The role of probability in solving the Monty Hall problem

[Excited Penguin]

I don't think we're even talking about the same game.

You pick a door, the guy opens a door (which is not your door, or the prize door. Important!!!)you stick or change, he reveals the winning door. Game over.

I'm saying if you repeat this game N times, with a genuinely random placement of the prize between the 3 doors each time, on average you will win 2/3 of the time by changing.

It's the mean of a probability distribution. Like I say, if you don't know what that is, you need to learn about it.

I have a first class maths degree, I know what I'm talking about here.

If by genuinely random placement you mean each door will be picked the same amount of times through n iterations of the same game, then yes.

You can either address this or not, but whatever degree you have is irrelevant.