Comment by gametheoretic | Hacker News Reader

Comment by gametheoretic | Hacker News Reader

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> To keep things equally likely, let's suppose Monty flips a coin.

Aha! But he can't! Do you see? He can't open a door with a car, so he can't flip a coin in the event that the car is behind a door other than yours. He is bound by the rules not to do so.

1/3 your door is good; 2/3 your door is bad. If bad, he MUST leave you with the good door to switch to. So in 2/3 of scenarios, you have a 100% likelihood of winning if you switch.

The answer to all 3 is 1/2. GG + "at least one is a boy" is not a possible world, but you are calculating the probability of the others, initially, as if it were, and then asking another question on top of it. You can't do that. BB is only 1/2 as likely as BG/GB if GG is a possible world for the question to begin with.

  >> To keep things equally likely, let's suppose
  >> Monty flips a coin.

  > Aha! But he can't! Do you see? He can't open a
  > door with a car, so he can't flip a coin in the
  > event that the car is behind a door other than
  > yours. He is bound by the rules not to do so.

Read again ... I said:

  > To keep things equally likely, let's suppose
  > Monty flips a coin.  Heads he opens the left-most
  > unchosen door that doesn't reveal a car, Tails he
  > opens the right-most.

So I allow for that. I have him always flip a coin to ensure that every branch of the game tree is equally likely, even though in 2 out of 3 cases it doesn't actually affect his choice of door. It's a standard trick that is proven to work in the real world. More, it's supported by the appropriate measure theory versions of probability.

Please, stop assuming everyone except you is an idiot.

> The answer to all 3 is 1/2.

No, it's 1/3 as everyone has pointed out.

Go and play the coin game described. Seriously, stop arguing and go and play it.

See?

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