Saturday 28 January, 2006

Odds are odd

Filed under: Numbers and stuff

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.


Posted by dan at 8:41am | Permalink | Comments (1) | Trackbacks (0)
Comments

Not this still.

I originally came across this problem some time back (like years)... it's very old.

At the time, of course it was debated and I recalled that the answer was the opposite of what one would initially imagine, and also that it was best explained by extrapolating to many more doors.

OK, in my defence when I read the original post I went looking for something to explain and found that page (not being bothered to type much).

Cunningly, I should have read it, because the idea that odds are unchanged in original problem, as argued in the reporter's article rely on the assumption that MONTY DOESN'T KNOW WHERE THE CAR IS!

However, that clearly isn't the case (or Monty is incredibly lucky) and hence odds are skewed as a result.

P.S. Dan, that's as close to an admission you are correct as you'll get. Of course you cannot take credit for any of it anyhow because this problem is as old as the hills and has been pondered many times on the 'net! ;)

Posted by Rob 7:57am, Monday 13 February 2006
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