re: Variable Change And The Movie 21

It amazes me people still cannot grasp that concept. With three doors, people ignore the odds of which one contains the prize 66% of the time(the switch) and focus on the final two doors 50% odds of them guessing correct door, not which one contains the prize.

Mythbusters did a show on this and here is a write up of the results.

LINK

If the student drives 100 mph, it’s a good chance he’s getting better mpg than if he drove 0 mph.

Eh. It's mind games. Technically, you could be stupid and pick the same door; literally, there are still three choices. Technically, you're still looking at the whole field of three, but the reality is you're looking at only two doors. Because there are still three doors, he now has a lesser percentage chance of picking the wrong door when you look at all three than if just two.

Now he can take a coin and flip it to choose which door to pick next--and that's 50/50. Of the subset of two doors, he has a 50% chance. Of the total three, he has a 66% chance. Which one makes you FEEL better about your chances, though?

If you're on The Price is Right on the punch-out game, and they eliminate 98 of the 100 sockets to win the prize (the correct choice is not 1-98; it's either 99 or 100), by this logic you have a 99% chance to win. Of the whole, that's true. But is the whole really still available? You have a 50% chance of picking the correct one as between 99 and 100. I think it's a matter of perspective as much as anything.

I mean the only time you wouldn't win is if your first pick was correct which will happen 1/100 times. I don't get people's disconnect with this idea.

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I disagree. It's not mind games. The fact that he turned over 98 wrong doors and left 1 unopened doors reveals objective information about that door. If you played that game 100 times, you would win 99 times if you switched your pic. It's objective mathematics, not psychology.

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Well, sure choosing the wrong door reveals objective information. That's why the incorrect doors are eliminated.

This thing is saying that I have three doors to choose from, but I'm actually only going to choose from two after the first round. It's having your cake and eating it, too. It's a third shot of getting it right, but it's actually two-thirds shot because I'm not actually choosing from three although I'm still looking at three.

I mean, are we picking from three (which is why we're still talking in thirds), or are we picking from two since one has been eliminated (which is why we're still talking in thirds but which is why I argue the reality is a 50% shot since I'm not going to pick the same wrong door)? If you take the two doors and run it a million times, the chances are always 50/50 that you pick the correct door because you are limited to two. I like this whole thing, and it's a clever. It's just clear to me that it's about whether you're looking at the whole field or only the ones you haven't eliminated yet.

The surgeon was the boy’s mom.

No you’re wrong. Don’t think about in terms of 3 think about in terms of 100 like my example. The only way you would be wrong by switching doors is if your initial pick was correct which will occur 1% of the time. In other words, there’s a 99% chance it’s the other door. That’s variable change.

If you did the 100 door example, it wouldn’t somehow change it to where your initial pick is right 50% of the time just because there’s 2 doors left. That’s retarded

And you know what, the plane is going to take off.

And he was standing on a block of ice.

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None of what you said made absolutely any sense to me until I could think of it like that. Good convo, thanks.

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Sorry if I came in hot there. I get excited when I actually know about something on here