4 ms·
When Monty reveals a goat, your odds increase from 1/3 to 1/2 if Monty is picking randomly and just happened not to reveal a goat (and if he revealed a car we s
by dllthomas 4y ago
When Monty reveals a goat, your odds increase from 1/3 to 1/2 if Monty is picking randomly and just happened not to reveal a goat (and if he revealed a car we start from the top, or you automatically lose, or you automatically win, or...), but to 2/3 if Monty will reliably reveal a goat. I think it's hard to say that you have no extra information in that latter case.
It's true that we can add other options (pick both doors) of equal likelihood, but it's because of our increased information that the reduced option of picking just one door isn't actually worse off.
- tsimionescu 4y agoThe GP knows all this, and agrees it's better to switch (look at the second paragraph). They just dislike the common formulation (that is given in terms of the extra information from the boot being opened), and find another formulation more compelling (your original choice is one door, while the switch is actually to the best prize from the other two doors, not simply to another one door).