Sunday, November 21, 2010

Surviving with Queens and Jacks in No Trump

Queens and Jacks, even if they are supported by other non-honor cards, are not very valuable in suit contracts, since tricks that can be won only after 2 or 3 leads of the suit often disappear. In no trump contracts, these middle cards take on more value as they can become stoppers in the suit and produce a trick. The following discussion assumes entries are not a problem.

1. Assume you are declaring a no trump contract. You hold QJx in a suit and dummy has xxx.
(a) What is the probability this holding will provide a stopper in the suit and produce a trick if opponents lead the suit?
(b) Does it make and difference if opponents do not lead this suit and force you to lead it?
(c) If your contract was dependent on this combination producing a trick would you still bid it?

2. Assume again you are declaring in no trump. You hold Qxx and when the opening lead comes down you see Jxx in the dummy.
(a) Is this combination any different that the first combination in result?
(b) If so, is it more or less vulnerable if opponents lead the suit?
(c) If your contract was dependent on this combination producing a trick would you still bid it?

3. Does the fact that declarer hold 6 cards in the suit have any practical significance in either case?

Here is the discussion of each issue:

1. The holding of QJx in any hand will produce a guaranteed stopper except where the A and K are both sitting behind the QJx. Thus, if held by declarer (always South), it is a winner when East holds AK (25%), or when the A and K are split between the two defenders (50% since they can split 2 ways) but loses to AK West (25%). Thus it is a guaranteed stopper and will produce a trick 75% of the time. With this holding it does not make any difference if opponents lead the suit or if declarer is forced to lead the suit, the probabilities remain the same. With a 75% probability I want to be in the contract every time. It’s like asking if you would like a 75% game. If West holds the AK, hopefully your disappointment will be shared by many others.

2. In the case where Qxx is in one hand and Jxx in the other, the situation changes somewhat. Note that if opponents lead this suit, it will produce a trick 100% of the time as long as declarer ducks on the hand to first play to the trick. With this holding you are happy to have the suit played on opening lead. That is the good news. The bad news is that if declarer if forced to play this suit it becomes a 50% proposition and will not produce a winner when the A and K are divided between the opponent’s two hands. If you merge the two probabilities you still have a 75% chance of making a trick, so I still want to be in the contract.

3. Note in each case you had 6 cards in the suit. One of the concerns is opponent’s holding in the suit will split 5-2 and they may be able to run 5 tricks before you get your track shoes on. The defenders will hold a 5+ card holding only 1/3 of the time and only 1/6 of the time will opening leader have that holding. This provides some additional element of safety. You probably noticed that QJx opposite xx will also produce a stopper and a trick 75% of the time. But now you only have 5 cards in the suit and the odds of one of the opponents holding 5+ cards in the suit has doubled.

If the suit is not led on the opening lead, this information can be helpful in planning your further play. Do you take the opportunity/risk to set up a trick in another suit for an overtrick or should you take your tricks and run. With QJx only one holding of four can hurt you. With Qxx opposite Jxx, two holdings of four can doom your contract. Do you run the risk for an overtrick? If the scoring is IMPs, whether a game or part score contract, I would take the guaranteed plus score and not take any risk for an overtrick. In matchpoints I would try for the overtrick with either a 75% or 50% chance of success. The odds feel right to me.

What if there is an overcall and partner makes a Western Cue bid? Do you treat QJx as a stopper? What about Qxx? We ask questions, you decide!!

If you are defending and sense that declarer may have one of these holdings it is seldom right to lead the suit unless you see your tricks are going away. When you declare, you may have sensed that it is often advantageous to put opponents in the lead and let them solve your problem. Now you know why.

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