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"....The truth is out there."

-- Dr. Jerome Jackson, 2002 (... & Agent Fox Mulder)

“There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.”

-- Hamlet

"All truth passes through 3 stages: First it is ridiculed. Second, it is violently opposed. Third, it is accepted as self-evident."

-- Arthur Schopenhauer






Friday, April 10, 2009

 

-- The Monty Hall Paradox --

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Straightforward explanation of the "Monty Hall" Problem via YouTube here:


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Comments:
I saw this presented on another bulletin board, and apparently the mathematics are relevant to a serious problem in cognitive psychology. I'm not sure what the situation was there, and as I'm no longer working in the field, and the original board poster wasn't that sophisticated in psychology, I didn't pursue the matter.

I also recognized, however, an identical application in a card position in the game of contract bridge (I used to be a middlin' level expert at that game, at least the Utah variety thereof). You can find an explanation of it under "Restricted Choice" in the Encyclopedia of Contract Bridge; basically it involves calculating the probabilities of deducing the location of a lower honor card, a queen or a jack when two hands, declarer's and dummy's, hold a combined nine cards in a single suit, including the ten in the hand opposite the one from which an original high honor card (Ace or King) is played. When one plays a top honor from one's hand with left hand opponent contributing a small spot card, dummy as well, and right hand opponent plays a jack or a queen to a trick, then the odds favor playing toward dummy and "inserting" the ten (a simple "finesse," which is merely an attempt to win a trick with a low card when there is a higher one outstanding).

As with the Monty Hall problem, this play has a higher probability of success than playing dummy's top honor (playing right hand opponent for an original holding of Q-J doubleton) even though it appears to be a coin toss situation. And curiously, it doesn't matter whether right hand opponent plays the queen or the jack; in effect they are "both goats" and the choice to play one of them was "restricted" as was the door Monty selected.

Of course unscrupulous players will resort to the more certain adage, "oen peek is worth two finesses," but generally bridge players strive to be ethical.

I do wonder, though, how I would play such a situation against a top player I competed against years ago who once betrayed the presence of a trump queen to me (in a close slam no less) because his hand shook ever so imperceptibly. It's perfectly ethical to base one's play on such observations, although they are done at one's own risk . . .

I suppose the Monty Hall problem offers similar opportunities, if one has a nose supremely sensitive to either "goat" or "new car smell"; barring such a situation, the identified course of action offers the best probability of success . . .

My apologies to any confusion I may have raised among the non-bridge players out there . . .

Concolor1
Salt Lake City
 
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