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URL:  https://boards.fool.com/lobodoug-the-game-just-changed-it-is-now-a-new-30398087.aspx

Subject:  Re: 5 Statistics Problems To Change Your View Date:  11/25/2012  10:38 AM
Author:  flyerboys Number:  409513 of 567823

Lobodoug:

The game just changed. It is now a new game, 2 doors, pick one, the odds are 50/50. Change, don't change...it does not change the odds.


tim:

Yup!!!


+++++++++++++++++++++++++++++++++++++

uuuhhhmmmm, NOPE!!!

PolymerMom and Atlantic Mag have it correct. The crux is correctly identified by Lobodoug, but not correctly understood. IT IS NOT A NEW GAME!!!

Two different ways you can readily chew on this

1) read, for example, this wikipedia article with its multiple presentations using Bayesian formulations, Monte Carlos, etc...: http://en.wikipedia.org/wiki/Monty_Hall_problem

OR

I had an obsessive friend who did not believe me when I told him this, and on a bet from me he simply went through 100 of the Monty Hall shows and found that the show's results (REALITY indeed) corresponded with the 2/3 chance predicted by statistical theory!


PolymerMom's excellent point was that "Common Sense" is alarmingly wrong, and I will add that our brains are wired to be excellent hunter/gatherer/lovers rather than excellent denizens of modern times with curtains and game shows -- or for that matter investment funds and sexting.

The phrase "Common Sense" has lost its original extremely useful meaning. It now means (as PM used it) understanding or reasoning that is basic or common, a human version of "horse sense". However, the original meaning is from Aristotle and meant a kind of 6th sense that combines and amplifies everything that can be brought in by the other senses -- the reasoning that occurs with the senses themselves communicate. This was taken a step further in the Scottish Enlightenment, which first popularized the English phrase common sense, but they meant by that a form of reasoning based on skeptically combining (communing) received traditional understanding, the input of the 5 senses structured through objective tests, and intuition -- in other words Scientific Testing.

It is useful to remember that original meaning of "horse sense" was ironic, that a horse will often have better understanding than found in "common sense" (in the modern sense of off-hand and off-the-cuff understanding). If your horse does not want to ford a river, despite your common sense telling you all is well, better think again, or you may drown. Or open the door with the goat!!

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