Wednesday, October 10, 2012

Sequences (part one)

If music be the food of love, then sequences are the life-blood of bridge. Every bridge writer remarks that defense is harder than offense, but in my opinion none have adequately described why. Yes, the declarer can see all of his "assets". But it's specifically the sequences that make the crucial difference. A defender can sometimes immediately see that one of his significant cards cannot be in sequence with his partner (the dummy holds the surrounding cards) but he can rarely be sure that partner has a fitting honor until later in the hand when there has been time for signalling. By then, it may well be too late.

Sequences are most important in the first couple of leads of a suit. After that, assuming leader is trying to develop long cards, the opponents are likely to start showing out of the suit or at least having to play their sequence-breakers and what cards are left are more likely, now, to be sequential.

The next best card combination after a sequence is a quasi-sequence, known as a tenace. That's to say we almost have a sequence but there is a card missing. A tenace is positional in normal play, in other words its effectiveness depends on the location of the missing card. However, even if the card is wrong, it may be possible to win both cards of the tenace on an endplay.

Sequences can be split between the two partnership hands and still be effective. In fact, such an arrangement can provide transportation between the hands. Tenaces can be split and retain some effectiveness but it is generally reduced. For example, AQJ opposite xx may provide three tricks if the king is right. But Axx opposite QJ will produce only two tricks even if the king is onside. Longer split tenaces fare better: A5432 opposite QJT9 will always produce five tricks if the king is onside, assuming one outside entry to the long card. Sometimes, a tenace can even kill a sequence sitting under it, for example AKT sitting over QJx.

Of course any sequence or tenace has to have a reasonable rank to be useful. Holding the 65432 in a suit (a straight flush) may look pretty but it has no value whatsoever as a sequence. When a suit has no significant sequences at any given point of the play, it may be said to be "frozen": whichever side leads the suit gives up a trick. We'll examine these more closely in part two.

On defense, the opening lead is particularly dangerous for the simple reason that you don't know which cards in your hand are part of a partnership sequence and you don't usually know where partner has a tenace sitting over the dummy. This is why having your own sequence(s) is so very important, lest you "blow up" a suit that was frozen. Leading from a safe sequence (AK, KQ, QJT, JT98) can never lose a trick in the suit directly but it can sometimes lose a tempo if there was something more urgent to do. How many times have we seen the Abbot lead from a sequence like KQJT only to have Brother Xavier remark after the hand "not the best of leads, Abbot."

For our first example we will go to another deal involving the Abbot and Brother Xavier (from Celestial Cardplay by David Bird, 2009). This time, the Abbot is, through the Good Lord's mysterious handiwork, partnering the disrespectful novice, Brother Cameron. In this hand we will see how the natural advantage of the defenders in having the opening lead is, as so often happens, nullified by the wrong choice of suit. And why does Bro. Xavier go wrong this time when he leads the obvious Q? Because the key sequence in his partnership's hands is hidden in his partner's hand.

Perhaps if Ethan had had a chance to double an artificial club bid, the story might have ended differently. But then the two club honors might have been split. There's something to be said for an attacking lead against a slam when you know dummy is coming down with a good suit but that was not clear on this auction. And to lead from an unsupported honor when you have such an "obvious" sequence in another suit, might require some good arguments in the post-mortem.

No, the reason that the slam came home, apart from a relatively lucky lie of the cards, was declarer's intrinsic advantage and the defender's corresponding disadvantage: the ability or inability to see your sequences. It's true that even a diamond lead sets the slam but for a different reason: the trump situation provides no entry to the diamonds after they have been set up (East has to be sufficiently alert to continue diamonds at trick 2).

To be continued.

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