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Apparently 6H (small slam with hearts as trump) can be made on this hand, irrespective of the distribution of opposing cards.

How?

You are south (holding 54, AKQJTx, -, 98765) . Dummy is north, the lead (by West) is a diamond.

AK32
652
JT
AKJT



54
AKQJT4
- 
98765

For those who might be unfamiliar:

This is a bridge hand and the hands are written as spades, hearts, diamonds, clubs or

spades
hearts
diamonds 
clubs

So north hand is actually:

  Spades:    AK32
  Hearts:    652
  Diamonds:  JT
  Clubs:     AKJT

Writing as spades,hearts, diamonds, club has become the standard practice.

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Can someone please add a [declarer-play] tag? –  Aryabhata Apr 26 '11 at 21:49
    
I haven't done a thorough check, but I think this is impossible when W has (T9876,9873,Q932,-) and E has (QJ,-,AK87654,Q432). NS will lose to the QC at some point, and so can't afford to lose any other tricks. This means they must clear out the trumps to start with, and S is only left with one trump as a winner. Consequently N will get stuck with the lead and lose one more trick in spades or diamonds. Have I made a mistake here? –  tttppp Apr 27 '11 at 11:48
    
@ttt: I believe it is possible even with that hand for West. –  Aryabhata Apr 27 '11 at 16:18

4 Answers 4

up vote 7 down vote accepted

I believe the following works:

Ruff (or trump) the diamond lead.

Now lead out the Trump Ace. If both opponents follow, then this is easy. You can take out opponents trumps and play the clubs. You can even try to finesse the CJ or T and try for an overtrick, when West has the Club Qxx. You have two trumps in hand, so you have an entry to hand after you unblock the clubs.

The problems happens when one of the opponents shows out on the Trump Ace.

Now draw three more rounds of trump. On the fourth trump, discard a diamond. Throwing the diamond is the key play: North hand is void in diamonds now. Now play AKJ of clubs. Opponents have to win this and if they return a diamond, you ruff in South hand, throwing the blocking club T from the dummy!

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+1 Very clever! –  tttppp Apr 28 '11 at 16:49
    
Yes, that was the key ... a way to get QC out from an opponent and also TC out from dummy. Very nice! –  Dave DuPlantis Apr 28 '11 at 17:01

So the trick (no pun intended) is to get to the remaining winner in your hand: once Q♣ is out, your clubs are good, but the only entry is by using your trump. To win club tricks in your hand, dummy must have only enough clubs to win tricks prior to the Queen's fall.

You trump the opening trick with 4♥ (1 trick). Run hearts through South to clean out West's trump (5), and on the last heart trick, slough dummy's 2♠. Lead clubs to finesse East's Q♣ ... East must take either the first or second club trick for her Q♣ to be good. When she does, she will have no more winners: QJ♠ lose to the board, Kx♦ is trumped in the hand, remaining clubs are taken on the board.

When East uses her Queen, you have 6 or 7 tricks won. If East leads a spade, you take that and the next trick with dummy's spades (8/9), followed by a spade from dummy to be taken with your last heart (10), which makes your remaining clubs good (11/12).

If East leads another club, you take it in your hand (7/8) followed by your last club(s) (9), then the heart (10), then across to dummy's spades (12).

If East leads a diamond, you take that with your last heart (7/8), but then there is no entry back to declarer's hand, and thus the final trick is a spade loser from dummy rather than the club winner.

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The problem with this is that east holding Qxxx of clubs might hold up the Q... +1 though :-) –  Aryabhata Apr 28 '11 at 1:17
    
@Moron, I don't think that's a problem: I'll edit to explain. –  Dave DuPlantis Apr 28 '11 at 1:23
    
@Moron, I take that back. I don't see a way around the resulting diamond lead. West will keep enough spades to prevent dummy from taking a third trick, which leaves East with two winners. –  Dave DuPlantis Apr 28 '11 at 1:54
    
eh ... if you have club winners on the board, those have to be played prior to the entry to your hand. –  Dave DuPlantis Apr 28 '11 at 2:06
    
If you play the Club Jack before playing AK, east can win the Club Q immediately and play a diamond, with AK blocking the club suit. (Or did I misunderstand your edit)? –  Aryabhata Apr 28 '11 at 2:15

If you know all the cards in a bridge problem (this is called "Double Dummy"), you can use a computer program called DeepFinesse, see http://www.deepfinesse.com/ to solve the problem. But it solves only problems where all 4 hands are known, so it doesn't solve the question "can you make 6 H against any distribution?".

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Yes, I believe even GIB does double dummy (and there are quite a few other DD solvers). This answer is kind of relevant in the sense that you pretty much end up with a few distributions for East/West you need to consider and those can be solved double dummy. Of course, it is more fun to not use the DD solvers :-) –  Aryabhata May 28 '11 at 2:19

The first thing I do is ask, what trumps are outstanding. They are 9873. That means I can draw them with four leads, but need to be careful about low trumps being overruffed.

The second thing I do is ask, which honors are outstanding. They are: QJ of spades, AKQ of diamonds, and Q of clubs. My AK opposite a doubleton takes care of the spades. I can trump the diamonds. My main worry, ironically, is the Q of clubs. But if that's my ONLY loss, I make six.

Here's how: 1) Ruff the diamond lead. 2 Draw all four trumps with AKQJ, discarding the diamond from dummy. You have one trump left in hand. 3) Take AK of clubs. 4) Lead J of clubs. If the queen hasn't dropped already, someone will take it. You have made seven tricks, lost one, have five more to go.

Opponents are out of trumps because you've drawn them. Realize that they only have four clubs between them, because you have nine. If they lead their last club, capture it with the 10 in dummy. Play AK of spades, ruff a spade in hand, then win the last club (five tricks). If they lead a diamond, ruff in hand, discarding the T of clubs from dummy. Lead the last two clubs (from hand), then cross over to the AK of spades (five tricks). If they lead spades, win the AK of spades. Win the T of clubs, then cross to hand with a spade ruff, and win the last club (five tricks).

Note how I counted trumps, clubs, tricks, honors, etc. This process is at least as important as winning the hand.

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