Quote:
Originally Posted by PairTheBoard
Maybe. Howver , for someone who knows nothing about the game except what they are told I don't think it's obvious to them that the host doesn't show the goat only when they've already picked the prize, just to mess with them. In fact, that's the first thing I would worry about.
Not everyone watched "Let's Make a Deal" nor has any idea how Monty Hall played the game other than what they are being told. At any rate, "Monty Hall" was not mentioned in the movie "21".
PairTheBoard
Yes, of course you're right that this problem is often poorly posed: there needs to be the explicit requirement that the "host" will
always open a second door without the "prize". I've seen this "mistake" almost ad nauseum ad infinitum, but there was at least one poker author that mentioned this "mistake".
I decided to watch the movie clip, and the often missed point is that the game show "host" may decide to only open a second door if the contestant's original choice is correct ( in which case, switching now gives a probability of zero ); at the other extreme, it's possible that the "host" only shows a second door when the "contestant's" original choice is incorrect ( perhaps the contestant is well-liked by the audience or a blood relative of the host
; if the original choice is correct, the "host" just opens the door that was chosen and reveals the "prize" ). It's also true that for
any number p in [0,1] that switching doors results in obtaining the "prize" with probability p, given that there is flexibility in the "host" choosing whether or not to reveal a second door.