I've always said to all my bridge partners and opponents that the single biggest challenge in all bridge hands you have played and will ever play in your life, is to find purpose behind every move of yours.
Here's a hand which illustrates my point.
I played this on BBO, and you can find the hand record at:
http://www.bridgebase.com/tools/handviewer.html?myhand=M-23871842-1323106937
This was the hand as I saw it, as declarer:
Dummy:
S:KJ
H:KJ765
D:AK86
C:T8
Declarer:
S:AQ982
H:32
D:753
C:AQ7
My partner opened 1 H, I responded 1 spade, partner rebid 2 D and I signed off in 3 NT.
I got the opening lead of the diamond Queen. I took it in dummy, unblocked the spade KJ, all following. Next, I finessed the club Queen by leading the 8, Righty plays low and I stick in my Queen.
Thus far, I don't think anyone will disagree with my line. I have 5 spade tricks, 2 diamond tricks, and a 50% chance at a 2nd club trick, which I've just taken. The Queen loses to the King, back comes the JD. There appears to be no purpose to ducking, so I took the Ace, righty pitching the spade ten.
Oh well, diamonds are 5-1. Time to assess. We have 8 tricks, which we can take only by expending the club ace. It is unclear if -1 will be bad if nothing works, but I figured it cost me nothing to try cash the spades and see what happens. Accordingly, I lead the ten of club, Righty again plays low, and I take the Ace, and follow it up with 3 more spade winners.
Righty having got rid of his 3rd spade, pitches 3 hearts, while Lefty follows to the 3rd spade, and then pitches 1 heart, 1 diamond.
How do you assess prospects? Has the heart guess narrowed at all?
This is a hand for which there is one and only one purposeful play available (assuming the purpose is to try to make 3 NT). I'll show you how I got there, and when you read how I got there, you'll see the point of the title about purposeful play.
First of all, Lefty can't have the heart ace. If Lefty had it, All Lefty has to do is keep 3 diamonds and the heart ace.
For that purpose (assuming Lefty had the Ace of heart), Lefty can boldly let go of his clubs with no fear of setting up a length-trick for you. This is because Lefty and Righty both know you did NOT start with club AQJx How do they know that?
From your line of play. If you started with AQJx, you'd have floated the club ten to the king, guaranteeing 3 club tricks without needing club pitches from opponent. Therefore, you didn't start with AQJx.
If you started with just AQJ, then the 4th club was expendable as opposed to the diamond actually discarded by Lefty.
Therefore, Lefty did NOT start with the Ace of heart.
Note that there is a key difference in inference here.
The first inference is, If Lefty started with the Ace of heart, you can NOT make this hand.
That's the easy part.
Next inference is, Lefty Indeed did NOT start with the Ace of heart! This is because, he pitched a diamond as opposed to the expendable club.
So we know Ace of heart is with Righty. So do we just play a heart to the Jack and hope the Queen is onside?
A donkey can do that, we're bridge players. Let's try to do better.
First, since we started with only 5 clubs, the opponents have not only a bunch of cashing diamonds, but also cashing clubs. And not only are their clubs cashing, they would know it if you play heart to the Jack(since they know you don't possess club AQJx, if you lead heart to the jack, as opposed to taking your 9th trick in the form of the JC, it implies you didnt have the 9th trick in the form of the JC).
And further, what about the club break?
If the clubs are 5-3 with Righty holding Jxx now, he can cash the clubs and the heart ace for down 1.
Therefore, if you have any purpose in this hand, you have to assume clubs are 4-4.
But it doesn't end there.
There are 2 key parts of inference left.
First, about the defensive inference logic, which is more difficult.
If clubs are 4-4, once you play a heart to the Jack and (presumed) Ace, They know the KH is providing the 9th trick, and therefore cannot help finding the cashing clubs. If the cashing clubs provide Lefty with an entry, he will cash his diamonds too. Thus if the clubs do admit an entry to LHO, they cannot help finding it.
Therefore, you need to assume the clubs do NOT provide an entry to LHO i.e. clubs are blocked up with RHO holding 2 cashing clubs.
Now let's go to the easy part of this inference. Basic counting.
We've taken 8 tricks and lost 1 trick.
4 cards remain in LHO's hand. 2 of them are good diamonds. Atleast 1 of them is a club. No club has been discarded, so if LHO INDEED has QH, then LHO has only 1 club and which implies RHO had 5 clubs. So, regardless of where the JC is, the QH will popup if LHO has the Queen, and Righty will see it, and will have no choice but to cash the JC. Even if Lefty had Jxx club and failed to unblock, Lefty gets in to cash 2 good diamonds.
Therefore, here is the BIG inference.
There is NO purpose, ABSOLUTELY none, to playing Lefty for the Queen of heart as well!!!
So what remains? Fold up the cards and give up?
There is one slim chance remaining: that Righty possesses AQ H (as we reasoned) but has failed to unblock his clubs!!!
Accordingly, I exited club. Righty had indeed started with J9xx club, and had indeed failed to unblock. Making 3 NT for 10 imps. And needless to say, Righty of course had AQ of heart.
Note that this was not a makeable 3 NT. I should be down 1. But that doesn't give any kind of justification for any line other than the line taken (assuming you were with me for the first 9 tricks). Because, all alternative lines (in the 4 card end position) lack purpose.
Also, the play I took DID have a non-zero probability of working. Give Lefty a starting club holding of K432, which gives Righty a starting club holding of J965. Then, the clubs were never unblockable.
Once you start off with that base distribution of missing cards, you can work out how many other distributions exist where Righty needs to be alert in order to set you.
Example Lefty's initial club holding is K532, and Righty's original holding is J964. To beat you, Righty needs to unblock clubs on the first 2 rounds, saving the 4 for his partner to overtake on the 4th round. I happened to run into one of the permutations where it is far easier to unblock, but nevertheless, the unblock didn't happen.
Also, once you get the clutter cleared out of guessing the heart suit, you also realize counting tells you the heart suit NEEDS to be unguessable if you want to stand a chance to make the contract.
Let's revisit the counting exercise above in a different way.
Lefty pitched 1 heart, 1 diamond. Righty pitched 3 hearts on the run of spades (having pitched his 3rd spade on the diamond continuation).
Between the two of them, opponents have pitched 4 hearts. And since dummy started with 5 and you started with 2, they are left with only 2 heart cards. If you play a low heart and hoping for Lefty to have the Queen, if Lefty DOES have the Queen you cannot make the contract! It goes Queen, King, Ace, and you may as well fold up your cards. Nobody at the table who is on lead has a heart left, and dummy's good heart, and your own 2nd heart all serve no purpose. You may as well concede down 1 if Lefty indeed has the Queen of heart. So really, you're hoping that AQ of heart are both behind dummy's King-Jack, something you don't normally hope for :-).
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