I'll start this narration with a war adage I read in an Agatha Christie novel (N or M, for those interested):
"There's time to recriminate after the war, but not during the war."
In order to not lead you in any direction, I'll give you the problem as I faced it.
This was the below hand I played on BBO
http://www.bridgebase.com/tools/handviewer.html?myhand=M-29858071-1324059618
I opened 1 NT, partner transferred me to spade and I super-accepted. Partner dutifully raised to game, and I got the lead of Ace, King and a 3rd round of club.
Dummy:
S:JT865
H:Q64
D:K
C:Q542
Hand:
S:AK7
H:A98
D:AQ865
C:76
How do you assess prospects? What would be the skeleton of your plan?
The skeleton of the plan would start with your action right now. You could try to win the QC, or try to ruff the club first and worry about the rest later.
Say you duck the club, Righty pitches a heart and you ruff. What now?
As the cards lay, you can no doubt make the hand. One of the many ways to make the hand is to unblock the KD, then lay down AK spade, and when all follow, take your 2 pitches on the AQD, pitching hearts. The opponent with QS can ruff and all's well.
But how would this work if spades were 4-1?
Someone would be left with Q9 spade. Further, they could decline to ruff the 3rd round of diamond, or ruff with the 9.
You could take the heart pitch (if they dont ruff), play ace of heart and ruff a heart. But from there you're toast.
2 trumps left, and the opponent with Q9 can win a trump lead and force out the last trump with a heart. You'd end up losing the spade 9 as well, to go with AKC and QS.
So the main threat to guard against is the 4-1 break.
Alternatively, if they ruffed with the 9, if you pitch Heart, 9S together with the QS would be the setting trick. So you'll need to overruff, and dummy will still have Q9 of heart and no apparent way to get rid of the heart loser. The closest you could try is to cash the club Queen pitching diamond, and then throwing Lefty in with the spade Queen. But if clubs are 5-2, he'd put you back on dummy with a club forcing a ruff, and you'll be stuck with the losing heart.
It is not clear what 4-1 breaks can be covered, but it seems obvious to me that its unnecessarily risky to draw trumps.
Since I'm not in a hurry to draw trumps, I may as well try to cash QC in case the suit is 4-3.
Hence, I tried to win the Q. RHO ruffed small, and I overruffed with the 7.
It is all the more imperative now to not draw trumps. Dummy now has a club loser which I haven't ruffed. All the more reason to not cash AK spade in a hurry. Accordingly,I unblocked the diamond King, and play a spade to the Ace.
Since I've not yet ruffed the club loser, I can't cash KS. Accordingly, I tried to cash AQD. If everyone follows to the AQD am in great shape. Pitch 2 hearts, Ace of H, H ruff,club ruff with the KS and ruff heart again and score one of JT spade.
However, LHO ruffs the QD with the QS. What to pitch in dummy?
It is tempting to throw the club loser away, but this is clearly a losing proposition. If you do so, then LHO can switch to heart if he's missing the king, and you'll be stuck with a heart loser.
Therefore, to continue to threaten to ruff out the club loser, it is proper to pitch the heart in dummy.
LHO now is forced to lead spade. Otherwise, you can ruff the club with the spade King and score the rest of dummy's trumps by pulling trumps, getting to dummy with a H ruff.
So LHO leads spade, removing your club ruff.
What is the recovery plan?
Dummy:
S:JTx
H:Q
C:5
Hand:
S:-
H:A98
D:54
The above end position is what I'm most interested in. I would demand that all my partners find the winning play in this end position. There's no point in playing the game if one does not, even by sheer accident, stumble into the only play available that could win. And, that play, even though it is not apparent to the naked eye, gives a 100% guarantee to make the 10th trick.
The 2 options available are:
Option 1:Ace of heart, heart ruff. You're stuck on dummy, and are 100% guaranteed to go down 1. The best you can do is play off trumps and hope for a blunder.
Option 2: leave hearts alone, ruff a diamond. Play off dummy's trumps. as with Option 1.
With 2 cards to go in dummy,when the last trump is led:
RHO has to keep the good diamond, and has to let go of a heart. Now you can safely pitch the diamond, keeping A9H.
LHO likewise sees the club threat in dummy, and is forced to keep the high club and let go of a heart.
With 2 cards to go, NEITHER opponent can keep 2 hearts. Queen of heart to the Ace will bring down ALL missing hearts.
This play works even if BOTH opponents were dealt the KJH. Because neither could keep 2 hearts in the end position: a textbook double squeeze.
Friday, December 16, 2011
Sunday, December 11, 2011
Purposeful Bridge 102: (Sometimes,) Either the devil is better, or the deep sea is better.
This is a story from the Sunday 2 session pair event (on the last day of the recently concluded Seattle Nationals) where I played with Myti.
The deal is presented as a defense problem: both defensive bidding, and defensive play.
You hold:
S:KJT3
H:AQ83
D:KJ9
C:J7
Your side is Red, opponents are Black, and your Righty (me) opens 1 NT. Playing DONT over Strong NT, do you overcall?
The answer is somewhat immaterial; I would overcall 2 H in a heartbeat, even at these colors. That's me. You could choose the conservative path of passing. I wouldn't quibble with a pass. What would give the game away is agonizing. Say you agonize over the decision, and eventually pass (to make the situation same as the situation I faced; I was the Notrump opener). Lefty bids 2 club, Righty bids 2 Diamond, and Lefty rebids 2 NT, alerted as 'may not have a 4card major'. Righty ponders and raises to 3 NT.
What would you lead?
If I were defending this hand, I'll lead the Jack of Spade. Sure, sometimes dummy shows up with A98x and I've given an extra trick way, but I expect declarer's AQ to score 2 tricks most of the time, and I expect our side to get the 2 spade tricks that appear likely on the auction (since 2 D denied a 4 card major).
Again, to put you in the situation my opponent was in as defender,say you elect to lead "passive", the Jack of club.Dummy is as follows:
S:Q54
H:J76
D:A532
C:QT8
The jack of club is won by the Queen.
Declarer next plays the diamond ace and another diamond to his ten, your Jack.
You don't want to break a major suit as you can visualize the spade ace, heart king with opponent.
Accordingly, you cash your KD and exit a club. Partner pitches a discouraging spade on the KD.
Declarer wins the club continuation with dummy's ten, and proceeds to cash 2 more clubs, on which you can afford to let go of 1 card in each major. On the 4th club, declarer pitches a diamond in dummy, and then cashes the 4th diamond in his hand.
Dummy is down to:
S:Q54
H:J54
You are down to:
S:KJT
H:AQ8
Dummy is yet to make a pitch on the 4th diamond, but you have to pitch first. What do you pitch?
At the table, my opponent pitched a heart, bringing herself down to AQ H KJT spade.
I promptly pitched a heart in dummy and led towards Jx heart.
My last 5 cards were:
S:Ax
H:Kxx
Opponent can win QH and switch to spade NOW, and I put up the spade Q and force out the heart ace with the jack, scoring KH and AQ spade.
With 2 diamond tricks and 4 club tricks, that was 3 NT making.
Even if you cash AQH at one go, it doesn't help.
So why is this article on this blog with this title?
The heart discard by my opponent at trick 9( leading to the 4 card end position) is a purpose-less discard.
The correct and deservedly winning decision is to bring yourself down to KJ spade, AQ8 heart. Then, based on declarer's discard+play, you have a way out to get more than your 2 natural H tricks.
For example, say declarer pitches heart in dummy again, and plays heart towards the Jx. You take your AQ H and exit heart and wait to score your KS for the setting trick.
If declarer pitches heart and instead plays ace and out a spade, you win the spade King and place the QH on the table. Dummy has Jx heart and a good spade,but by leading Q and not low, you've killed the JH as an entry.Partner has kept T9x heart so partner guards the heart if declarer wins the king of heart and leads a heart back at you.
If declarer pitches spade in dummy and leads low towards Jxx heart, again, you win the QA heart and exit heart, waiting for your KS.
If declarer pitches spade in dummy and plays ace and out a spade, you win the king and lead low heart, letting the jack win.
As long as partner started with 4 spades, declarer cant win the heart in either hand gainfully, even if declarer had KTx Heart for example.
This was a little 'advanced' problem in end-play avoidance. My opponent wasn't up to the challenge, and let me make an unmakeable 3 NT.
This was my hand:
S:A7
H:K42
D:QT84
C:AK64
From the auction stage itself, I had decided to play my LHO for all the missing cards. The agony over my 1 NT opening was perceptible to all at the table, and I could not help bidding 1 for the road on end-plays that were bound to arise from such a lop-sided distribution of missing high-cards.
If you agonize over your call over the 1 NT opening from opponent (with the defensive hand) and elect to lead passive, you better find the right discard at the end :-)
The crux of LHO's (constrained by the opening lead) problem is to make a discard that LHO knows gives up something, but hopefully doesn't give up too much. And when you work out the holdings partner (with his admittedly scarce values) can contribute, there are a few "outs" partner can give you, if you find out the correct play of keeping the valuable 3rd heart as an exit card. Even when giving up a trick (in this case, the potential trick and suit blocking ability provided by the spade ten), the choice must be to find a purposeful way to give up a trick/potential trick: that's the name of the game.
On the surface, the discard at trick 8 looks like a choice between the devil and the deep sea. But sometimes, either the devil is better than the deep sea or vice versa :-).
The deal is presented as a defense problem: both defensive bidding, and defensive play.
You hold:
S:KJT3
H:AQ83
D:KJ9
C:J7
Your side is Red, opponents are Black, and your Righty (me) opens 1 NT. Playing DONT over Strong NT, do you overcall?
The answer is somewhat immaterial; I would overcall 2 H in a heartbeat, even at these colors. That's me. You could choose the conservative path of passing. I wouldn't quibble with a pass. What would give the game away is agonizing. Say you agonize over the decision, and eventually pass (to make the situation same as the situation I faced; I was the Notrump opener). Lefty bids 2 club, Righty bids 2 Diamond, and Lefty rebids 2 NT, alerted as 'may not have a 4card major'. Righty ponders and raises to 3 NT.
What would you lead?
If I were defending this hand, I'll lead the Jack of Spade. Sure, sometimes dummy shows up with A98x and I've given an extra trick way, but I expect declarer's AQ to score 2 tricks most of the time, and I expect our side to get the 2 spade tricks that appear likely on the auction (since 2 D denied a 4 card major).
Again, to put you in the situation my opponent was in as defender,say you elect to lead "passive", the Jack of club.Dummy is as follows:
S:Q54
H:J76
D:A532
C:QT8
The jack of club is won by the Queen.
Declarer next plays the diamond ace and another diamond to his ten, your Jack.
You don't want to break a major suit as you can visualize the spade ace, heart king with opponent.
Accordingly, you cash your KD and exit a club. Partner pitches a discouraging spade on the KD.
Declarer wins the club continuation with dummy's ten, and proceeds to cash 2 more clubs, on which you can afford to let go of 1 card in each major. On the 4th club, declarer pitches a diamond in dummy, and then cashes the 4th diamond in his hand.
Dummy is down to:
S:Q54
H:J54
You are down to:
S:KJT
H:AQ8
Dummy is yet to make a pitch on the 4th diamond, but you have to pitch first. What do you pitch?
At the table, my opponent pitched a heart, bringing herself down to AQ H KJT spade.
I promptly pitched a heart in dummy and led towards Jx heart.
My last 5 cards were:
S:Ax
H:Kxx
Opponent can win QH and switch to spade NOW, and I put up the spade Q and force out the heart ace with the jack, scoring KH and AQ spade.
With 2 diamond tricks and 4 club tricks, that was 3 NT making.
Even if you cash AQH at one go, it doesn't help.
So why is this article on this blog with this title?
The heart discard by my opponent at trick 9( leading to the 4 card end position) is a purpose-less discard.
The correct and deservedly winning decision is to bring yourself down to KJ spade, AQ8 heart. Then, based on declarer's discard+play, you have a way out to get more than your 2 natural H tricks.
For example, say declarer pitches heart in dummy again, and plays heart towards the Jx. You take your AQ H and exit heart and wait to score your KS for the setting trick.
If declarer pitches heart and instead plays ace and out a spade, you win the spade King and place the QH on the table. Dummy has Jx heart and a good spade,but by leading Q and not low, you've killed the JH as an entry.Partner has kept T9x heart so partner guards the heart if declarer wins the king of heart and leads a heart back at you.
If declarer pitches spade in dummy and leads low towards Jxx heart, again, you win the QA heart and exit heart, waiting for your KS.
If declarer pitches spade in dummy and plays ace and out a spade, you win the king and lead low heart, letting the jack win.
As long as partner started with 4 spades, declarer cant win the heart in either hand gainfully, even if declarer had KTx Heart for example.
This was a little 'advanced' problem in end-play avoidance. My opponent wasn't up to the challenge, and let me make an unmakeable 3 NT.
This was my hand:
S:A7
H:K42
D:QT84
C:AK64
From the auction stage itself, I had decided to play my LHO for all the missing cards. The agony over my 1 NT opening was perceptible to all at the table, and I could not help bidding 1 for the road on end-plays that were bound to arise from such a lop-sided distribution of missing high-cards.
If you agonize over your call over the 1 NT opening from opponent (with the defensive hand) and elect to lead passive, you better find the right discard at the end :-)
The crux of LHO's (constrained by the opening lead) problem is to make a discard that LHO knows gives up something, but hopefully doesn't give up too much. And when you work out the holdings partner (with his admittedly scarce values) can contribute, there are a few "outs" partner can give you, if you find out the correct play of keeping the valuable 3rd heart as an exit card. Even when giving up a trick (in this case, the potential trick and suit blocking ability provided by the spade ten), the choice must be to find a purposeful way to give up a trick/potential trick: that's the name of the game.
On the surface, the discard at trick 8 looks like a choice between the devil and the deep sea. But sometimes, either the devil is better than the deep sea or vice versa :-).
Wednesday, December 7, 2011
Purposeful Bridge 101: Setting the tone
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 :-).
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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