The role of probability in solving the Monty Hall problem

[Aractus]

Nobody is claiming that you will every time if you change doors though, so I don't understand.

I honestly thought this 'problem' was very easy. I admit the first time it was introduced to me I chose to stick, until I sat back and thought about it and someone did the probability tree with me and I saw that the 50/50 choice was an illusion.

Oh well. At least we've got pool on our side now ^_^ GJ dude.

I thought the 'problem' was easy as well, until I realised that it's all based on what Monty does. If you don't know that he always opens a Goat then all bets are off. If you were the first contestant on his show and believed he was randomly selecting a door then it'd give you no advantage to switch - and if you thought that he would have opened the car if he could have then it means you must have selected the car. Most of the time a game-show is going on the contestants have no idea how the host selects anything. If they know, for example, that the host will try to give them hard questions then when the host asks "what are your favourite trivia categories" they should say "mind your own fucking business, Monty" or give a list of shit they know nothing at all about. If they know that's how he plays that is.

So the original answer the question is "no, there's no benefit to switch unless you have reliable information that Monty never opens the door to the prize immediately".