Monty Hall Dilemma - Winning a GTI on a Game Show

[BTJ]

Rocket it's not about the choice in isolation. The problem is bigger than that. The fact remains that you have a one in three chance when you select the first door. If you retain tht door you retain that probability.

[pixl]

Do we start on schroedinger's cat?

Stop it!

[Buller_Scott]

well %$#@ me drunk... this is insane.

i was right, and everyone who doesnt agree with me 100% is wrong. now, greetings aside...

this talk of the host playing a part is interesting. if you take into account that the host KNOWS which door houses the gti, and presuming that the host's function in this wank fest is to attempt to curtail the guy's winning the gti, AND that the host MUST allow the person to switch, then yes, the chances of winning the gti are 2/3.

but NOT because of magic or counterintuitiveness or whatever, but simply because one of the doors is not a probability at all- it's a certainty- the host will make you pick a goat, you confirm 1/3 of the doors as being a failure, and the host allows you to switch. 2/3. done.

take the host's knowledge and conniving, scheming, pre-planned ways out of the equation, and THEN you're dealing with REAL probability, as practiced in math (not in the quiz section of the paper).

if, however, all this talk about the host's past, his discussion with the producer, the game fixing and all that is dismissed, then the odds revert back to 1/2. or rather, they evolve into 1/2.

good one, guys! a thread like this each week and i can stop trying to bloody solve sudoku.

edit: sorry, i just read the riddle again. the whole thing is hinged on the host selecting the first door, knowing that it will be a certain failure. this initial certain failure lending itself to the odds being 2/3 instead of 1/2 speaks to the riddle's explanation refusing to acknowledge the dynamism of a real life scenario. basically, the riddle's explanatory success hinges on the events in the riddle (opening doors) being allowed to unfold, but NOT the timeline of the event (and with the timeline, the odds).

funny thing is, at the time that the host tells the person that they have to make a decision as to whether or not to switch, things look like this: there's a 50/50 chance that he will switch FROM the door with the gti behind, and a 50/50 chance that he will switch TO the door with the gti behind it. hence 50/50. could go either way.

see my dubfest example. 20 tickets sold, ten eliminated as duds, you hold one of the last ten. your odds of winning (even if the host knew beforehand that the ten tickets you were to successively select when you switched) are NOT eleven in twenty.

[schoona]

You love it Scotty.
Just like I love the puss...
Cat is on thw agenda for next week

[Timbo]

The role of the host is central to the game. He will always reveal a door with a goat behind it. The change in probabilities which (should) prompt the player to switch derives from this.

Schroedinger's cat is about quantum physics, isn't it? If you think about that stuff too hard, pretty soon you'll doubt your existence

[Buller_Scott]

yeah, i constantly refer to the OP as a ''riddle'' because i saw a very similar scenario in a riddle book, and as such i took for granted the importance of the host in this case.

gotta ch-ch-check this schroedinger cat thing out.

[team_v]

Schroedinger's cat is about quantum physics, isn't it? If you think about that stuff too hard, pretty soon you'll doubt your existence

Bingo about the cat.
Wiki it, very interesting but your head starts to hurt a bit after too match quantum physics.

[Flighter]

Wrong. And that picture is also wrong as it doesn't show all the options and combinations.

What are the other options and combinations exactly?

[gti]

Regardless of statistics etc I will still stick to my initial choice.

[Flighter]

I'm somewhat of a sceptic since there will always be a 50/50 chance on your second choice, however looking at your options (which I stole from the wiki) it looks like this, crazy, but switch does *statistically* win twice as often if you get a chance to make a second choice:

I think another problem the naysayers are having in accepting that switching is a better option is that they are assuming the two selections are independent events.

By way of explanation, flip a coin two times, and the result of the second flip is independent of the first (meaning it wasn't influenced in any way by the first), and hence the odds are 50/50 each time.

Next consider trying to pick the ace of spades from a well shuffled deck of cards. The odds for this would be 1 in 52. If you replace the card, shuffle and pick again, the odds remain 1 in 52, making the selections independent. If you do not replace your initial selection, the odds shorten to 1 in 51 (assuming your first selection wasn't the ace of spaces of course), as the loss of one card creates a dependency between the two selections, which affects the odds on the second selection.

The Monty Hall problem isn't a case of independent events, as Monty eliminates one of the doors, creating a dependency between the two selections. This is especially so as Monty isn't eliminating a door at random, but rather knowingly eliminating a goat. This means this doesn't remain a case of random probability, but instead turns into one of conditional probability.

This answer is easily demonstrated at home with the help of a friend, so there is an opportunity for those who doubt its veracity to try it and see for themselves. The more you do the exercise the more the results of switching will indicate a win 67% of the time (meaning that if you did the exercise, say, 100 times, about 67 times out of the hundred times you did it you would have won the car by switching. I'm not suggesting that you need to do it this many times to see the trend though).

[abreut]

Regardless of statistics etc I will still stick to my initial choice.

You realise that is the definition of insanity

[gareth_oau]

I agree fighter. In my initial skepticism, I was lazy, and failed to read the situation properly.

However, as its been a debated topic, I went back to the original posting and have a re-read it.

i now agree that switching increases your probability of winning, but doesnt guarntee it

but it should be understood that if you did choose the car first up (and of course, you don't know this), and still switched, then switching guarantees you loose.

Of course, if you chose the car initially, then switched and lost, you will be the laughing stock of the whole world, even if your choice to switch was statistically better

[Buller_Scott]

hold on hold on......

i think that this debate had pretty much come to a stalemate and isnt progressing anywhere.....

it'd probably be in the best interests of all involved (as well as the debate) if we started with a clean slate at square one.

this time, i think i will try to prove the 2/3 theory correct via mathematical exemplification. perhaps if some of the others also shift sides it might provide a bit more clarity when their argumentative style is applied to the opposite side of the debate?

sounds reasonable, yeah guys?

[BTJ]

http://www.theproblemsite.com/games/monty_hall_game.asp

PLay it. learn. deal with it.

I cant see how people are still arguing the toss. the host cant manipulate mathematics. It doesnt matter if he opens a door with a goat in it.

If you stick with your choice you are sticking with your original 1/3 choice.

[bombsquad21]

has anyone suggested listening out for the goat?