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Yo Eleven

In a recent club game using computer generated hands, I recently picked up a most amazing collection: AQ, void, void, AKQJ10987632!  A solid 11 card suit and an outside AQ. After smiling a bit, sure that someone was playing a trick on me, I looked around for the Director to see if he was going to bring the little game to an end. But no one was interested so we played on. The bidding and final contract were not the basis for my fascination -- there was no entry to dummy so a favorable lead was needed to make 7 -- but rather I began to wonder if this was the BEST hand I had ever been dealt -- and further, what was the likelihood of being dealt a hand of this ilk.

In doing some research on card combinations and probabilities, I ran across an interesting article by "Durango Bill" entitled Bridge Probabilities and Combinatorics, www.durangobill.com/BrSuitStats.html. The article indicates that a distribution of 11, 2, 0, 0 occurs once in 1.14971E-007 hands. It's been a while since my college math classes so I asked a friend who knows of such things, what this reference suggests. He told me that the reference is "scientific notation" and that the number translates to a probabiliity of 0.000000114971. If I am reading that right, it means that a hand with this distribution occurs about once in 10,000,000 hands. Yikes! And my hand was not a hand of any distribution -- but a solid 11 card suit and an outside AQ.

That got me thinking. Was this just an amazing rarity or were the folks who produce such hands just having fun?

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