Sunday, February 28, 2010

Are You Smarter Than a 5th Grader? Here's 5th Grade Math

In Friday’s Game at Citrus Springs on my last board the hands were:



Sitting South I opened 2 clubs with this nice 4 Losing Trick Count hand and 5 Quick Tricks. Since we have a system that shows control cards over strong 2 club bids, my partner bid 3 clubs showing an Ace and a King in different suits. Sleuth that I am, I identify the King of spades and Ace of diamonds. What excuse could I offer for bidding anything less than 7NT. Bang! The tremor set my Diet Coke can in motion but thankfully it stayed upright!

LHO opens the Queen of clubs and the “pleased as punch” smile drains from my face. We got a problem Houston! At 7 NT there is no end play, and with only 11 top tricks there is no squeeze. It is clear that making the slam is going to be based on the play of the 7 card spade suit. I first set out to establish a couple of phony decoy threat cards hoping to crowd somebody’s hand and lure the defenders into making a telling spade discard. I take the Ace of clubs, the King of clubs and the Ace-King of hearts. Everybody follows suit. Now I have given them three potential winners to stew about, the Queen of clubs, Queen of hearts and Jack of spades.

Next I play 4 rounds of diamonds with West following suit and East playing one diamond and pitching a couple of hearts and a club. I then go into the tank trying to remember the four blogs that I have written on bridge probabilities.

(a) I do remember that “all other things being equal” that finessing the Jack of spades would be a 50% probability, but are all other things equal? Its biggest appeal is that if it is wrong, it will put a sudden end to this misery.

(b) Now I need to test if all other things are equal. Emile Borel, the noted French physicist, also wrote the first definitive treatise on bridge math in the late 1930’s entitled Theorie Mathematique du Bridge. Borrowing from his physics expertise, he laid down the “law of attraction” that length in one suit attracts shortness in another and that shortness attracts length. An adjunct to this is his “law of vacant places.” Once you have fully identified the distribution of one suit (in this case diamonds were 4-1) the likelihood of a defender holding any particular card in another suit is directly proportional to the non-diamond cards that he held. West originally held 9 non-diamond cards and East held 12 non-diamond cards, so the odds are 12 to 9 that East has the Jack of spades. Now the success of the finesse has become about a 43% probability.

(c) What about the 7 card spade suit. I remember that when the opponents hold an even number of cards they are likely to break unevenly. Even if spades are 4-2 as predicted, the missing honor could be doubleton, but that only happens in the newspaper. If it happens it will happen as i will first lead the Ace and King
in the spade suit.

(c) There is another rule that says when opponents have the 5 or 6 cards in a suit, finesse for the King or Queen, but not the Jack! In order to square that with the 7 card rule above, it must be that holding the ten in the suit makes a difference. Behold, I have AKQT in spades. This enhances the 3-3 split to 52.4% probability. Actually this rule is based on another probability rule called the “Deletion Principle” which also explains that time honored saying “8 ever, 9 never.”

I play the King o f spades from the dummy and Ace of spades to my hand and now lead a spade toward dummy. Both defenders follow to the Ace and King and LHO follows to the third lead of spades. The moment of truth! I am committed to taking the play with the best probability. At this point making 7 NT has become a side issue, I just want to make sure that if I lose bragging rights, I have an iron clad excuse for blowing the contract. I play the Quuen of spades and the Jack comes “oh so slowly” out of East’s hand.

I am thinking that this must be a cold top. Six no trump is unbeatable no matter what the lead or how you play the spade suit. How many pairs are going to bid 7NT in matchpoints and then also get the 5th grade math correct? Yesterday morning I quickly checked the results and found that out of 13 pairs playing the hand, one other team bid the Grand and they actually made it. I give credit to Eve Taylor sitting south and Lorraine Carrier her partner.

You may be saying that all that math is tiring and hard to remember. Actually the detail stuff is all window dressing, but nevertheless valid. If you remember the finessing rule for 5 and 6 cards you will make 7 no trump.

You can access my four earlier blogs on the odds and ends of bridge by looking in the archive in the right hand margin of the blog. I wrote about the Law of Attraction and the Law of Vacant Places in Odds and Ends of Bridge (Part1) dated August 28, 2007. I covered the finessing rule with 5 or 6 cards outstanding in Odds and Ends of Bridge (Part 2) dated September 6, 2007 and about the Deletion Principle in Odds and Ends of Bridge (Part 4) dated September 12, 2007. It also proves that at my age the only chance you have of remembering something is if you write it down and tape crib notes on your right wrist. Now you know why I never wear short sleeve shirts!!

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