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I don't think he leaks information. He invites you to switch from a game with a 1-in-3 chance to a game with a 2-in-3 chance. If you stick, you are staying in t
by irthomasthomas 4y ago
I don't think he leaks information. He invites you to switch from a game with a 1-in-3 chance to a game with a 2-in-3 chance. If you stick, you are staying in the 1-in-3 game, but if you switch then you are changing to a 2-in-3 game. That's all there is to it.
Edit: I should have checked before I posted, obviously it's 2-in-3 when you switch. But it's same idea, you have better odds when you switch because then it's like you are entering a new game with only 2 doors.
Still hard to believe that Erdos wouldn't believe this. He spent his life couch surfing at other mathematicians but not could convince him until he saw a monte-carlo simulation, apparently.
- dagenix 4y agoIf you switch, your odds of winning are 2/3.
- irthomasthomas 4y agoOh yes, thanks.
- jjbinx007 4y agoNo, that's not right. You need to read up on it more as it's clear you haven't truly understood the puzzle. The host knows what's behind the doors so he'll always eliminate a wrong answer. In the opening, you pick one door. That's a 1 in 3 chance of being right. So there's a 2 in 3 chance it's in either of the two remaining doors. He simply eliminates a wrong answer. Thus, 2 out of 3 times you win by switching. You win 1 in 3 times by staying with your original choice.
- crwilcox 4y agoA common way to explain this is to increase the number of doors. You have 100 doors, select one blindly, and have a 1% chance of being correct. The host removes all but one other door. Do you stay with the door you chose, a random guess of 100, or the one remaining after the host has removed all others? A door that is now statistically much more likely to be the correct choice?
- irthomasthomas 4y agoGood idea. That makes it extremely obvious. Hard to believe that Erdos didn't believe this until he did monte carlo simulations.