The Monty Hall problem continues to bubble. It's strange how certain scenarios play havoc with your intuition, allowing your mind to jump to conclusions that are mathematically off, sometimes way off.
In trying (and failing) to explain the rationale behind the problem the other day to my hosting provider, we went on to explore a similar scenario. Instead of there being three doors, imagine there are 100. And instead of the host opening only one door, imagine he opens all but two (the one originally chosen plus one other), all opened doors coming with an accompanying bleat.
Even in this scenario, he believed that switching offered no benefit to the contestant. So I upped the ante.
Imagine I've put a red sticker on the shoe sole of one person in the world. Now I ask him to choose anyone in the world (without them lifting their feet). (He chose someone from China, after confirming that he wasn't allowed to choose himself.) I then eliminate 5,999,999,998 people one by one (assuming there are 6bn. people in the world), all of whom are bereft of a red sticker. So there are two people remaining: his original choice and the one remaining person I didn't eliminate.
Even under this scenario, he was of the opinion that switching offered no benefit, even though the reality means that your odds of success increase by 599,999,999,900%. That's 599 billion percent.
It seems that once your mind is convinced of something, it takes a lot of evidence to prove you wrong. Even overwhelming odds failed on this occasion.
