the best way to understand this problem is to scale it up to 100 doors.
>you pick 1 door
>host reveals 98 other doors showing goats
>would you like to switch?
then it immediately becomes obvious why you should switch. you picked with 1/100 odds, now the only door left is picked with 50/50 odds.

the best way to understand this problem is to scale it up to 100 doors.
>you pick 1 door
>host reveals 98 other doors showing goats
>would you like to switch?
then it immediately becomes obvious why you should switch. you picked with 1/100 odds, now the only door left is picked with 50/50 odds.