Whether Monte Hall is counter intuitive is a function of how the question is phrased.
When you phrase it in a way that underlines the mechanical nature of the host's decision, people get it right. When you phrase it in a way that suggests the host's choice is itself random, people get it wrong.
I think the first formulation primes people to think of it from the perspective of the host, which is the right perspective for this problem.
When you phrase it in a way that underlines the mechanical nature of the host's decision, people get it right. When you phrase it in a way that suggests the host's choice is itself random, people get it wrong.
I think the first formulation primes people to think of it from the perspective of the host, which is the right perspective for this problem.