That Wiki explanation is a bit long-winded. Easier to say "the chance of you picking the car to start with is 1/3. So the chance of it remaining behind another door is 2/3. It's not the door the host opens, so the 2/3 chance must be the other door".
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Many people say it is not 50/50 and go into long explanations about it.
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If you don't believe it, try it. You'll soon find they are correct.
---------- Post added at 14:19 ---------- Previous post was at 14:00 ----------
ps. If you want some software to help you, here's some we prepared earlier:
https://www.cableforum.uk/board/show...9#post34854319