Lets make a deal

That would have worked Tim

EXCEPT that the whole point of the exercise is that you do NOT know if the first door has a goat, a car or a naked man behind it, not even after you have initially chosen it....

Okay?

You are still no nearer to knowing, as you conduct this experiment, whether you have already picked the prize

- or else why would you even be asked to consider picking another door, you would either say

1. I like this prize best out of the alternatives so I am not opening any more doors thanks

or

2. I dont fancy this much, give me another chance

That wouldnt take up much of a thread would it now....

Its true...

You had 1 in 3 chance of getting the correct door for the star prize.

The host then choses from the remaining 2 doors.

If you failed in your 1 in 3 (66% chance of failure) attempt to get the star prize - the host is forced to choose the goat in his/her attempt, thrust increasing the probability that the remaining door is more likely to have the car.

Think of it this way... You pick one door.

The host picks the remaining two.

Just before he opens the door to the goat, do you want to stick with what you have choosen 1 door or swap for the other 2 doors?

The maths is a bit more tricky than that its not 66% chance of winning the prize because you have to take into account that you may have indeed choosen the star prize in your lucky attempt.

Do this often enough it shows that it is more favourable to swap.

>>EXCEPT that the whole point of the exercise is that you do NOT know if the first door has a goat, a car or a naked man behind it, not even after you have initially chosen it....<<

I know that! Read what i wrote again.

>>If you failed in your 1 in 3 (66% chance of failure) attempt to get the star prize - the host is forced to choose the goat in his/her attempt, thrust increasing the probability that the remaining door is more likely to have the car.<<

...no, the host is forced to choose the goat REGARDLESS of if you choose the prize door or not! Hence it doesnt make a difference. Only that if you pick the prize the first time, the host has to make a decision - but that is not relevent because you wouldnt know.

Of the two ramaining doors one has the prize behind - this is true regradless of your first decision.

You choose one of three - one of the doors you didnt choose is opened with a goat behind- you choose one of the two remaining doors.

The above applies whether you picked the correct door in the first place or not.

Also, but not relevent to this discussion, the overall probability ends up at 50/50, so from the begining you have a 50/50 chance of winning the car. (Because there is one goat, you cant win - as the host reveals it).

Tim

Let change the format of the show.

You are basically doing the same thing, but the show format is changed slightly different, you still only win 1 prize, but can choose from the two doors remaining.

Choose the door which DOESN'T have the star prize...

You choose door 1.

The host says OK, lets reveal what behind Door 2 and door 3 to see if it has the Star prize.

Lets see what behind door 3 first, surprise, surprise... its a goat.

Shall we see what behind door 2?

In this format, is this sequence of event 50/50?