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RE: The role of probability in solving the Monty Hall problem
March 13, 2016 at 8:28 am
Wait. Are you trolling me?
Are you screwing with me? I can't believe you'd just ignore the maths and say "no but you're wrong".
I think you're screwing with me.
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RE: The role of probability in solving the Monty Hall problem
March 13, 2016 at 8:33 am
Yes rob, you are right about getting the most beneficial results after n tries if you switch as the probability of choosing a door that has a goat behind it is higher than that of the probability of choosing a door that has a car behind it initially.
On which case switching the door would not be because of probabilistic reasons but because of statistical reasons. Remember when I said you could flip a coin and get heads 1million times in a row but this doesn't guarantee you getting heads next time around?
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RE: The role of probability in solving the Monty Hall problem
March 13, 2016 at 8:34 am
Nope I'm not trolling you, you really are wrong.
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RE: The role of probability in solving the Monty Hall problem
March 13, 2016 at 8:35 am
(This post was last modified: March 13, 2016 at 8:35 am by robvalue.)
What?
You're screwing with me. You must be. What is "statistical reasons"? Yes, the probability is in your favour if you switch. I don't know how much clearer I can make it.
Haha. OK fine, I'll leave you be then.
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RE: The role of probability in solving the Monty Hall problem
March 13, 2016 at 8:41 am
(This post was last modified: March 13, 2016 at 8:43 am by Excited Penguin.)
Rob, you just don't get it, do you. It's not about probability in the least. We already know that mathematically your answer is correct, but the fact is that we're saying you shouldn't use probability at all in that instance. Why? Well, because there's nothing to guarantee that you won't end up infinitely choosing to switch to the wrong door.
When you add up the number of options however, that problem dissolves and your probability theory proves to be effective. For instance when there are a million doors to choose from. But not when there are only a few of them.
--- THe problem is still there, but it's much more of a leap to say that you won't get the right answer as the number of doors increases.
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RE: The role of probability in solving the Monty Hall problem
March 13, 2016 at 8:45 am
(March 13, 2016 at 8:41 am)Excited Penguin Wrote: Rob, you just don't get it, do you. It's not about probability in the least. We already know that mathematically your answer is correct, but the fact is that we're saying you shouldn't use probability at all in that instance. Why? Well, because there's nothing to guarantee that you won't end up infinitely choosing to switch to the wrong door.
When you add up the number of options however, that problem dissolves and your probability theory proves to be effective. For instance when there are a million doors to choose from. But not when there are only a few of them.
--- THe problem is still there, but it's much more of a leap to say that you won't get the right answer as the number of doors increases.
What do you mean infinitely choosing the wrong door?
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RE: The role of probability in solving the Monty Hall problem
March 13, 2016 at 8:46 am
(This post was last modified: March 13, 2016 at 8:49 am by Excited Penguin.)
Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.
(March 13, 2016 at 8:45 am)Mr.wizard Wrote: (March 13, 2016 at 8:41 am)Excited Penguin Wrote: Rob, you just don't get it, do you. It's not about probability in the least. We already know that mathematically your answer is correct, but the fact is that we're saying you shouldn't use probability at all in that instance. Why? Well, because there's nothing to guarantee that you won't end up infinitely choosing to switch to the wrong door.
When you add up the number of options however, that problem dissolves and your probability theory proves to be effective. For instance when there are a million doors to choose from. But not when there are only a few of them.
--- THe problem is still there, but it's much more of a leap to say that you won't get the right answer as the number of doors increases.
What do you mean infinitely choosing the wrong door?
I mean you'll choose to switch to the wrong door once. Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.Then again. Then again. Then again.
...
It is misleading to think that it's truly 2/3 to switch to the car. And that's because there is nothing to say that you will select those three doors the same amount of times while playing the same game repeatedly, for instance door X 3 times, door Y 3 times, and door Z 3 times as well, which would have to hold true in order for the probability you're claiming to be truly accurate. You with me?
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RE: The role of probability in solving the Monty Hall problem
March 13, 2016 at 8:49 am
(This post was last modified: March 13, 2016 at 8:53 am by Mr.wizard.)
The probability does not change, if you use a pick and hold strategy you will win 1/3 of the time, if you use a pick and switch strategy you will win 2/3 of the time, it's that simple, no it does not guarantee you a car but it is in your best interest to switch mathematically.
The probability holds true, take the 3 door game and play it 50 times ( plenty of simulators on the net) using a pick and hold strategy, then with a pick and switch strategy, you will notice that the probability holds true.
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RE: The role of probability in solving the Monty Hall problem
March 13, 2016 at 8:51 am
(March 13, 2016 at 8:49 am)Mr.wizard Wrote: The probability does not change, if you use a pick and hold strategy you will win 1/3 of the time, if you use a pick and switch strategy you will win 2/3 of the time, it's that simple, no it does not guarantee you a car but it is in your best interest to switch mathematically.
I repeat myself, that would only be true if you knew for sure that no matter how many times the game is played, the number of times each door is picked will be the same, for instance 999999 times each.
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RE: The role of probability in solving the Monty Hall problem
March 13, 2016 at 8:51 am
(This post was last modified: March 13, 2016 at 8:52 am by robvalue.)
I don't think we're even talking about the same game.
You pick a door, the guy opens a door (which is not your door, or the prize door. Important!!!) you stick or change, he reveals the winning door. Game over.
I'm saying if you repeat this game N times, with a genuinely random placement of the prize between the 3 doors each time, on average you will win 2/3 of the time by changing.
It's the mean of a probability distribution. Like I say, if you don't know what that is, you need to learn about it.
I have a first class maths degree, I know what I'm talking about here.
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