Play this

[kenberg]

As I drink morning coffee I am giving a little thought to Jim's approach, thinking just about the 3-2 case. If W has Hx it works, if W  Hxx it doesn't, that takes care of 12 of the cases. If W has KQ tight it doesn't work since Jim plans ot finesse if W hops up. And if W has KQx then it doesn't work either. So that leaces the four cases where both honors are with E. Jim's approach (I guess any approach) works if E holds KQ tight. If E has KQx then Jim loses two tricks but still in the contract if E has the A because there is no entry to the long spade in the E hand. If I did this right that's 52.5 % of the 3-2 splits, plus whatever we get from W erroneously hopping up. With Hx it doesn't matter if he hops up, Jim drops it anyway, with Hxx he might, but he shouldn't.

I'll take a look at the 4-1 splits later.

Ok, I'm back.

For the 4-1 splits the key point is that two tricks will not be enough for the contract (barring some sort of miracle in clubs).  When the diamonds are 4-1 then Jim's route is apt to require giving up two diamonds: If W has a stiff honor he will, of curse, rise when a small !d is led. Now the finesse will work, but since E started with Hxxx the finesse only nets two tricks. Similarly, if W has a stiff spot, then the small will go to the T taken be an honor from E.  Declarer gets in and the plan, when the T loses to E, is to lay down the A when next in.  This fails to drop the other honor, so declarer must give up a . This will be ok if E has the A since the defense will be taking one , one and two .  If declarer played three rounds of first, this might go wrong since the remaining could be the fifth trick for the defense.

So, when E has four , I think it all comes down to where the A is. If W has four , I think the contract is doomed. With KQxx W will rise and clear , while if E has a stiff H then he takes it and clears .

So, if are 4-1, I think the chances are about 25%. If this approach is to bring in the contract, W has to be the one with the stiff, and E has to have the A.

So I think.

[jcreech]

Think about the entry problem.  How do you get to dummy twice to take the double hook?  The only possibilities are the clubs and hearts. 

The club is sure, but is only available once, and then you either block the suit, or you likely set up something for the defense.
 
So let’s look at the hearts.  Do you:
  1.   lead the Q, sort of hoping that they take their A, making the K a sure entry, or
  2.   lead small, making the Q stiff
     a.   hoping that if West has the ace, they duck, and
     b.   if they fly the ace, will you overtake the Q to take the 2nd hook advertising that the hearts are now wide open

The advantage of the Q is that they may take the A before they know the count on the suit.  The disadvantage is that it is a sign of desperation to get a second entry to the board or why not lead another club.  The advantage of the small is that if the A is onside, you get to the board without revealing your vulnerability in the suit, but if you lose, you risk losing 2 or 3 more hearts.

On the actual hand, with East having the Kxx and the A, I would not take the Q to deny a second entry to the dummy. However, with the spots and honors dropping like crazy, it works out that East is endplayed in both hearts and diamonds anyway.  But if you lead small to the K, East wins and exits with another heart to endplay declarer - which is what happened to Jack.

[kenberg]

This hand has a variety of features, as often they do. I decided  early on to settle for two club tricks. The reason is that even if I start with the A and lead to the K it is far from clear that I should cash the Q since, unless the clubs break very well, sets up a club trick for the defense. If I can bring in the diamonds I hardly care how many club tricks I get. I don't want them first getting two spades, one heart, one diamond, and a club. So that's why, once I decided I would try to bring in diamonds, starting with to the board and running the T, I just led a small to the board at T2.

Now about leading the Q. (These re frist thoughts, see below for a follow-up) Similar considerations apply, or so I thought. If I lead small to the K and it is taken by the A, I am n ot dead yet. Maybe, after my T lost to an honor, the remaining honor is  about to drop and I am fine. If I start by leading the Q, all playing small,  and then continue with another , that second !h might well be taken by the A. This I did not like.  I did not think it through But it is possible, maybe unlikely but possible, E held AQJxx or AQTxx or some such. The best way to preserve all of my options seemed to be to lead small toward the K right off. But maybe I need to think this through further.

Followup: 
Suppose I win the spade. lead a club to the board, run the T losing to an honor. 
Now suppose I lead the Q and it goes spot, spot, spot, all small. Now I ead the 4 and W produces the T. Do I know what to do? If I play small, probably E can play smaller, he will do so, W will cash out the spades, and then lead a to the A. Down 1. But if I cover the T  with the K, E produces the A, leads a back to the J that might well be in the W hand, and then W cashes spades for down 1.

I did not go through all of this in my head, I just thought it best to start by leading small toward the K.  But looking at it a bit more, I think that this was right.

[wackojack]

I am glad this post got so much interest and thoughtful analysis.  My objective was understand whether or not my play at the table gave me the best chance of making the contract.  The informed comment has now satisfied me that I did give myself the best chance. 

This type of problem for declarer often comes up where you have to choose between "double hook" with possible entry problems or Qx or Kx in one hand.  Estimating percentage chances is, as Ken explained, an inexact science.  Nevertheless it is a very useful tool for making comparisons between different proposed lines of play.  It is perhaps not practical to do this at the table, but post analysis gives you a better feel for seeing the best line at the table when you next have a similar problem.

[kenberg]

I like discussing hands, probably the main reason is that I find it interesting. But I think it is also useful. On some occasions the correct line is absolutely clear cut if declarer thinks of it. Far more often, it is not clear cut. A detailed probabilistic analysis at the table is often not practical, but i think it is both interesting and useful to review the hand later. At the table there will be a certain amount of "Well, that looks best". Reviewing later helps develop such judgment.

In this hand:
To bring in the diamonds we have to think: Maybe both honors are on our right, maybe they are split, if they are split then maybe the one on our right is a doubleton. Or maybe we can get back with a heart to repeat the finesse. And  that seems like enough possibilities to make it a plausible line. Detailed calculations can wait.

Michael Rosenberg is often cited as having a very strong ability to think through all of the details, with probabilities attached, at the table. What can I say, I'm not Michael Rosenberg.

There are plenty of times I later look at a hand and say "I should have thought of that". Reviewing hands helps for the next time, at least fir me it does.