Saturday, March 29, 2008

Take Your Finesses in the Right Order to Maximize Probabilities

It is well known that I have more than a passing interest in odds and probabilities as they relate to the game of Bridge. I can’t say that the knowledge I have acquired has made any significant difference in my life, but at times it does steer me into the correct line of play for maximizing my opportunities. Often good players, who know nothing about bridge probabilities and could care less, make the same plays because of their vast experience. I am still waiting for that life change to happen!!

Playing yesterday with my excellent partner Howard Christ at Citrus Springs we were dealt the following hands.

Howard (North) AKxx, Axx, Qxx, JT.
Tommy (South) QT, xx, Axx, AKQxxx.

We play Kaplan Sheinwold (updated) so our opening 1 No Trump bids are 11-14 hcps. Howard dealt and opened 1NT. In spite of the voices of the Bridge Gods begging me to respond 3NT, I fell in love with my 7 tricks off the top (partner must have at least 2 clubs), and my distributional values. I bid 4 clubs (Gerber) and speed past 3 NT. Horror of horrors, partner shows 2 Aces and now I really am in a fix. There is no turning back, so I ask for Kings and partner shows 1 King. Since I have already waived goodbye to all sensible contracts, I slam down a stack of bidding cards with 6 clubs on top.

West, an experienced player, leads a small trump against my slam taken by the Jack in the dummy. Why do people lead trump against a small slam? It should set your nose twitching. As Howard said, they usually have something to hide! Now I need a plan for declaring this hand that will end up with 12 tricks.

My attention is immediately drawn to the spade suit. Since opponents have 7 spades between them, dropping the Jack in three swings is a distinct underdog. (I later looked it up, about a 25% probability). Another choice is a simple finesse in the spade suit, finding the Jack with East is a 50-50 proposition. If that works, I have 4 spades, 6 clubs, a heart and a diamond. But I wonder, is the Jack of spades one of the cards that West is hiding? Another possibility is finding the King of diamonds with West. That is also 50-50, but a more appealing choice given the lead.

Then I remembered a hand that I saw a couple of years ago in Pat Peterson’s class on “The Play of the Hand.” In that hand Declarer had have two choices to make his contract, splitting a 7 card diamond suit 3-3 or taking a simple finesse. While the finesse was the better opportunity, the example pointed out that when you have two chances, you should play them in a manner so that if the first chance fails you can still try the second chance. In that example, you play on the 7 card diamond suit first since if the suit does not split 3-3, you can still try the finesse. If you try the finesse first and it loses, you never get a second chance, you’re cooked!

Somehow I got the flash that this hand was full payment for staying awake in Pat’s class. If I try to finesse the diamond King first and my queen loses to East's King , I can still try the spade finesse, but if I do it the other way around and the spade jack is off side, I never get to the diamond finesse. After pulling trump, on trick three I laid down a small diamond. As soon as it hit the table I saw a small flinch come from West -- now I know what she was hiding. West put up the Kimg and the contract was home. A cold top. Now the location of the jack of spades is academic and only of interest to statisticians.

So, here is the lesson and you are not even going to have to pay Pat to learn it. When you have two chances to make your contract, arrange your play if you can so that if one chance loses, you can still try the second chance. Even if you are not a numbers guy, you would have to be impressed that getting the order of play correct changed a simple 50% chance into a 75% probability. Having two bites at the apple is always better than one.

You are probably wondering who held the Jack of Spades. To be honest, I was so excited about making this contract that I can’t remember. Probably West, she’s pretty sneaky!

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