You are asked to pick a door | |||||
you pick the prize door | you pick wrong door a | you pick wrong door b | |||
Wrong door b is removed | Wrong door b is removed | Wrong door a is removed | |||
you swap | you stick | you swap | you stick | you swap | you stick |
you lose | you win | you win | you lose | you win | you lose |
out of the 3 options from swapping 2 of them will win, so the probability is 2/3 chance of winning. Out of the 3 options for sticking 1 will win so the probability is 1/3. So you are twice as likely to win if you swap.