Monty Hall Dilemma - Winning a GTI on a Game Show

[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.

[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.

[Flighter]

*sigh* re-read my last post BTJ because your entire post is a waste of time... You (and others) are completely missing my point regading 50% or 50:50 or 1 in 2. The original choice when there are three options has NOTHING to do with my point.

Meh. I don't care anymore.

You appear to be falsely assuming that because there are two doors left the odds somehow shift back to 1 in 2. They do not, as this is not a case of random probability (like tossing a coin), but rather one of conditional probability. This has been mentioned in the past, but you still appear to cling to the notion that somehow a choice from 1 in 3, or 1 in 1000 or whatever miraculously becomes 50:50 as soon as all but two of the doors are opened. It therefore appears that in your case a little bit of knowledge is more dangerous than none at all, for in the latter instance you would probably be more open minded about simply trying it for yourself. I'm assuming that you haven't tried it because you haven't reported that you either (a) ran the simulator and were proven right, or (b) you ran the simulator and were proven wrong. Interestingly, this presents two outcomes too, but the odds aren't 50:50 in this case either, as the odds you were proven right are zero.

Then again, maybe the Monty Hall problem is another of those global conspiracies everyone else is in on and the joke is on you.

[Rocket36]

*sigh* re-read my last post BTJ because your entire post is a waste of time... You (and others) are completely missing my point regading 50% or 50:50 or 1 in 2. The original choice when there are three options has NOTHING to do with my point.

Meh. I don't care anymore.

[BTJ]

Rocket,

after the door has been opened revealing a goat, leaving two doors to open your chances are not 50;50 if you stay with your original choice. Youve got that don't you?

Youre original choice was a one in three chance and if you stay with your original door, you stay with your original odds.

Put it like this.

3 doors.

You pick one.

Host opens the first door. Goat.

Host doesnt ask you to switch or stay and opens another door. Goat

You have a car behind your door! Yay!

1/3 correct?

Same again

3 doors.

You pick one.

Host opens the first door. Goat.

Host asks you switch or stay? Stay

Open the second door, goat.

You have a car! Yay!

1/3 chance

Now play that out over time and the odds are not in your favour that you are originally going to pick the car.

It is not a 50/50 or 1/2 chance if you stay with your original choice. If you only make one decision it doesnt matter if the door is opened because you arent removing it from the odds by switching, you are playing your original guess and original odds, not a 1/2 choice.

[schoona]

I can think of 2 scenarios where there is a 50/50 chance.

1. The host opens one door (goat) before the contestant makes his intial choice.
2. THe contestant picks a door. The host then opens another door without knowing where the car is, and it turns out to be a goat.

Thats just moving the goal posts. Pointless....

[Rocket36]

So if Australia plays Brazil in the final of the World Cup, does that mean we have a 50% chance of winning? (Since there are only 2 option:win or lose, draw is not permitted).

I hope you don't work for Tabcorp!

No - that's completely different scenario where there are quite clearly more than two possible outcomes.

Rocket, whatever the case, you've not yet agreed with those of us who have said that you should switch after the first goat is revealed because doing so doubles your chances from 1/3 to 2/3.

No - because that has nothing to do with my point, which is that where there's a choice that only has two possible outcomes, the chances are 50% or 50:50 or 1 in 2. And THAT IS A FACT THAT CAN'T BE DISPUTED. Like the toss of a coin... Pick heads or tails... The chance of being right is 50% or 50:50 or 1 in 2. Pick one of these two cards/windows/doors/etc... The chance of picking the right one is 50% or 50:50 or 1 in 2.

And as far as I can tell from your post above, you still believe you have a 50% chance of winning if you stick with your original choice and this, as has been explained in many different ways, is not correct.

Where have I said that? Your choice between two options is 50% or 50:50 or 1 in 2. That's all I'm saying.

You now appear to be suggesting that you would be willing to switch even though you believe your odds would not change.

If you believe that, why would you switch?

WTF? How do I appear to be suggesting that? If you start using the term ODDS, is in odds of winning this particular game, then that's different as ODDS take into account more than the choice of two options.

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.

As you claim there is no benefit to switching, I cannot understand why it was unreasonable for anyone to infer that you would be disinclined to go against your initial instinct.

Not claiming that.

After all, if you believe the odds will not change whether you switch or not, most people would probably be more disappointed if they switched and lost than if they stuck with their initial choice and lost.

Whatever the case, as you seem to be firmly of the belief that the odds are 50% after the first goat has been revealed, your position on switching would seem to be more influenced by whimsy than by reason.

Like I said, ODDS of winning THIS SCENARIO is completely different to the mathematical fact that having two possible outcomes, no more, no less for anything means that the chance of picking one is 50% or 50:50 or 1 in 2.

funny reading this thread and watching people hold on for so long to the thought that it is a 50/50 chance.

How they can come to this conclusion when they made their choice from one of three doors makes me laugh.

1 of three doors would be 33.3% or 1 in 3. But the people talking about 50% or 1 in 2 aren't talking about three doors. They're talking about two.

No short of drawing diagrams for people, I can't be much clearer that all that. If you still don't understand that the second choice is a is 50% or 50:50 or 1 in 2 chance of picking one or the other then there's nothing that will explain it to you.

[Achtung Tiggy]

funny reading this thread and watching people hold on for so long to the thought that it is a 50/50 chance.

I can think of 2 scenarios where there is a 50/50 chance.

1. The host opens one door (goat) before the contestant makes his intial choice.
2. THe contestant picks a door. The host then opens another door without knowing where the car is, and it turns out to be a goat.

[BTJ]

funny reading this thread and watching people hold on for so long to the thought that it is a 50/50 chance.

How they can come to this conclusion when they made their choice from one of three doors makes me laugh.

Top thread.

[Treza360]

hahahaha.... no....... have you seen how many pages of **** there is!

Well here's the link. Play and learn: Simulator
Cheers,
Trent

[GTom]

Did you even play the games linked to earlier in the thread?

hahahaha.... no....... have you seen how many pages of **** there is!

[Timbo]

1/2 < 2/3 chances of loosing
1/2 > 1/3 chances of winning...


....I personally wouldn't change though....

That's the natural, intuitive process. But the game doesn't work to that logic. So, you'll probably lose 2 out of every 3 games.

[Treza360]

I look at it this way.
You have a 2/3 chance that the door you picked is incorrect.
When offered the chance to change the first door is out of the eqn. as you can't pick that door again you're left with a 1/2 chance the prize is behind the door.
1/2 < 2/3 chances of loosing
1/2 > 1/3 chances of winning
So you have a greater chance of not getting the prize with 3 doors in play.
That said you might have been lucky enough to pick the right door to begin with
I personally wouldn't change though....

Did you even play the games linked to earlier in the thread?

[GTom]

I look at it this way.

You have a 2/3 chance that the door you picked is incorrect.

When offered the chance to change the first door is out of the eqn. as you can't pick that door again you're left with a 1/2 chance the prize is behind the door.

1/2 < 2/3 chances of loosing
1/2 > 1/3 chances of winning

So you have a greater chance of not getting the prize with 3 doors in play.

That said you might have been lucky enough to pick the right door to begin with

I personally wouldn't change though....

[Dubya]

Can someone please tell me where I've said I wouldn't switch and that I have a 50% chance of winning? ALL I HAVE SAID is that when you have a choice between two options, with ANYTHING the result is one or the other, or 1 in 2, or 50:50. Therefore, the second choice has a 50% chance of picking the car. and a 50% chance of picking the goat.

Give someone two choices, get them to pick one only and they hav e a 50:50 choice. THAT is basic maths and if you don't understand that I'm sorry, go back to primary school.

Oh, and I live in Melbourne at the moment.

Rocket, whatever the case, you've not yet agreed with those of us who have said that you should switch after the first goat is revealed because doing so doubles your chances from 1/3 to 2/3.

And as far as I can tell from your post above, you still believe you have a 50% chance of winning if you stick with your original choice and this, as has been explained in many different ways, is not correct.

You now appear to be suggesting that you would be willing to switch even though you believe your odds would not change.

If you believe that, why would you switch?

As you claim there is no benefit to switching, I cannot understand why it was unreasonable for anyone to infer that you would be disinclined to go against your initial instinct.

After all, if you believe the odds will not change whether you switch or not, most people would probably be more disappointed if they switched and lost than if they stuck with their initial choice and lost.

Whatever the case, as you seem to be firmly of the belief that the odds are 50% after the first goat has been revealed, your position on switching would seem to be more influenced by whimsy than by reason.