Just a note to Torbjörn and Divad. You two guys are too smart for me. But I don’t believe Torbjörn. There must have been a flaw in your program. Maybe in your random number generator. And Divad mentioned Marilyn Vos Savant. If you don’t recognize the name, she was supposedly the worlds smartest genius. I had correspondence with her years ago because I mentioned her in the strip. So I started following her advice column. One day a guy wrote in about a social problem that he was having. And she answered it as such. She didn’t recognize the statement of his problem was an example of Russell’s Paradox.
It’s always possible that I made an error in the Monty Hall test program, but the result seemed to match the theory. (That’s why you should always try to make at least two errors, so that if you’re lucky they’ll cancel each other out. )
The simplest explanation I’ve heard (but would not have thought of myself) is that there’s a 1/3 chance that you pick the car on your first guess, and a 2/3 chance that you didn’t. There is of course a 0 chance that the car is behind the door that gets opened, so the choice becomes to either stick with your original 1/3 chance, or switch to the new 2/3 chance.
Still feels weird, though.
No. Sorry. You can say “The moon is made of green cheese” and it wouldn’t make a difference.
Maybe it’d help if I understood where I got it wrong, then. The way I understand the problem, the host must use his knowledge to always reveal a goat. That gives me three cases:
Case 1: Player randomly picks car. Host reveals goat 1 or 2. Player sticks, he wins. Player switches, he loses.
Case 2: Player randomly picks goat 1. Host must reveal goat 2. Player sticks, he loses. Player switches, he wins.
Case 3: Player randomly picks goat 2. Host must reveal goat 1. Player sticks, he loses. Player switches, he wins.
In this scenario, the player who sticks has a 1/3 chance of winning, and the player who switches has a 2/3 chance of winning. But I’ve heard it argued that the host, despite knowing what’s behind the doors, must still reveal one at random. That give me six cases:
Case 1: Player randomly picks car, host randomly reveals goat 1. Player sticks, he wins. Player switches, he loses.
Case 2: Player randomly picks car, host randomly reveals goat 2. Player sticks, he wins. Player switches, he loses.
Case 3: Player randomly picks goat 1, host randomly reveals car. Player sticks, he loses. Player switches, he loses.
Case 4: Player randomly picks goat 1, host randomly reveals goat 2. Player sticks, he loses. Player switches, he wins.
Case 5: Player randomly picks goat 2, host randomly reveals car. Player sticks, he loses. Player switches, he loses.
Case 6: Player randomly picks goat 2, host randomly reveals goat 1. Player sticks, he loses. Player switches, he wins.
In this scenario, the player who sticks has a 2/6 chance of winning, and the player who switches also has a 2/6 chance of winning. (Why am I watching this game show?)
In a third scenario, the game show is hosted by uncle Sid and all the cars are provided by Elvis Zimmerman. In which case you’ll lose either way.
I know nothing about the host and the random reveal. I don’t think I ever saw the program. All I know is that my friend 45 years ago brought it up. But you’re right. Sid should have been the host and Elvis should have been Vanna White. But you’re Swedish. You don’t know who Vanna White is. She was the gal on Wheel of Fortune. She was on that show 40 years ago and still is, and she is still drop dead gorgeous. How do they do it? She must be a botox silicone clone.