Monty Hall Dilemma - Winning a GTI on a Game Show

[Buller_Scott]

[QUOTE=Spilledprawn;478589]

IF the host revealed that OUR DOOR had a goat and invited us to change, then our chances are resolved to 50/50 (only this removes the dependancy of the original choice)

[QUOTE]

isnt that precisely what happens in this particular scenario, that the host knowingly selects the first door to be opened as one which houses a goat, THEN he asks if you want to switch?

a couple of thread pages ago, there was some discussion in which the function of the host was established as intentionally opening a door which he knew housed a goat, before asking the contestant if he wants to switch.

[schoona]

http://www.youtube.com/watch?v=7SjFJImg2Z8

[Spilledprawn]

no to claim, but i did 4 unit maths in year 11/12. that was 13 hours of math classes a week BEFORE homework/ study/ assignments. i KNOW probability, and any comprehensive mathematical explanations in this thread are REAL, and CANNOT be disproved by some playing cards from the local $2 shop. my explanations have a basis in mathematics, in mathematical probability.

i?

It's interesting you place so much value on "mathematical probability" above "some playing cards" when the cards will actually prove the reality

Okay, before we start the game we know with absolute conviction that out of the 3 doors, one has a car and two have goats.
We make our choice of the doors - and have a 2/3 chance of picking a goat
We know that of the two remaining doors - at least one will have a goat.
We know that the host will reveal a goat, it doesn't matter which one of the two remaining doors that goat is behind, we already know it exists, and knew it when we made our original decision. We are therefore better off switching.

IF the host revealed that OUR DOOR had a goat and invited us to change, then our chances are resolved to 50/50 (only this removes the dependancy of the original choice)

If the host doesn't open any doors at all, and you're invited to change, the chance remains 1/3

Please try it with a set of cards, it will only take a few minutes. It isn't magic, it is just maths.

[Buller_Scott]

you're being way too presumptuous.

it's not about ''being the big man, being humble, being honest", nor about being "terrified" to admit that someone on the other side of the fence may be right.

no to claim, but i did 4 unit maths in year 11/12. that was 13 hours of math classes a week BEFORE homework/ study/ assignments. i KNOW probability, and any comprehensive mathematical explanations in this thread are REAL, and CANNOT be disproved by some playing cards from the local $2 shop. my explanations have a basis in mathematics, in mathematical probability.

i am only too willing to admit that my earlier explanations were somewhat presumptuous as i had neglected the vital fact that the game was rigged by way of the host's intention to reveal a goat behind the first door, and that that fact lends itself somewhat as an odd in the contestant's favor, should you be determined to treat progression of time throughout the gameshow as static, and mutually exclusive to the progression of the opening of doors.

in the same way that the proponents for the 50/50 argument may be ''afraid to admit'' whatever it is we should be admitting, the proponents for ''2/3'' seem to be ''afraid'' to explain just how a game show's events can proceed when time is not?

[Flighter]

I give up!

I'm not surprised. This is so obvious from both the video and diagrams that people have posted, plus the multiple explanations that this is not a case of random probability. Heck the only reason it is so interesting is *because* it seems counter-intuitive.

Of course this is also easy enough to try at home, yet I bet there are those among the disbelievers who probably won't do this because they deep down they know they will be found to be incorrect and are afraid to admit as much, even if only to themselves. John F. Kennedy's ratings in the political opinion polls *rose* after he admitted to the public that he blew it with the Bay of Pigs fiasco, but not everyone understands that it's okay to be human and hence be wrong sometimes.

[Timbo]

I give up!

[team_v]

The host opens a door, revealing a goat. Previously, that door had a 1 in 3 chance of hiding the car, but it didn't. It had a 2 in 3 chance of hiding a goat, it did, BUT IT WASN'T A RANDOM CHOICE by the host.

Critical to the logic here is that the host is always going to pick a door hiding a goat. IT IS NOT A RANDOM CHOICE, it is a game.

The issue I have is that since the host is always going to reveal a goat, why bother even including that information/door in the scenario since it will never be the car and hence, removes 1 door from your next choice, resetting the statistical probablility of one of the remaining 2 doors holding the gti to 50/50.
The host may have known but your choice was still random and the statistics then say you have a 50/50 chance.

1 door has been revealed and has a goat.
2 doors remain, 1 (goat) and 1 (GTI). (statistics will reset due to the fact there are now only 2 choices)
50:50 chance.


Yes originally the chances of your door were 1/3 however a door has been revealed, removed from your choice (if you want the GTI) and thus you only have 2 doors remianing so the 1/3 chance is no longer valid as there is only 2 doors you would logically choose from.


However, we can all rest happily in the knowledge that no matter what choice we make, one of the 3 eventualities that split off from this scenario will win the GTI so we will have won in some alternate universe if we don't win in this one.


Also take note that most game show hosts will try to make you choose another option anyway if you are going for a big prize (see who wants to be a millionaire and all that)
They only help you out when the prize pool is quite small.

[Timbo]

Regardless of what ANYONE says, the second choice is ALWAYS going to be 50/50. That is mathematical FACT and anyone who disagrees with that is simply wrong. When choosing between two things, whatever they are, it's ALWAYS 50/50, or 1 in 2.

Geez, Rocket, you're a stubborn bugger

Yes, you would be ABSOLUTELY correct, if we were dealing with simple probabilities here, as expected when dealing with RANDOM choices. But we are NOT dealing with simple RANDOM CHOICE probabilities here, we're dealing with Bayesian probability, where probabilities change during a process because of additional information. In this case, a dependency.

Original, blind choice: 1 in 3 you'll pick the car; 2 in 3 you'll pick the goat

The host opens a door revealing a goat. This gives you new information. It is absolutely intuitive to conclude that the probability your original door hides a goat is 1 in 2. BUT THAT'S INCORRECT, and is the common mistake people make when thinking about this problem, including lots of mathematicians.

The host opens a door, revealing a goat. Previously, that door had a 1 in 3 chance of hiding the car, but it didn't. It had a 2 in 3 chance of hiding a goat, it did, BUT IT WASN'T A RANDOM CHOICE by the host.

Critical to the logic here is that the host is always going to pick a door hiding a goat. IT IS NOT A RANDOM CHOICE, it is a game.

So, you are now facing two doors. Oh, so very, very easy to conclude the odds are now 1 in 2, so no need to change. But hesitate. Think. (PLEASE...it may help you win a car one day )

Try this:

"The chances that my door now hides the car would be 1 in 2 IF (and only if) the revealed door had been chosen randomly. But it wasn't. This isn't random probability. This is a game

"When I made the first choice, the chances were 2 in 3 I'd pick a goat. Monty opened another door, revealing a goat. Even though he's done that and it seems my chances of the car are now 1 in 2, actually the probability for my original door remains 2 in 3 for the other goat. So I'd be better off changing to the other door because the chances it contains the car are now 2 in 3" (see the calculation)

[Buller_Scott]

oh no she di'dent!

[gregozedobe]

Regardless of what ANYONE says, the second choice is ALWAYS going to be 50/50. That is mathematical FACT and anyone who disagrees with that is simply wrong. When choosing between two things, whatever they are, it's ALWAYS 50/50, or 1 in 2.

I vote for Rocket36 for the award of "Statistician of the year" (for being so positive in his opinion and able to ignore inconvenient facts like there were 3 doors, and the host deliberately opened one that he KNEW had a goat behind it).

I'm sure there are a few Canberra-based spin doctors who could use a man with these skills

[Rocket36]

Regardless of what ANYONE says, the second choice is ALWAYS going to be 50/50. That is mathematical FACT and anyone who disagrees with that is simply wrong. When choosing between two things, whatever they are, it's ALWAYS 50/50, or 1 in 2.

[VW Convert]

has anyone suggested listening out for the goat?

Using your sense of smell would probably be a better choice!

Cheers

George

[bombsquad21]

has anyone suggested listening out for the goat?

[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.

[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?