Here's what I don't get....
When you've picked your first door, you can decide to change or not. You don't have to commit.
I see the chances overall as 50/50 as should you have picked the door straight away or not, the quizmaster knowing which remaining door(s) hides a goat, can fling one open revealing that goat.
Now here's the thing.
If he DIDN'T know which remaining door held a goat, and flung one open revealing a goat, then I would agree that your chances are now 66% because he's doubled your chance of winning by removing one of the wrong choices for you. This "doubled chance" still does not require you to change your mind!
If he DOES know which door hides a goat, then there will always be such a door, so sticking or changing your original choice makes no difference.
Your best bet in such a situation would be to try and get a tell on the quizmaster instead!
In FUTURES we are perhaps looking at the same problem in the future of DX which is how this thread started.....
I am currently short euro, short GPB, and long swiss.
This exposes me to dollar strength, but limits my being short squeezed too much as my CHF acts as "upside insurance".
Obviously, I have to take the view that GPB hasn't got a lot of upside left as well, which I believe to be the case.
Going back to DX and Monty Hall I would argue this.
Does ANYONE have a higher chance of being right this market IF they reverse their positions right now?
Does reversing your position at this point increase your odds to 66%?
In my book "Does it f--k!" but let's here some argument to the other side!