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The Monty Hall Problem
“When the host opens a door using information, the two remaining doors do not automatically become equally likely.”
01 / SUMMARY
In short
If the prize was placed randomly, you choose one door, and the host always opens another prize-free door before offering a switch, the original choice remains at 1/3 and switching wins with probability 2/3.
03 / SCENE
In the wild
Your first door is right only one time in three; in the other two, the host's rule concentrates the prize behind the only available switch.
04 / LIMIT
The limit
The 2/3 result depends on the host's protocol. If doors are opened blindly or switching is offered only sometimes, the probabilities can differ.
FINAL NOTE
What remains
Before splitting probability evenly, model what the person revealing information knew and which rules they followed.