Monty Hall Dilemma - Winning a GTI on a Game Show

[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]

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?)

[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]

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]

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.

[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'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]

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:

[JustCruisn]

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

[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.

[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?

[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.

[cme2c]

If I'm not mistaken, the "3 deuces" are known amongst the Mopar crowd as a "6 pack"

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

[INOV8]

The movie '21' taught me this!!! Who says TV is no good for kids

[Flighter]

So, Greg, you'd know what "3 deuces and a 4 speed" meant...

If I'm not mistaken, the "3 deuces" are known amongst the Mopar crowd as a "6 pack"