I suppose the thing about the Monty-Hall problem which makes it ‘difficult’ is that there is another agent with more information than you, who gives you a systematically ‘biased’ account of their information. (There’s an element of ‘deceitfulness’ in other words.)
An analogy: Suppose you had a coin which you knew was either 2⁄3 biased towards heads or 2⁄3 biased towards tails, and the bias is actually towards heads. Say there have been 100 coin tosses, and you don’t know any of the outcomes but someone else (“Monty”) knows them all. Then they can feed you ‘biased information’ by choosing a sample of the coin tosses in which most outcomes were tails. The analogous confusion would be to ignore this possibility and assume that Monty is ‘honestly’ telling you everything he knows.
Yeah it’s remarkable isn’t it?
I suppose the thing about the Monty-Hall problem which makes it ‘difficult’ is that there is another agent with more information than you, who gives you a systematically ‘biased’ account of their information. (There’s an element of ‘deceitfulness’ in other words.)
An analogy: Suppose you had a coin which you knew was either 2⁄3 biased towards heads or 2⁄3 biased towards tails, and the bias is actually towards heads. Say there have been 100 coin tosses, and you don’t know any of the outcomes but someone else (“Monty”) knows them all. Then they can feed you ‘biased information’ by choosing a sample of the coin tosses in which most outcomes were tails. The analogous confusion would be to ignore this possibility and assume that Monty is ‘honestly’ telling you everything he knows.