Monty Hall Dilemma - Winning a GTI on a Game Show

[Swallowtail]

This IS a mathematical issue. Nothing else. And it's a simple one once you look past your initial response. The simulator Timbo links to is spot on - 41 from 60 wins with switch, 22 from 60 wins with stick. Higher numbers and it would approach the true probability of 66.7% even closer.

Regardless of whether one door WILL be opened, you are choosing from three. If the math is beyond you or you can't be bothered reading it and trying to understand it then at least write out the possibilities so you will see the options...

[Dubya]

You only ever had a 50% chance of winning.

Shouldn't that be 33%? Three doors, only one with a car.

I thought there was consensus that upon first choosing a door there was a 33% chance of picking a winner.

The thing the 50/50s have not explained is how the odds your first pick was correct rise from 33% to 50% upon learning which of the two other doors hides a goat.

You already knew one of them hid a goat. How does knowing which doors hides the goat make your first pick a 50% chance.

That information only has value if you switch to the other, unopened door, effectively allowing you to cover two doors instead of just one. So a 67% chance if you switch.

Cause regardless, the host will open a door, showing a goat. REGARDLESS. (cause he knows where they are)

IF the host RANDOMLY chose a door to open, (and picked a goat) then it would be be different.[/quote.]

You seem to be suggesting that if the host reveals a goat, the odds are different depending on whether he knew the goat was behind the door before he opened it.

But since the host will also show you a goat (regardless of whether you picked a goat or the GTI on the first choice) Which leaves you with two choices. You will always get to the point where you have only two choices. First part of the game is a there only for reverse physchology. (spelling)

That's right - two choices, but each has a different probability of yielding a favourable result.

Sticking with your first guess give you a 33% chance of winning the GTI - nothing can change this. Knowing which of the two other doors hides a goat makes no difference if you decide not to switch as you already knew one of them hid a goat. Whether it is door 2 or 3 makes no difference to your odds.

Switching to the two other doors, one of which just happens to be open, offers a probability of 67% of winning the GTI. Because they cover 67% of the field whereas your first choice covers 33% of the field.

You always had a 50% chance of winning.

Surely not 50% when you pick one from three?

(note this is a game of chance, not probability, no 50/50 game is probability ie coin toss)

While I am uncertain of the distinction, and game of chance it certainly is, there are probabilities associated with each possible outcome and there is a 67% chance one of the two doors you did not choose will hide a goat whether the host has opened one those to doors or not.

[Timbo]

Because there is no cake!

Schroedinger's cat ate it all.

True...and it was yellowcake, too

[team_v]

True...and it was yellowcake, too

That settles it, the cat is dead (In this universe anyway)

[Dubya]

Yea Sorry, I didn't bother to read all 14 pages of theories and such. I just thought I'd throw mine in there to mix it up further.

I approached the problem from an engineering perspective, rather than a mathematical one. Hence why I 'simplified' the problem, before 'solving' it.

Does that mean you have "switched"?

[Jarred]

by my train of thought, switching is an emotional response. The two doors have a 50/50 chance of having the prize, so really, it comes down to luck! A switch would only because by some insecurity/nerves/reverse physcology cause by something that's outside of the simplified problem.

Basically: Do you feel lucky, punk? Well. Do ya?

[Dubya]

There is no need to test something that is mathematical FACT.

ANY choice where there are ONLY 2 OPTIONS is a 50/50, or 1 in 2 chance... It's not a theory.

On the contrary . . .

In theory, if you toss a coin 100 times you will get 50 heads and 50 tails.

In reality you might get something like 44 heads and 56 tails.

So, the "fact" that coin tosses result in a 50/50 outcome is only a theory, not a fact.

The theory is if you choose a door and stick with it you will win 33% of the time.

In reality, you might lose three times in a row and so have 0% success.

In theory, if you switch doors after the goat is revealed, you will win 67% of the time.

In reality, if you switch doors three times consecutively, you might win 3/3 times and so have 100% success.

The only FACTs are:

- There are two theories:

- One is a counter-intuitive theory that is founded in logic (the switching theory); and

- another theory that is based on flawed logic/intuition and says that it makes no difference whether you switch.

Now Coreying wrote elsewhere that what is logical depends on your "perspective".

I do not think logic is subjective.

However, if Rocket would get out three playing cards (2 x same, 1 x different) he would see in very short order that his theory is not supported by reality, whereas the 67% theory holds more or less true.

A shame he won't even test his own theory.

[Dubya]

by my train of thought, switching is an emotional response. The two doors have a 50/50 chance of having the prize, so really, it comes down to luck! A switch would only because by some insecurity/nerves/reverse physcology cause by something that's outside of the simplified problem.

Basically: Do you feel lucky, punk? Well. Do ya?

I seem to have erred . . . you're sticking with your 33% first choice . . . your post about not reading all 14 pages led me to believe you were acting on a misapprehension.

[Jarred]

No. I think you seemed to have misread my point in it's entirety.

Step back once step.

The game show host will ALWAYS show you a goat - regardless wether you picked a goat or the GTI.

It simplifies down: You never had three options, only two. you can only choose a goat or GTI (two options not three). hence why uou have a 50/50 chance, and hence why it comes down to chance/luck. (regardless of wether you change your choice after the first illusion.)

(to eleborate: regardless of whether you pick a goat or GTI from the first 3 doors, the host can always pick a door with a goat. which eliminates one door and leaves you with two doors> one with a goat, one with a GTI. thats the part where it boils down to 50/50. The host's choice of door isn't dictated at all by your choice, He always chooses a goat, it's merely an illusion to create the insecurity in your choice, more for TV ratings than anything else.)

just my take on it all anyways.

[Rocket36]

Sorry I should have been clearer when defining exactly what I was referring to when I was referring to fact. The CHANCE you will win is 50/50 (or 1 out of 2) when there is two choices. THAT is mathematical FACT and cannot be disputed. Since the second choice is only ever from 2 options, you have a 50% CHANCE of winning and a 50% CHANCE of losing.