MONTY HALL DILEMMA

[Ghost Post]

Understanding that you can double your chances of winning if you always change your mind consider the following.

If just after you change your mind an innocent bystander from outside is pulled in and offered a choice of either of the 2 remaining doors and he always decides to pick the door that you didn't select what happens ?

Person A should double his chances if we are to believe the majority opinion. On the other hand person B who has no involvement of the history to that point quite definitely has a 50/50 chance of picking the right door. And yet, if person A really does double his chances then person B should increasingly frustrated that he is losing more than he is winning over a period of time even though he has a 1/2 chance. Does person B's world really change because of the history of person A's world ? Hmmmm

[HyToFry]

[Tom]

I seem to remember their being a discussion about this; it's about whether probabilities are attatched to physical things or not .. and they're not. E.g. is the chance of a flipped coin being a head 50%? Not if you have enough information about how the coin is thrown.

So, the person coming in. If they know what has been going on so far, then they have the same prob as the contestant for the doors. If they don't know, then they have 50% for each. It's about information.

It's like "I've flipped a coin. What is the prob. it is a head?" For you it's 50%. For me it's either 100% or 0%, as I know which side it landed on. However, you don't say that we are both living in "different worlds".

[Tom]

Oh, I should have read the preceding posts properly. If he always "randomly" decides to pick the door you didn't, then he is on one hell of a statistical fluke, which obviously screws up his results.

[Wonko the Sane]

As HyToFry said, if he always picks the door that you didn't, his chances are 1/3, not 2/3, because it isn't random.

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It's not the size of the spork, it's whether or not it's made of #7 recyclable plastic.

[Andy]

If he knows what's going on in general, and knows which door you ended with, but not which door you picked originally, then his choice indicates his opinion of your intelligence.

[GiarcIII]

Why does the Monty Hall Problem cause such a stir.

Consider 3 doors, 1 Car, 2 Goats

I Select a Door

I have Either selected a car or one of the goats.

The Host then has either a choice of goat (if I have picked the car) or he must pick the remaining goat

The remaining door will conceal a car if I picked a goat on the first trial or a goat if I picked the car.

The reveal by the host tells me nothing except which door to change for.

The Sample Space Is as Follows

ME Host Door 3
Goat1 Goat2 Car
Goat2 Goat1 Car
Car A Goat Other Goat

If before we play the game I decide not to change then I win 1 out of 3 times

If before we play I decide to change then I will win 2 out of 3 times. Therefore I will change my mind.

[Ghost Post]

According to the Monty Hall solution, changing your choice increases your odds of winning from one in three to two in three. The problem that I have with this solution is YOU ONLY GET TO PLAY ONCE. Even if you played three times, you don't necessarily win once by sticking with your first choice, nor twice by changing your mind. I played the simulation twenty-four times and the results still didn't conform to the prescribed probability. This brings up a broader question: What relevance does probability have when applied to a singular instance. Imagine a test that, statistically, only one in ten high school seniors will pass. Given a group of 100 students, it is safe to assume that ten students will, in fact, pass. But is it meaningful to say that a student has a one in ten chance of passing. I realize this analogy is a bit flawed, but I think it makes the point. I find this topic fascinating, and would appreciate input from someone who knows more about statistics than I do.

[Ghost Post]

So if I understand, your question really has nothing to do with the Monty Hall puzzle in particular.

I mean, if you could only get to play once, and were not allowed to switch, you would have the same problem with saying you have a one in three chance of winning, right? If, on the other hand, you don't have a problem with that, then you should be able to accept a two in three chance of winning if you switch.

[Wonko the Sane]

MSG, look at it with the deck of cards example. Say someone offers you a deck of cards, face down, and says "pick any card, you win if you have the ace of spades at the end of the game". If you have the ace of spades, they'll drop 50 random cards, leaving them with one. Otherwise they'll drop all but the ace of spades. Then they'll offer you the chance to switch. Are you going to switch? Even if you can only play once?