Yeah but my point is the probability is dependant on you having pre-knowledge of his intentions.

(March 14, 2016 at 5:32 am)robvalue Wrote: Nice work pool, I admire you giving it serious thought

It is very, very counter intuitive. I'm a dab hand at probability, but it suckered me right in first time I saw it. The door opening is a kind of misdirection; it doesn't tell you what it appears to tell you, because of the way that monty fucker has to choose.

I've got a really hard probability question if anyone is interested. Maybe I should do another thread for it. I've as yet not been able to solve it. That is very embarresing for me to admit!

Well after a build up like that - do tell:  what's the problem?

(March 14, 2016 at 8:48 am)Aractus Wrote: Yeah but my point is the probability is dependant on you having pre-knowledge of his intentions.

Yes, but that is structurally that is part of the problem.  There is no alternate version of the problem in which Monte's behavior is indeterminate.

(March 14, 2016 at 8:48 am)Aractus Wrote: Yeah but my point is the probability is dependant on you having pre-knowledge of his intentions.

Sort of. The probability is based on knowing he will always reveal a door you didn't choose. Otherwise he might only reveal another door if you have already chosen the prize. But, if he must reveal a door, his intentions are irrelivant. If he reveals a goat, your best bet is to switch. If he revealed the car, but didn't let you chose it, there's no option to consider.

(March 14, 2016 at 10:49 am)Whateverist the White Wrote: Yes, but that is structurally that is part of the problem.  There is no alternate version of the problem in which Monte's behavior is indeterminate.

Imagine you've never watched the show before, and you appear on stage. You can't know whether he will: intentionally pick the goat, intentionally pick the prize, or pick randomly. With incomplete information you don't know what the best course of action for the probability of your success is - it depends on how Monty plays the game.

(March 15, 2016 at 12:36 am)Jenny A Wrote: Sort of. The probability is based on knowing he will always reveal a door you didn't choose. Otherwise he might only reveal another door if you have already chosen the prize.  But, if he must reveal a door, his intentions are irrelivant.  If he reveals a goat, your best bet is to switch.  If he revealed the car, but didn't let you chose it, there's no option to consider.

Incorrect, I already proved it. If he intentionally picks the car, but has opened a goat that means you must have selected the door with the car, and switching in that case will guarantee you loose. His intentions are the only reason there's a benefit to switching.

(March 15, 2016 at 1:48 am)Aractus Wrote:

(March 15, 2016 at 12:36 am)Jenny A Wrote: Sort of. The probability is based on knowing he will always reveal a door you didn't choose. Otherwise he might only reveal another door if you have already chosen the prize.  But, if he must reveal a door, his intentions are irrelivant.  If he reveals a goat, your best bet is to switch.  If he revealed the car, but didn't let you chose it, there's no option to consider.

Incorrect, I already proved it. If he intentionally picks the car, but has opened a goat that means you must have selected the door with the car, and switching in that case will guarantee you loose. His intentions are the only reason there's a benefit to switching.

If he must show you a door you haven't picked, than his intentions are irrelivant. He can't show you the car because that would spoil the game. Therefore he will show you a goat. And you will learn from that that switching is the better option.

Yeah...

But this is a mathematical problem. These things are given in the premise.

Actually it's not given in the premise most of the time. Look at how people quote the Monty Hall problem - they hardly ever specify that "Monty will never open the door with the prize first" they just say "Monty opened a goat what should you do?" If people are quoting the problem correctly, yes you should switch. If they haven't told you that "Monty will never open the door with the prize first" then there's no statistical advantage to switching.

Agreed, in those cases they have misrepresented the problem and the answer would change.