Monty Hall Dilemma - Winning a GTI on a Game Show

**team_v** · 10-03-2010, 01:01 PM

Originally Posted by Dubya

Not so, I have to say:

From the outset you have a one in three chance of selecting the door with the car first off.

This means that there is a 67% chance that the car is behind one of the two doors you did not choose and a 33% chance it is behind the one you first chose.

These percentages do no vary after the door with the goat behind it is opened.

We already knew there was a goat behind one of the two doors you did not select; now we just happen to know behind which of the two other doors the goat was hidden.

As the two doors we did not choose initially still have a combined 67% chance of having the car behind them, with the knowledge that the GTI is not behind the door that has been opened, if you swap, your chances of the car being behind your second choice are 67%, not 33% or 50%.

So if you swap, on average, you will win twice as often.

This is as pointless as the MT vs DSG thread.

You have 3 doors, 33% chance each.
Remove 1 door, only 2 doors remain.
Removing 1 door means that you can no longer use the 1/3 chance breakdown you have used previously and as such must revert back to 1/2 chance unless you actually count choosing the goat as an option.
since you are not going to choose the goat, 1 of the remaining 2 doors has the GTI, the other doesn't so you have a 50% chance no matter which door you choose.

Having said that, you then have to apply Murphy's law stating if you have a 50% chance, 90% of the time you will choose wrong.

And schroedinger's cat also screws with the results.

Bloody Garath beat me to it.
Stupid work getting in the way of my forum viewing time.

**gareth_oau** · 10-03-2010, 01:55 PM

team v, you really shouldn't be allowing work to get in the way of priorities - go chat to the boss!

**ccpl** · 10-03-2010, 02:06 PM

As stated plenty of times already in this topic, its complete BS.

If you take into account that your original choices include a 1/3 chance of winning, and then the host improves the odds by taking away one of the choices, then yes, given the original odds, you now have a 2/3 chance of winning WITH EITHER DOOR.

But as stated previously, the variables have changed, and so must the odds - so you now have a 1/2 chance of winning.

People try to use mathematics to solve the equation, and just end up complicating the problem - when all they really need is simple arithmetic:

1 + 1 + 1 = 3
3 - 1 = 2

To demonstrate the flawed mechanic, the whole idea of 'switching your door' giving you a 2/3 chance to win, relies on the first mechanic - that you did not choose the prize in the first place (which is an original 1/3 chance). If you happened to win that 1/3 chance, then 'switching your door' gives you a 0/3 (original) and 0/2 (progressive) chance to win.

Should you happen to choose a goat first (2/3 chance), the 'switch mechanic' gives you a 2/3 (original) and 1/2 (progressive) chance to win

HOWEVER

If you take into account that the modified fraction chance values can not exist until the original fraction chance value has been solved (ie: door chosen) - then it becomes obvious that in order to correctly calculate the odds, the variables must be processed first.

Which again is simple maths:

1 + 1 + 1 = 3
3 - 1 = 2

**FJ Steve** · 10-03-2010, 02:19 PM

But....but....what if there wasn't a GTI behind the "3rd" door?

In fact...what if they had 3 goats behind the 3 doors.....and only wheeled the GTI up to show you what you missed when you made 2 dud choices....

What's the odds with that?

**team_v** · 10-03-2010, 03:01 PM

Originally Posted by Dermot

There are so many variables;

Is the GTI 3 door or 5 door
Manual or DSG
Does it have Dynaudio?
Are the goats the same age?
Are the goats male or female?

Is the goat an option for the GTI?
Can i get the GTI in goat leather trim?

Is it possible to chip the goat?
Is the goat DSG only?