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JoshuaZ comments on Bayes' Theorem Illustrated (My Way) - Less Wrong

126 Post author: komponisto 03 June 2010 04:40AM

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Comment author: JoshuaZ 04 June 2010 04:57:19PM *  10 points [-]

Think about it this way. Let's say you precommit before we play Monty's game that you won't switch. Then you win 1/3rd of the time, exactly when you picked the correct door first, yes?

Now, suppose you precommit to switching. Under what circumstances will you win? You'll win if you didn't pick the correct door to start with. That means you have a 2/3rd chance of winning since you win whenever your first door wasn't the correct choice.

Your comparison to the roulette wheel doesn't work: The roulette wheel has no memory, but in this case, the car isn't reallocated between the two remaining doors, it was chosen before the process started.