Monty Hall Dilemma - Winning a GTI on a Game Show

[Rocket36]

So Flighter is another person that can't read... I'M NOT TALKING ABOUT THE ODDS. Jesus Christ!!! People need to STOP making assumptions and actually READ what I'm saying.

As for your smart arse under tones and attempts to belittle me Flighter, well I'm sure you feel way better about yourself but you won't get me to bite. Back in your box.

[Dubya]

If I was playing this particular game, I would switch (obviously). That doesn't change the fact that out of two options, the chance of picking one is 50% or 50:50 or 1 in 2.

If Rocket believes that the chance of picking the right door is 50%, can he set out his rationale for switching?

If the 50% chances he claims he has of picking a winner amongst the two remaining doors is relevant (as he seems to be claiming), why should it be obvious that he would switch from his first choice?

By his rationale, this would seem to give him the same 50/50 chance of winning.

67%ers state that one's chances of winning double (ie from 33% to 67%) if you switch.

If all Rocket is saying is that one has a 50% chance of picking right when given two options, I do not know why something so axiomatic needs to be stated in the context of the Monty Hall Dilemma.

Everyone knows about 50/50, however such a probability does not arise in the normal playing of the game, as has been explained in many different ways.

So it remains a bit of a puzzle as to why Rocket feels compelled to labour such an obvious point as 50/50 when it is irrelevant in the context of the Monty Hall Dilemma.

I can assure Rocket, the reason people are resisting his line about 50/50 is not because they do not understand it, but rather because it is wholly irrelevant to solving the Monty Hall Dilemma, as they have tried to say.

Perhaps Rocket can explain once and for all:

- Why he believes 50/50 has anything to do with the Monty Hall Game; and

- Why it should be obvious that he would switch,

as the two concepts are logically irreconcilable.

[Timbo]

All Rocket is saying is that the probability, given two doors, is 1 in 2 or 50:50, which I think we all understand, and is not in contention. Why he continues to say that, given it is totally irrelevant to the probabilities associated with the dilemma, escapes me!

[Rocket36]

The second choice in the context of the chances of picking something out of the two options is ALWAYS 50/50 regardless of the circumstances that surround that choice.

The second choice in the context of winning in this scenario is quite different, is based on odds and NOT chance, and it's NOT something I have been basing my point on AT ALL.

All Rocket is saying is that the probability, given two doors, is 1 in 2 or 50:50, which I think we all understand, and is not in contention. Why he continues to say that, given it is totally irrelevant to the probabilities associated with the dilemma, escapes me!

Since people were using the term CHANCE a LOT I have been trying to point out that chance is always 50/50 in this scenario when referring to the second choice. The odds of winning are completely different.

[Dubya]

Since people were using the term CHANCE a LOT I have been trying to point out that chance is always 50/50 in this scenario when referring to the second choice. The odds of winning are completely different.

Based on that one could infer that Rocket believes that the "odds" of winning, whether you switch or not, are 2:1.

But, no, when playing the game as described:

- The chance (or probability) that you will win if you do not switch is 33%.

- The chance that you will win if you do switch is 67%.

50% does not come into it in any way if you are playing the game as described. If it does come into it, why would you go against your gut instinct and switch?

Odds are the inducement a bookie would offer someone to encourage them to bet on the outcome of the game and are expressed as the inverse of the probability (or "chance") when no margin is added. However, the terms "probability", "chances" and "odds" are being used to mean the same thing and so are interchangeable for the purposes of this discussion. Only the inverse of the bookie's odds for each outcome would add up to more than one due to their profit margin (eg odds of $1.90 on the toss of a coin).

But the probabilities/chances for each possible outcome for this game will all add up to 1 (eg 33% + 67% for the first-chosen door and the other closed door, respectively).

The problem seems to be that, so far, Rocket has talked about a 50/50 "chance" (when it is 33/67 after the first goat is revealed) but has not said what he believes the completely different "odds" of winning are. But we can infer from this that Rocket believes the "completely different" (but related) odds are 2:1.

However, Rocket only gives half a view and unfortunately it is misleading as the chances/odds/probability are never 50% in this game.

Bottom line is, Rocket has said:

He has a 50/50 chance yet he would still switch, but without providing his rationale for doing so.

It simply does not make sense to say that you would "obviously" switch if you believe each choice provides an equal chance of success.

[Jarred]

You're taking this all very serious arent you Dubya?

Was monty hall a great uncle of yours or something?!

[Rocket36]

Bottom line is, Rocket has said:

He has a 50/50 chance yet he would still switch, but without providing his rationale for doing so.

STOP MISQUOTING ME!!! I have NEVER said the chance of WINNING THIS SCENARIO is 50/50. ALL I have said is that when there are two choices to pick from and you can only pick one, that you have a 50/50 chance of picking the car. AND THAT IS TRUE!!! The chances of winning based on ANY other information are not a factor in that. And I have not once said I would switch based on a 50/50 chance.

If you can't read what I'm saying, don't respond.

[Dubya]

STOP MISQUOTING ME!!! I have NEVER said the chance of WINNING THIS SCENARIO is 50/50. ALL I have said is that when there are two choices to pick from and you can only pick one, that you have a 50/50 chance of picking the car.

And if you pick the car you win, so a 50/50 chance of winning, is what Rocket is saying, if one may be so bold.

Or is Rocket suggesting that "winning" and "picking the car" are not the same?

Or that a 50/50 chance of picking the car does not mean a 50% probability of winning the car?

No wonder people are confused.

AND THAT IS TRUE!!! The chances of winning based on ANY other information are not a factor in that. And I have not once said I would switch based on a 50/50 chance.

But previously:

If I was playing this particular game, I would switch (obviously). That doesn't change the fact that out of two options, the chance of picking one is 50% or 50:50 or 1 in 2.

More confusion.

So on what statistical basis would Rocket switch?

Rocket has already explained how one's chances of picking the car (aka "winning") are 50/50, so why would Rocket switch?

If you can't read what I'm saying, don't respond.

I have no idea what Rocket's position is or the distinction he is attempting to make.

However, once and for all:

Can he kindly explain why he would swtich?

Can he explain what the probabilities are of winning the car:

- if he switches? and

- if he sticks with his initial guess?

That is what this thread is all about.

50/50 does not come into it in terms of "chance" or anything else.

So why does Rocket keep saying there is a "50/50 chance".

And why does Rocket not answer the question or explain why he would "obviously" switch?

All we have seen is 50/50 - nary a mention of 1/3 and 2/3 chances after the first goat is revealed, strongly suggesting Rocket does not subscribe to the theorem that switching after the first goat is revealed doubles the contestant's chances from 33% to 67%. A principle with which Rocket appears to have been arguing against from the outset.

[Rocket36]

OH... MY... GOD...

Pick ONE of these options only:

A or B.

Picked one? OK... You had a 50/50 chance of picking whatever you picked.

Pick ONE of these options only:

Card A (with the car) or Card B (with the goat).

Picked one? OK... You had a 50/50 chance of picking whatever you picked. STOP THINKING ABOUT THE FACT YOU STARTED WITH 3 CARDS!!! That way you might have a chance at understanding this exceedingly basic concept I'm explaining. The fact you have additional information that means you are more likely to pick what you want out of those two, doesn't change the fact that you can only pick ONE OUT OF TWO!

If you still don't get it, then I suggest registering for some primary school classes... I'm done.

[Timbo]

Rocket -- of course we all understand that. Don't be so precious. This is about chances in a game with rules. These rules affect the chances associated with choices at different points in the games, since you are given, not one choice, but two

The game doesn't start with two doors; it starts with three, and you are told that behind one of the doors is a car, and behind the other two are goats. You are asked to pick one door. At this point, your chances of picking a goat are 2 in 3, and of the car, 1 in 3. You pick a door.

The host now picks one of the other two doors, opens it, and reveals a goat. The host knows what is behind each door and the rule is that he'll always reveal a goat.

The host then asks you if you want to keep your original chosen door, or change to the remaining door. What do you do?

Yes, you have a choice of two doors at this stage. But NO, the chance that the door you originally chose hides the car is NOT 1 in 2, or 50:50; it is, as proven, 1 in 3.

This is because THAT door still derives the 2 in 3 chance of hiding a goat associated with your choice in the first round, when there were three doors. Whereas, if you change your choice to THE OTHER DOOR, the chances it hides the car are NOW 2 in 3. Despite what one's intuitive logic makes you think, there is NO 50:50 chance EVER in this game, as explained above and throughout the thread. The End