What is the best way to combine chances?

[jcreech]

The opponents bid to 6NT by South on a less than wonderful auction.  The lead was the T. There are chances galore, but what is the best way to combine those chances without squeezing one hand or the other in the process.

  AKQJ3
  K75
  QJ7
  K8


  8
  AJ32
  AT3
  AQ432

You have 10 top tricks, so what is the best route to build tricks 11 and 12.  As you can see, 5 spades if 4-3, 5 clubs if 3-3, 4 hearts if Qxx onside, and 3D if K is onside.  Playing spades is the safest long suit to test, but starts to squeeze the South hand.  Anything else starts to risk losing tricks.

[kenberg]

[Added: This would not have worked as the cards lay, and I am thinking it was not the best line.]

I am pretty sure that I would start by assuming that the clubs  are no worse than 4-2.  Of course I might change my mind later. Some of this will depend on what happens as the hand goes on.

So up with the !c K at T1. If Rho follows with the J I will have to decide what to make of that but suppose he follows low. I suppose if clubs were 3-3 this hand would not be posted, but at the table I don't know that so I now lead the  8 to the A. If either side shows out then we are done with the suit, but perhaps everyone follows? Perhaps it should now depend on just who followed with what, but I think I now lead the Q and throw the Q from the table. I suppose someone shows out. I have now pretty much committed myself to playing another round of . This brings me up to 4+2+1+4=11 sure tricks. I hope to not have to take any finesses. On that fourth I will pitch the 5 from dummy.

Now they are in, but who is in? Could be either way. If Lho is in, surely he gets out by leading a else he hands me my 12th trick. If it is Rho with four , it is probably best for him to get out with a as well. That 3 is a (highly) recessed menace and killing the entry is no doubt right. But if Rho wins the 4th  and he then leads a red card I will take my three red winners and end in hand, and cash the last throwing the last red card from the table. The board now has AKQJ3 and my hand is 8 / J3 / T3. If are 4-3 I am home, but also I am home if either opponent started with long   together with either the K or rhe Q since he must hold on to all of his .

So most likely the opponents, when in with the , play a . This kills the entry for the squeeze I was hoping for, but all is not lost. Small to the A, cash the throwing the J from the table, back to the board with the K, maybe the Q drops and I claim, if not I run the top . If they split. fine. If not, the end position will be 3 and 7 on the board, AT in my hand. If haven't split, who has the length? If Lho has the length then he has only one red card left. I will have to decide whether he blanked his T or whether it lies no my right. Of course if Rho was dealt the Q  then he had to hold on to that so maybe the double squeeze, centered on , has worked. i will have to judge this the end.

[jcreech]

Here is the rest of the story:

                AKQJ3
                K75
                QJ7
                K8
  T6                  97542
  86                  QT94
  K9542              86
  T976                J5

                8
                AJ32
                AT3
                AQ432

At the table, declarer won the K, took the diamond finesse then when it lost, LHO exited with a spade, declarer continued the spades, but when they didn't split, took K followed by the heart finesse. Essentially combining the chances of three suit combinations.  My estimate of the chances of success for this line was 88.7%.  75% from one of two finesses plus the chance that the spades break 4-3  (70/128) applied to the remaining 25%.

I think the way to combine the chances of all four suits is to win the K, then take the diamond finesse.  Assuming that LHO takes the K and returns a spade, declarer continues by playing two more round of clubs, pitching a heart from dummy.  When the clubs do not break, play a heart to the K and play four rounds of spades.  When the spades do not break, play a heart to the J.  When that wins, claim.  By adding the additional suit to the combination, I think it brings the chance of success to 92.9%, but adds the risk of going down more than one.

Two additional thoughts:

I think declarer was right to not consider the clubs because of the lead.  If clubs were breaking 3-3, then it was unlikely to have been the opening lead.

If the E-W hands were reversed, I believe a squeeze might develop (I haven't looked carefully), but in the actual layout, the I think the black suit threats can disappear before the respective squeeze materializes.

[kenberg]

Yes, that seems right.  Starting with diamonds is sort of a 2 for 1. Maybe the finesse work. Great. But if not, then you have lost one trick and you are up to 11 winners, which possibly could lead to some squeeze possibilities as well as the finesse. For example, if Rho is the one with the long spades then, as declarer cashes the clubs and diamonds, he will have to hold all five spades and thus come down to two hearts. This could be useful if he originally was 5=4=2=2. Of course if his original heart holding included the Q the finesse was going to work. But if he held xxxx and Lho held Qx then this will be exposed. Declare, after running spades , has Kx on the board (one heart was thrown on the club), and one known spade. Declarer cashes the K and leads a small , Rho following. Which means that Rho has no more hearts. No matter, Lho started with only two and so the A drops the Q.   It's not all that much, but it adds a little.