The solution is said to be yes, because you have 1/3 probability to stay and 2/3 probability to switch. The answer to this problem has annoyed me to an extent. Why is the host completely ignored as a variable to calculate the probability? I think there is an error in this solution due to the fact that the host and his actions are completely ignored. Example: This algorithm will create the same result, 1/3 does not switch, 2/3's switch. Now if I introduce the host as a variable: With this algorithm, the probability changes to 1/3 and 1/3 and shows that you have equal chance to win, if you do or do not switch doors.