall has 3 curtains rather than 10,000,000 doors. So, above, substitute the number 3 for 10,000,000 and go through the exercise. Also, if you are so inclined, you can test this empirically, and, possibly make a lot of money in the process.

Flatballer

That's the way I finally got my co-worker to believe the answer. I explained it with the 1 million door example that the wiki article shows. It definitely makes it much more intuitive.

I also explained it to him by showing that if you didn't pick the car the first time, you win by switching 100% of the time. If you pick the car first, you lose by switching. So 2/3 times you win by switching (since 2/3 of the time you didn't pick the car first), 1/3 times you lose by switching. That's the explanation that makes the most sense to me.

big john

I got an hour and a half.