4 ms·

I think there's an unfortunate trend throughout a lot of human activity to make things complicated. The prototypical example in my mind has always been the Mont

by nilkn 12y ago

I think there's an unfortunate trend throughout a lot of human activity to make things complicated. The prototypical example in my mind has always been the Monty Hall problem, where you often see convoluted explanations or detailed probabilistic calculations, but the solution is just plain as it can be when you consider that if you switch you win iff you chose a goat and if you stay you win iff you chose the car. I've also always been a fan of Feynman's assertion that we haven't really understood something until it can be explained in a freshman lecture. At the end of his life he gave a now famous explanation of QED that required almost no mathematics and yet was in fact quite an accurate representation of the theory.

marvy 12y ago
Ok, that is the best Monty Hall explanation I've ever heard.
jodrellblank 12y ago
car: switch and lose. Goat: switch and win. Is OK as far as it goes, but it's not enough explanation to cover why you should switch. You need probability in the explanation because of the two goats/one car choice in part one .. and here I am trying to explain it again. You already know how it works, but you don't see that your explanation of it doesn't explain it. After they removed one answer, you have more information... Because the choice isn't balanced... If it was as simple as you suggest, it wouldn't make a good part of a game show. Everyone would see straight through it.
- Lost_BiomedE 12y ago
  It always seemed a bit easy to me without running through probabilities due to the fact that the game show host was forced to choose goat (which is different depending on where the car is). The idea of a forced non-random choice is more clear to me than a probability explanation, but you need probability to demonstrate a proof.
cbd1984 12y ago
> The prototypical example in my mind has always been the Monty Hall problem, where you often see convoluted explanations or detailed probabilistic calculations, but the solution is just plain as it can be when you consider that if you switch you win iff you chose a goat and if you stay you win iff you chose the car. The problem here is, when two people disagree, they both think the problem is simple and they both think their answer is trivial. The thing is, they haven't solved the same problem. In the standard formulation, where switching is the best strategy, Monty's actions are not random: He always knows which door has the good prize ("A new car!") and which doors have the bad prize ("A goat.") and he'll never pick the door with the good prize. If you hear a statement of the problem, or perhaps a slight misstatement of the problem, and conclude that Monty is just as in the dark as you are on which door hides which prize and just happened to have picked one of the goat-concealing doors, then switching confers no advantage. A large part of simplicity is knowing enough to state the problem accurately, which circles back to your paragraph about Feynman: Understanding his initial understanding of QED required understanding everything he knew which lead him to his original understanding of the problem QED solved; for his final formulation of QED, he understood the problems in terms of more fundamental concepts, and could therefore solve them using those same concepts.
- nilkn 12y ago
  Actually, if Monty chooses randomly and just happens to pick a door with a goat you should still switch, because it's still true that you will win if you switch iff you chose a goat but you'll win if you stay iff you chose the car already. The host's method of selection is not relevant given a priori the observation that the host selected a goat. The host's method is relevant if we forgo that observation and iterate the game repeatedly.
  - deleted 12y ago
    [deleted]
sbov 12y ago
Your explanation makes it sound like its a 50/50 chance.
- basch 12y ago
  there are two goats, you win if you choose either first and switch. the problem is deceptive because it doesnt explicitly say they ALWAYS remove a goat. The answer becomes obvious when you ask "There are three doors, one has a prize. Would you like to select one door or two doors?"
DanBC 12y ago
I thought the point of the modern Monty Hall problem is to introduce students to probability and thus it's important for them to list the various probabilities. They're learning how to do it. Other people need to check the working to see if the student understands what to do. Here's a nice example of this teaching: http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2010/readings/MIT6_042JS10_chap18.pdf http://ocw.mit.edu/courses/electrical-engineering-and-comput...

by nilkn 12y ago

marvy 12y ago

Ok, that is the best Monty Hall explanation I've ever heard.

jodrellblank 12y ago

car: switch and lose. Goat: switch and win. Is OK as far as it goes, but it's not enough explanation to cover why you should switch. You need probability in the explanation because of the two goats/one car choice in part one .. and here I am trying to explain it again. You already know how it works, but you don't see that your explanation of it doesn't explain it. After they removed one answer, you have more information... Because the choice isn't balanced... If it was as simple as you suggest, it wouldn't make a good part of a game show. Everyone would see straight through it.

Lost_BiomedE 12y ago
It always seemed a bit easy to me without running through probabilities due to the fact that the game show host was forced to choose goat (which is different depending on where the car is). The idea of a forced non-random choice is more clear to me than a probability explanation, but you need probability to demonstrate a proof.

cbd1984 12y ago

> The prototypical example in my mind has always been the Monty Hall problem, where you often see convoluted explanations or detailed probabilistic calculations, but the solution is just plain as it can be when you consider that if you switch you win iff you chose a goat and if you stay you win iff you chose the car. The problem here is, when two people disagree, they both think the problem is simple and they both think their answer is trivial. The thing is, they haven't solved the same problem. In the standard formulation, where switching is the best strategy, Monty's actions are not random: He always knows which door has the good prize ("A new car!") and which doors have the bad prize ("A goat.") and he'll never pick the door with the good prize. If you hear a statement of the problem, or perhaps a slight misstatement of the problem, and conclude that Monty is just as in the dark as you are on which door hides which prize and just happened to have picked one of the goat-concealing doors, then switching confers no advantage. A large part of simplicity is knowing enough to state the problem accurately, which circles back to your paragraph about Feynman: Understanding his initial understanding of QED required understanding everything he knew which lead him to his original understanding of the problem QED solved; for his final formulation of QED, he understood the problems in terms of more fundamental concepts, and could therefore solve them using those same concepts.

nilkn 12y ago
Actually, if Monty chooses randomly and just happens to pick a door with a goat you should still switch, because it's still true that you will win if you switch iff you chose a goat but you'll win if you stay iff you chose the car already. The host's method of selection is not relevant given a priori the observation that the host selected a goat. The host's method is relevant if we forgo that observation and iterate the game repeatedly.
- deleted 12y ago
  [deleted]

sbov 12y ago

Your explanation makes it sound like its a 50/50 chance.

basch 12y ago
there are two goats, you win if you choose either first and switch. the problem is deceptive because it doesnt explicitly say they ALWAYS remove a goat. The answer becomes obvious when you ask "There are three doors, one has a prize. Would you like to select one door or two doors?"

DanBC 12y ago

I thought the point of the modern Monty Hall problem is to introduce students to probability and thus it's important for them to list the various probabilities. They're learning how to do it. Other people need to check the working to see if the student understands what to do. Here's a nice example of this teaching: http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2010/readings/MIT6_042JS10_chap18.pdf http://ocw.mit.edu/courses/electrical-engineering-and-comput...