It is really important to make it clear that: 1) Monty always opens another door (regardless of what is behind the door initially chosen by the contestant). He

It is really important to make it clear that: 1) Monty always opens another door (regardless of what is behind the door initially chosen by the contestant). He will never open the door the contestant chose. 2) Always opens a door with a goat behind. 3) These rules are known to the contestant These premises are not intuitive, and some versions of the problem does not make them explicit, which is why it is more of a "gotcha" riddle. In particular, the version quoted in Wikipedia does not make any of that clear. It just mentions the particular case of the host opening another the door with the goat. But without knowing the above "rules", this just means there is 50% chance per door now.