Monty Hall Dilemma - Winning a GTI on a Game Show

[gregozedobe]

Give the man a Kewpie doll! Pontiac called it a tripower.

Yes, all proven ways of getting your fuel consumption down into single figures. Unfortunately in those days they were measuring in mpg, and unlike l/100km, single digits mpg is NOT a good thing I'd hate to do a lot of driving in one of those beasts these days if I was paying for the fuel out of my own pocket.

[Flighter]

Give the man a Kewpie doll! Pontiac called it a tripower.

Did Holden have a catchy name for the triple side-drafts on the XU-1?

[gti]

I'd stick to the # I originally chose. If someone asked you to swap lotto tickets with you would you swap knowing the probabilities are the same. Maths isn't my forte but I certainly wouldn't be swapping nor choosing a different door.

[JustCruisn]

http://www.youtube.com/watch?v=VM3teHj3ZgY

[The_Hawk]

I'd stick to the # I originally chose. If someone asked you to swap lotto tickets with you would you swap knowing the probabilities are the same. Maths isn't my forte but I certainly wouldn't be swapping nor choosing a different door.

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:

[Rocket36]

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:

Wrong. And that picture is also wrong as it doesn't show all the options and combinations. What it should do is break down what also happens when you don't switch. If it did that you would see an even 50/50 split of winning/losing.

This whole argument is all probability and it's very basic. Regardless of what anyone says, or what wiki says, it's as simple as follows:

First choice is 1 out of 3 chance of picking the car.
Second choice is 1 out of 2 chance of picking the car (regardless of whether or not you've picked it already).

Basically, you will always have a 50/50 chance of winning this. You never have a 33% chance of winning because even when you pick the car on the first choice, probability is reset when you get to make a second choice, even if that second choice is to stick with the first choice.

[The_Hawk]

Basically, you will always have a 50/50 chance of winning this.

I agree, second time around it's always going to be a 50/50 shot at the car.

...But then that diagram does actually show all the options. Seems if you blindly take the option to switch choices after being shown one of the goats you technically increase your chances to 2/3 (based on the original three doors you could have chosen).

[Rocket36]

I agree, second time around it's always going to be a 50/50 shot at the car.

...But then that diagram does actually show all the options. Seems if you blindly take the option to switch choices after being shown one of the goats you technically increase your chances to 2/3 (based on the original three doors you could have chosen).

Second time around is all that counts.

But regarding switching the second time around, that's only half your options. The other half is to not switch. You need to take ALL options into account if you're going to talk about your chances of winning. And if you do take into account that you can switch or not switch, you only ever win 50% of the time.

[Buller_Scott]

ahhhh yeah my sister gave me a riddle book with this one.

the book said the chances of winning the gti were now 2/3, even though (as a math jock in high school- 4 unit baby!) in my mind, the odds remain at 50/50 by process of elimination (of the first door).

the flaw with the ''riddle'' is that it's using a static set of probabilities: whilst the chances of getting the gti are 1/3 initially, they eliminate one of the doors and yet retain it in as an element, telling you "door one's been exposed and thus you've increased your chances to 2/3 as you're now certain of what's behind door 1".

my view: it's still 50/50. the moment you open a door, it's outta the picture (from a math standpoint).

[Rocket36]

the book said the chances of winning the gti were now 2/3

Anyone or anything that says the chances of winning were now 2 out of 3 are being foolish as they're basing that on the very start of the options AFTER the circumstances have changed. The ONLY thing that counts is the circumstances by which you end up winning or losing and that is ALWAYS going to be 50/50 because there are ALWAYS only 2 options and you don't know which is the winning decision.

So you start out with a 1/3 chance and finish with a 1/2 chance. Because one of the 3 has been removed from your choices and is therefore not 2/3.

[Buller_Scott]

that's right. which is why i didnt really take well to this riddle book, because i actually enjoy the math involved, and the book didnt mesh.

hey, are you no longer living in melbourne? did our ridiculous self importance scare you away? ($14 a kilo for friggin cage chicken, non-clearways on hugely busy inner cbd and other arterial roads, bike pelotons forcing cars off the road and overpriced-but-inefficient public transport?)

[The_Hawk]

Second time around is all that counts.

But regarding switching the second time around, that's only half your options. The other half is to not switch. You need to take ALL options into account if you're going to talk about your chances of winning.

If you look at the odds when not switching you still at a one in three option since you picked one from three. Yes the last two doors are 50/50 regardless of if your given the choice to switch. and take it up.

my view: it's still 50/50. the moment you open a door, it's outta the picture (from a math standpoint).

Absolutely 100% agree, it's down to a 50/50 chance on that last door... but then look at the options, if you do switch, out of the three options you could have originally chosen, TWO out of three possibilities end in a correct choice when you switch...

Stupid stats.

[Buller_Scott]

yeah, stupid riddle books. they're trying to confuse people by sweeping "we're changing variables, mid-formula" under the carpet.

a-holes. someone should rat 'em out!

[BTJ]

Have to chime in here.

People on the side of 50:50 chance on the second choice are wrong.

You should switch.

Whilst it appears 50:50 and indeed would be if your only option was one of two, but you option is one of three. Just because the door is open does not exclude it from the odds.

3 doors. You make a choice. that is a 1 in 3 chance.

If you choose to stay with that choice it is still a 1 in 3 chance because you made that choice when there were 3 available. (although obviously there are only two doors left to open)

Your initial choice has a greater probability of being wrong than right.

[Buller_Scott]

but that's the thing- my viewpoint from a practical standpoint, is that when door 1 has been opened, its no longer to be counted as it's now not an element in ''probability'' as it is now a certainty- a certainty that has been ruled out as NOT housing the GTI.

the maker of the riddle banks on people not understanding the dynamism of his riddle (not HER riddle, because if it was a female, there'd be many, many, many more variables, all constantly changing, and the ''certainties'' would continually revert back to being ''uncertainties''. not to mention the fact that working out the riddle would be much more gruelling, time consuming, exhausting, and depressing).

bottom line is, the riddle is dynamic- the numbers change (by way of eliminating uncertain elements) and thus, so does the probability.

look at it this way: if there was a dub-fest on, 20 raffle tickets sold for a GTI prize, and your ticket turns up a dud, but you get to switch, that means that you've still got your chance at the prize, but there's only 18 tickets to contend with. then, yours turns up dud again, but you get to switch, and now there're only 17 to contend with. so on and so forth until you get down to ten. if, at that point, the emcee says that the tickets have to be revealed, your shot at the car is now only one in ten. it is NOT eleven in twenty (namely, it is NOT the odds of [ten (the number of tickets you've revealed as failing tickets) + one (the ticket in your hand)] : twenty (the original number of tickets sold).

there are ten tickets left, you've got one shot. those are NOW the odds.

the riddlemaker is trying to fool people into thinking that, atleast with my dubfest example, that every time the person switches tickets (and a dud ticket is eliminated from the pool) that those dud tickets somehow are added to the number of tickets that the person is holding onto BECAUSE they have now been revealed to the ticketholder as certainties (certain failures). pretty logic, but it's not true. without the person knowing whether or not his ticket is the one AT the time that the emcee orders the remaining people to turn in their tickets, his chances, by way of possession of one ticket only, are precisely equal to those of the people who also hold one ticket only. the fact that he knows the numbers of ten tickets that have turned out to be failures, is not relevant to his one chance of winning a GTI when he's standing next to 9 other guys at the lectern/podium who're also holding their tickets out.