Don’t you think we would have remembered if Monty had ever screwed the contestant, and showed the Grand Prize as the first door the contestant didn’t win?
“Ok. Let’s look at one of the doors you didn’t select. ….… You didn’t select the Grand Prize! Hurrah! So, do you want to keep your loser door, or take the other loser door?”
Whatever Monty may or may not have know about probability theory, he surely knew that doing that wouldn’t make for an entertaining climax to his show. As long as he was committed and able to avoid that scenario, the usual analysis is fine.
Even if Monty was feeling bitter one day, and decided to screw the contestant, or they just made a mistake and opened the wrong door, that really isn’t the point of the problem.
Of course your best strategy is different for Screw You Monty than for Let’s Have an Exciting Climax to the Show Monty, but that shouldn’t surprise any of us. Any optimal strategy has to assume a prior on the behavior of Monty. No Free Lunch.
Don’t you think we would have remembered if Monty had ever screwed the contestant, and showed the Grand Prize as the first door the contestant didn’t win?
“Ok. Let’s look at one of the doors you didn’t select. ….… You didn’t select the Grand Prize! Hurrah! So, do you want to keep your loser door, or take the other loser door?”
My understanding was that Monty Hall knew which door contained the prize. After he revealed a non-prize door, he more strongly encourage players to move when their initial guess was correct.
I don’t think you need to take data.
Don’t you think we would have remembered if Monty had ever screwed the contestant, and showed the Grand Prize as the first door the contestant didn’t win?
“Ok. Let’s look at one of the doors you didn’t select. ….… You didn’t select the Grand Prize! Hurrah! So, do you want to keep your loser door, or take the other loser door?”
Whatever Monty may or may not have know about probability theory, he surely knew that doing that wouldn’t make for an entertaining climax to his show. As long as he was committed and able to avoid that scenario, the usual analysis is fine.
Even if Monty was feeling bitter one day, and decided to screw the contestant, or they just made a mistake and opened the wrong door, that really isn’t the point of the problem.
Of course your best strategy is different for Screw You Monty than for Let’s Have an Exciting Climax to the Show Monty, but that shouldn’t surprise any of us. Any optimal strategy has to assume a prior on the behavior of Monty. No Free Lunch.
My understanding was that Monty Hall knew which door contained the prize. After he revealed a non-prize door, he more strongly encourage players to move when their initial guess was correct.