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It always amazed me that so many academics got it wrong. Once you understand the way the actual game works, it's pretty obvious that you gain a statistical adva

It always amazed me that so many academics got it wrong. Once you understand the way the actual game works, it's pretty obvious that you gain a statistical advantage if you switch.

savanaly 12y ago
I know right? I don't blame them for getting it wrong at first glance-- I'm pretty sure 999 out of 1000 humans would. But the mathematics of the probabilities can be written down on a napkin they are so simple, so how was no one able to convince these scientists with a clear, concise technical proof? They really needed a computer simulation, as I've seen it claimed?
- function_seven 12y ago
  > But the mathematics of the probabilities can be written down on a napkin they are so simple, so how was no one able to convince these scientists with a clear, concise technical proof? I'm even more appalled that no one tried, you know, actually running the game. Have someone take a quarter and two pennies, mix them up under cups, let you choose one, show you a penny, then switch or not. Repeat several times. Switch places. When you're playing the role of Monty, the truth will reveal itself...
  - MichaelGG 12y ago
    I have a close friend that was incensed about my explanation about how he was misunderstand. He even ran a broken simulation that showed he was right. When I corrected his source code with detailed comments, he further accused me of trying to fool him and make fun of him. Didn't speak to me for a month. Bizarre. But I suppose this kind of thing that goes against instincts can really upset people.
dllthomas 12y ago
Note that it can depend on the wording of the question. Monty must know that he's revealing a goat for it to work out 2-to-1. If he picks randomly, your odds are 1-to-1 after he's revealed the goat.
- JohnTHaller 12y ago
  Monty knows he's revealing either a goat or the modest prize. If you pick the goat, he reveals the modest prize. If you pick the modest prize, he reveals the goat. If you pick the big prize, he could reveal either the goat or the modest prize, but IIRC, he would reveal the goat.
  - dllthomas 12y ago
    I agree that that was the intended formulation of the original question. That doesn't mean it's fair to assume it's what everyone should understand from every (possibly flawed) attempt at restating it. I don't know whether I've seen the precise wording of the version that sparked the controversy, so I don't know how clear it was on the point.

It always amazed me that so many academics got it wrong. Once you understand the way the actual game works, it's pretty obvious that you gain a statistical advantage if you switch.

savanaly 12y ago

I know right? I don't blame them for getting it wrong at first glance-- I'm pretty sure 999 out of 1000 humans would. But the mathematics of the probabilities can be written down on a napkin they are so simple, so how was no one able to convince these scientists with a clear, concise technical proof? They really needed a computer simulation, as I've seen it claimed?

function_seven 12y ago
> But the mathematics of the probabilities can be written down on a napkin they are so simple, so how was no one able to convince these scientists with a clear, concise technical proof? I'm even more appalled that no one tried, you know, actually running the game. Have someone take a quarter and two pennies, mix them up under cups, let you choose one, show you a penny, then switch or not. Repeat several times. Switch places. When you're playing the role of Monty, the truth will reveal itself...
- MichaelGG 12y ago
  I have a close friend that was incensed about my explanation about how he was misunderstand. He even ran a broken simulation that showed he was right. When I corrected his source code with detailed comments, he further accused me of trying to fool him and make fun of him. Didn't speak to me for a month. Bizarre. But I suppose this kind of thing that goes against instincts can really upset people.

dllthomas 12y ago

Note that it can depend on the wording of the question. Monty must know that he's revealing a goat for it to work out 2-to-1. If he picks randomly, your odds are 1-to-1 after he's revealed the goat.

JohnTHaller 12y ago
Monty knows he's revealing either a goat or the modest prize. If you pick the goat, he reveals the modest prize. If you pick the modest prize, he reveals the goat. If you pick the big prize, he could reveal either the goat or the modest prize, but IIRC, he would reveal the goat.
- dllthomas 12y ago
  I agree that that was the intended formulation of the original question. That doesn't mean it's fair to assume it's what everyone should understand from every (possibly flawed) attempt at restating it. I don't know whether I've seen the precise wording of the version that sparked the controversy, so I don't know how clear it was on the point.