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goobers, on Apr 11 2008, 05:08 PM, said:
Maybe I just have a different definition of absurd.
Randomly place goats/car.
Randomly choose a door.
If door = car, win.
If door = goat, lose.
Loop.
PS I am not smart enough to understand your program
Randomly place goats/car.
Randomly choose a door.
If door = car, win.
If door = goat, lose.
Loop.
PS I am not smart enough to understand your program
Oops. I just saw that you said: get a car, win. No The switcher loses if his first choice is a car, wins if hios first choice is a goat. That is, after Monty opens the door, the odds are 2 to 1 the car is behind the door that Monty hasn't opened and the guest did not, at first, choose. I'll leave the post that I wrote, assuming that you meant: The switcher wins whenever his first choice is a goat, thus 2/3 of the time.
Once you fet this far there is hardly a reason to run the program.
The problem was that people thought, wrongly, that this was equivalent to something like: Contestant is presented with three doors, host opens one to show a goat, now we ask which of the remaining two doors is the car behind.
Of course the above problem is not equivalent. But what I said before is that if a person does not understand the problem then he might well program the computer incorrectly. If you do understand the problem, as probably everyone reading this does, then there is no need to run the computer. I don't think anyone doubts that if you write a computer program that randomly designates 1,2,3 as a car, the other two as goats, and then have the computer randomly select one of the three numbers then the long term behavior will give the car 1/3 of the time.
looking back, it may be difficult to see how so many people, many with mathematical training, went astray. The fact is that they did. I myself have been known to say and do stupid things so they have my sympathy. At any rate, until these folks think the problem through, I suggest not letting them near a computer.
Note: When Restricted Choice was first put forth, I believe by Reese, there was also (so I understand) a great deal of controversy. Further, after it was accepted and maybe still today, it is not that unusual to see people applying it where it doesn't apply.
So maybe there is some subtlety in it.