Match 2 - Board 34

Board 34
Our side vulnerable

♠ K 7 6 5 2 ♥ 8 3 ♦ A K 10 8 5 ♣ A

RHO opens with one club. I bid one spade. LHO makes a negative double, partner passes, and RHO bids one notrump. I bid two diamonds. LHO passes, and partner corrects to two spades. Partner doesn't need much to raise over a negative double. So either he has a terrible hand or a misfit. We may be too high already.

Fortunately, RHO takes us off the hook. He bids two notrump. Since opener is limited, this bid has little value as a natural call. It should be unusual, suggesting a 2-2-4-5 pattern. Responder should have length in one minor or the other for his negative double. So the knowledge of a minor-suit fit and the doubleton spade makes it incumbent upon opener to bid with that pattern. (Given my two diamond bid, the minor-suit fit is proabably in clubs, but it doesn't have to be.)

Jack did not alert two notrump, so presumably he does intend the bid as natural. Perhaps he worked out, by dealing out random hands for his partner, that it was right for him to bid, and two notrump was least committal way to compete. If so, then I still have a strong suspicion that he's 2-2-4-5. What other "balanced" pattern could he have that would make it the percentage action to compete unilaterally?

I pass, and two notrump ends the auction. A diamond looks like our best lead. Since I expect partner to be short in diamonds, it's better to lead low than to lead an honor. A typical layout might be

	NORTH ♦ x x
WEST ♦ A K 10 8 5		EAST ♦ 9 x
	SOUTH ♦ Q J x x

or

	NORTH ♦ x x
WEST ♦ A K 10 8 5		EAST ♦ J x
	SOUTH ♦ Q 9 x x

The systemic lead is fourth best. But I'm afraid the diamond eight may look high. Partner may think I'm leading a high spot to induce a spade shift when he gets in. To make sure he knows diamonds is our source of tricks, I lead the diamond five. Partner knows declarer doesn't have five diamonds. So, the five should not confuse him.

	NORTH ♠ 9 8 3 ♥ Q J 9 5 4 ♦ J ♣ Q 10 9 6
WEST ♠ K 7 6 5 2 ♥ 8 3 ♦ A K 10 8 5 ♣ A

West	North	East	South
			1 ♣
1 ♠	Double	Pass	1 NT
2 ♦	Pass	2 ♠	2 NT
(All pass)

Great! Dummy has a stiff jack. Should I have led an honor? Actually, I guess it didn't matter. I need partner to have an entry anyway to come to six tricks. So a low diamond lead is just fine. Even if I had led an honor, I would be leading low at trick two. So what's the difference?

I must say I don't care for dummy's pass over two diamonds. A singleton diamond and a club fit? Why not bid two hearts? Wasn't he planning on bidding two hearts if I had passed? Why should my bidding his singleton make his hand suddenly better suited for defense?

Partner plays the three and declarer follows with the four. Partner's card should be attitude, indicating that he doesn't have the ten.

What is declarer's shape? Partner would not have corrected to spades with four diamonds, so he must have three diamonds  and declarer must have four. Further, he probably would not have corrected with 2-3 in my suits. (He might give a false preference with a good hand, but I know he doesn't have a good hand.)  So he must have three spades, giving declarer either a 2-2-4-5 pattern or a 2-3-4-4 pattern. As I said before, declarer's unilateral action makes more sense if he's 2-2-4-5, so that's what I'm going to assume. I also suspect declarer has the ace-queen of spades to have bid two notrump in the teeth of partner's two spade bid (although that wouldn't be true if two notrump were intended as unususal). So that gives declarer

♠ A Q ♥ ? x ♦ Q x x x ♣ K ? x x x

and leaves partner with

♠ J 10 x ♥ ? x x x ♦ x x x ♣ ? x x.

The opponents are playing 16 to 18 notrumps. So declarer might have up to 15 HCP for his one notrump rebid. That means he could have either the ace or the king of hearts. But if partner has the heart ace, he has a two spade bid over the negative double. So I'm inclined to place declarer with the heart ace and partner with the heart king and the club jack. Not bad for trick one! I know everyone's shape and can place every honor down to the ten of spades!

Of course, I'm wrong. At trick two, declarer leads the four of hearts from dummy, partner plays the ace, and declarer plays the king. I give count with the eight. Hmmph. Partner should have raised with jack-ten third of spades and an ace. If he had, I would have made a game try of three diamonds, and we would have reached three spades. If three spades makes, there's not much I can do about it. But if three spades is going down one, plus 50 will be a fine score. That seems like what we're destined to get. Partner will play a diamond, and we'll take four diamonds and our two aces.

Wrong again! Partner plays the jack of spades--queen--king. I can clear diamonds myself to come to a different six tricks. But maybe we can do better. What if I play a spade to declarer's stiff ace? Declarer has four heart tricks (assuming from his unblock that he has the heart ten), one diamond, and one spade. Down two. He can't afford to knock out the club ace, or I will play a spade to partner for a diamond return, and we can run both our suits. Nice spade shift, partner. You found a way to beat it an extra trick.

I cash the diamond ace just to clarify the diamond suit for partner. Declarer pitches a club from dummy, partner plays the six, and declarer plays the deuce. I switch to the seven of spades--eight--ten--ace. Oops. What happened? How can declarer have three spades? Does he have

♠ A Q 4 ♥ K 10 ♦ Q x x x ♣ K J x x

or

♠ A Q 4 ♥ K ♦ Q x x x ♣ K J x x x ?

I can't see bidding over two spades with either hand. But Jack and I don't always see eye-to-eye about these things. These layouts would make partner's bidding more sensible. I was wondering why he didn't raise with jack-ten third of spades and the heart ace. Perhaps he doesn't have three spades. Perhaps he did give a false preference.

Now I've let them make this, trying for an extra undertrick. And what exactly did I expect that extra undertrick to be worth? There may be some minus 100s our way. There might also be some minus 110s, since I think more people will be defending club partscores than notrump partscores. So there may be a huge difference between our beating this one and allowing it to score. Furthermore, we may well be the only pair with a chance to go plus 50 or plus 100, so there may be no difference at all between down one and down two.

Declarer plays the deuce of clubs--ace--nine--three.  I cash the diamond king and concede the balance. Making two.

	NORTH ♠ 9 8 3 ♥ Q J 9 5 4 ♦ J ♣ Q 10 9 6
WEST ♠ K 7 6 5 2 ♥ 8 3 ♦ A K 10 8 5 ♣ A		EAST ♠ J 10 4 ♥ A 7 6 2 ♦ 7 6 3 ♣ 8 4 3
	SOUTH ♠ A Q ♥ K 10 ♦ Q 9 4 2 ♣ K J 7 5 2

So declarer was 2-2-4-5.  Partner's spade ten was clueless. Not only should he know from the auction that declarer has the spade ace, but my carding told him as well. I cashed the diamond ace to clarify that suit, then I led my highest spade to assure partner that I didn't have a spade honor.

As it happens, my assessment of our matchpoint position was wrong (making me wrong for the third time on this deal - or is it the fourth?). There is no difference between plus 50 and minus 120, and there is a difference between plus 50 and plus 100, although a small one. The one pair who played a club partscore their way made four, scoring 130. And no one was minus 100 our way. Most East-West pairs reached game and went for between 200 and 800. Minus 120 is worth eight matchpoints. One other pair defended two notrump and beat it two tricks, so we could have scored nine matchpoint had we done the same.

Even though my play turned out not to matter--and stood to gain if partner hadn't lost his mind--I still think it was wrong. I didn't stop to assess the risk-reward ratio of my play. Even though it's unlikely declarer has three spades, it's hardly impossible. So I think I should have settled for down one. I just got lucky that there was no difference between plus 50 and minus 120.

Score on Board 34: -120 (8 MP)
Total: 282 (69.1 %)

Current rank: 1st

Von Zedwitz

I'm going to pause at this point in the match to report on an actual deal, from the finals of this year's Von Zedwitz Double Knockout. For those of you unfamiliar with the format of this event, it operates similarly to a standard knockout, except that you must lose twice before you are eliminated. The finals generally consists of one undefeated team and one once-defeated team. If the undefeated team wins, it has won the event. If the undefeated team loses, then there is a rematch, and the winner of the the rematch wins the event. In other words, if you make it to the finals as the undefeated team, the only way not to win the event is to lose two matches in a row.

Back when I was actively playing, I found myself in this position twice. Both times, my team lost both the first match and the rematch to come in second. The second time this happened, the final match was particularly exciting. The critical deal - and the match and the event - hinged on whether or not declarer held the eight of hearts.

This year, my partners at Gargoyle dragged me out of retirement to play in the event again. And, last week, I found myself once again entering the finals as the only undefeated team (the team consisting of Josh Parker, Bruce Rogoff, Eric Robinson, Marty Fleisher, Jeff Aker, and me).

Fortunately, history didn't repeat itself. We won the first match, rendering the rematch unnecessary, despite the fact that I butchered the deal I'm about to show you.

Board 9
Opponents vulnerable

♠ A K 5 4 ♥ J 8 2 ♦ K 7 ♣ K Q J 4

I open one notrump (15-17) in third seat, and partner bids two hearts, a transfer to spades. I think the right bid is three clubs, showing four spades, a maximum in high cards, and concentration in clubs. But we haven't discussed pre-acceptances. Some people play that three clubs in this auction shows a doubleton. I'm also not sure what a three-heart rebid by partner would mean. Would it be a re-transfer or a heart suit? I decide to keep the auction simple by bidding a straight-forward, if misdescriptive, three spades. Partner raises to four, and LHO leads the nine of hearts, showing the ten or shortness.

	NORTH ♠ Q J 6 3 2 ♥ A Q 7 4 3 ♦ 10 8 6 ♣ --
	SOUTH ♠ A K 5 4 ♥ J 8 2 ♦ K 7 ♣ K Q J 4

West	North	East	South
	Pass	Pass	1 NT
Pass	2 ♥	Pass	3 ♠
Pass	4 ♠	(All pass)

If spades are three-one and hearts are three-two, I shouldn't have any trouble. My biggest concern is four-one hearts. I could duck this trick and hope the opponents can't take the first four tricks. But there are lots of ways they would be able to do that: (1) if the nine is singleton and East has the diamond ace, (2) if the nine is singleton and East has queen-jack of diamonds, or (3) if East has a singleton king and West has the ace of diamonds. In addition, what do I do if East wins the heart king and plays a small diamond? If the nine was a singleton, I must play low. (East can't have the diamond ace, or he would have beat me by force, so low guarantees my contract.) But if the king was a singleton, I must rise, hoping the diamond ace is onside.

What happens if I go up with the heart ace at trick one? I draw trumps (let's assume I must draw three rounds) and play a heart from dummy. First, suppose East shows out. I play the jack. West wins and plays a low club. I ruff in dummy and play a diamond. If the diamond ace is onside, I'm home. If it isn't, West wins and plays another club. This one I can't afford to ruff. I have to duck and hope West has the club ace. So, if I go up with the heart ace and West has king-ten-nine fourth of hearts, I need either two-two trumps or one of the minor-suit aces onside.

What if East follows when I lead a heart toward my jack? If I play the jack and West shows out, I can no longer establish hearts. Again, I will need to find one of the minor-suit aces onside. Of course, I could insert my old nemesis, the heart eight. West would have led the ten from ten-nine doubleton. So, once East follows low, the only possibilities for West are a singleton nine or king-ten-nine tripleton, the latter being a rather unattractive holding to lead from. Wouldn't it be great if this turned out to be the critical deal of the match and the eight of hearts again proved to be key? Except this time I would be on the receiving end of the eight's favors.

All in all, hopping with the ace looks like a better idea than ducking. I call for the ace, and East follows with the six. I play a spade to the ace, and West pitches the deuce of diamonds. Oops.

Given the diamond pitch, West's likeliest pattern is 0-4-5-4, leaving East with 4-1-3-5. King-ten-nine fourth is not an attractive lead. So there is a fair chance West has both minor-suit aces. Personally, I would bid over one notrump with that hand. But the opponents, for some reason, aren't playing Astro, so West probably doesn't have a suitable action.

Except for the fact that I must draw four rounds of trumps instead of three, the play would appear to follow pretty much the same lines as I envisioned early. I am going to need to find one of the minor-suit aces onside. I draw four rounds of trumps and play a heart to the jack. West wins and shifts to a low club. I pitch a diamond, and East follows low. Now I'm home. I win with the jack and pass the eight of hearts. Now club king--ace--ruff and run the hearts. If the diamond ace is onside, I can make an overtrick if I guess East's pattern. If he comes down to two diamonds, I must hold king-doubleton of diamonds. If he comes down to the diamond ace and a club, I must hold one diamond and one club. I see no reason to think my original assessment of his shape was wrong, so I play accordingly. The diamond ace is offside, so I make only four.

	NORTH ♠ Q J 6 3 2 ♥ A Q 7 4 3 ♦ 10 8 6 ♣ --
WEST ♠ -- ♥ K 10 9 5 ♦ A 5 4 3 2 ♣ A 10 3 2		EAST ♠ 10 9 8 7 ♥ 6 ♦ Q J 9 ♣ 9 8 7 6 5
	SOUTH ♠ A K 5 4 ♥ J 8 2 ♦ K 7 ♣ K Q J 4

At the other table, West leads the diamond ace, so declarer has no problems.

I said at the beginning of this post that I butchered this deal. Do you see my error? Neither West nor I noticed that I gave him a chance to beat me in this position:

	NORTH ♠ 6 ♥ Q 7 4 3 ♦ 10 8 6 ♣ --
WEST ♠ -- ♥ K 10 5 ♦ A 5 ♣ A 10 3		EAST ♠ -- ♥ -- ♦ Q J 9 ♣ 9 8 7 6 5
	SOUTH ♠ -- ♥ J 8 ♦ K 7 ♣ K Q J 4

When I lead a heart to the jack, West must win and play the club ace, not a low one. I can't afford to ruff this; I must pitch a diamond. West now exits with the ten of hearts, smothering that pesky eight, and I'm left with two diamond losers.

To make this by force, I must arrange to be in my hand when we reach this position. Then I lead the club king and, whether West covers or not, pitch a diamond. Now there is no defense.

Match 2 - Board 33

Board 33
Neither vulnerable

♠ A 10 5 ♥ Q 7 6 5 2 ♦ 8 7 4 ♣ 8 5

Partner passes, and RHO opens an old-fashioned 16 to 18 one notrump. I pass, and LHO raises to three. I lead the five of hearts.

	NORTH ♠ J 7 4 ♥ 4 3 ♦ Q J 10 6 ♣ K J 7 2
WEST ♠ A 10 5 ♥ Q 7 6 5 2 ♦ 8 7 4 ♣ 8 5

West	North	East	South
		Pass	1 NT
Pass	3 NT	(All pass)

Three notrump! Unless declarer has an eighteen count, I don't expect other pairs to be in this game. We'd better beat it.

I'm going to break with the usual format of this blog and give you a defensive problem. I have to do it this way, because if I tell you my thoughts as the play progresses, it will spoil the problem. Partner plays the jack of hearts, and declarer wins with the ace.  Declarer leads the queen of clubs--eight--deuce--four, then the six of clubs--five--jack--ace.  Partner plays the eight of hearts to declarer's ten and your queen. What do you do and why?  The why is important. 'What' doesn't count unless you get the 'why' right. (Well, actually it does in real life; but it doesn't here.)

Now let's back up and go through the play again the Gargoyle Chronicles way. I lead the heart five. Partner plays the jack, and declarer wins with the ace. Declarer obviously has ace-king-ten. He can't disguise his holding from me, but he should have won with the king to disguise his heart strength from partner. Winning with the ace marks him with a second stopper (either the king or something like ace-ten-nine fourth).

Declarer leads the club queen. I give count with the eight, and partner follows with the four. A bell should go off at this point. It appears that partner has ducked the club ace. As a general rule, when defending three notrump, third hand doesn't go around ducking tricks without a good reason. For one thing, how does he know he's not ducking declarer's ninth trick? That consideration doesn't apply here because of declarer's foolish falsecard of the ace at trick one. But, if he had won with the king, partner might have to worry about a layout such as,

	NORTH ♠ J 7 4 ♥ 4 3 ♦ Q J 10 6 ♣ K J 7 2
WEST ♠ x x x ♥ A Q x x x ♦ x x x ♣ x x		EAST ♠ K x x x ♥ J x x ♦ x x ♣ A 10 x x
	SOUTH ♠ A Q 10 ♥ K 10 x ♦ A K x x ♣ Q x x

Another reason it might be wrong for third hand to duck is that it might be important for him to win the first trick for the defense in order to retain his partner's entry:

	NORTH ♠ J 7 4 ♥ 4 3 ♦ Q J 10 6 ♣ K J 7 2
WEST ♠ x x x ♥ Q 10 x x x ♦ A x x ♣ x x		EAST ♠ K x x x ♥ J x x ♦ x x ♣ A 10 x x
	SOUTH ♠ A Q 10 ♥ A K x ♦ K x x x ♣ Q x x

To make this, declarer must guess which minor-suit ace West has and lead that suit at trick two. He guessed wrong. But if East ducks, declarer can switch to diamonds and make his contract.

So why is partner ducking? The likeliest reason is that he has the diamond king and wants to deprive declarer of a dummy entry. In a layout such as,

	NORTH ♠ J 7 4 ♥ 4 3 ♦ Q J 10 6 ♣ K J 7 2
WEST ♠ K x x ♥ Q x x x x ♦ x x x ♣ x x		EAST ♠ Q 10 x ♥ J x x ♦ K x ♣ A 10 x x x
	SOUTH ♠ A x x x ♥ A K 10 ♦ A x x x ♣ Q x

partner must duck to prevent declarer from reaching dummy for a diamond finesse. In a layout such as,

	NORTH ♠ J 7 4 ♥ 4 3 ♦ Q J 10 6 ♣ K J 7 2
WEST ♠ K x x ♥ Q x x x x ♦ x x x ♣ x x		EAST ♠ Q 10 x ♥ J x x ♦ K x x ♣ A 10 x x
	SOUTH ♠ A x x x ♥ A K 10 ♦ A x x ♣ Q x x

partner can't stop declarer from reaching dummy. But declarer needs two dummy entries to take all his diamond tricks. Ducking kills one entry, and that's good enough.

For the time being, I'm going to place partner with the diamond king on the basis of his duck. Although I'm going to stay open to the possibility that I'm wrong. Partner may have some other reason for ducking that I haven't thought of yet.

Declarer continues with the club six. He can't have queen doubleton, since partner would have played the three at trick two. And declarer would not play this way from queen fourth without the ten. So declarer must have either specifically queen-ten-six-three or queen third.

Partner takes dummy's jack with the ace and plays the eight of hearts. That means declarer began with ace-king-ten-nine. Declarer plays the ten and I win with the queen.

If I'm right that partner has the diamond king, it looks right to return a heart, putting declarer back in his hand. Is that good enough to beat him? It's good enough only if declarer is three-three in the minors and if partner has the spade queen. In that case, declarer can take only three hearts, two clubs, and three diamonds for eight tricks.

If I'm wrong about the diamond king, is there anything I can do? Declarer will have nine cashing tricks, but there is room in partner's hand for the king-queen of spades. So if declarer does have the diamond king, I may beat it by switching to ace and a spade.

Partner is just as likely to have been dealt king-queen of spades as he is to have been dealt king of diamonds-queen of spades. But if I play partner for the former, I don't care what declarer's shape is in the minors. If I play partner for the latter, I'm playing declarer to be specifically three-three in the minors. So, a priori, my percentage play is to switch to spades. Still, I can't imagine why partner would duck the club with king-queen of spades. I think the inference that he has the diamond king is strong enough to go against the a priori odds. I return the seven of hearts (suit preference, since I think partner knows the heart count already).

Declarer plays the four of spades from dummy, partner plays the spade deuce, and declarer wins with the heart king. He plays the nine of clubs (which confirms he started with three) to dummy's jack.  As long as we're doing defensive problems this week, here's another: What do you discard on this trick?

 It seems natural to discard a diamond, but I don't want declarer to know I don't have the king (assuming he isn't as clever as I am and hasn't deduced that fact from partner's play at trick two). So I pitch the spade five.

By holding on to all of my diamonds, I'm hoping to persuade declarer that this is the layout:

	NORTH ♠ J 7 ♥ -- ♦ Q J 10 6 ♣ 7
WEST ♠ A 10 ♥ 6 2 ♦ K x x ♣ --		EAST ♠ Q 8 6 ♥ -- ♦ x x x ♣ 10
	SOUTH ♠ K 9 3 ♥ 9 ♦ A x x ♣ --

The defense needs three tricks. If declarer takes the diamond finesse, I duck. If he repeats the finesse, I win and play a heart. We get four tricks for down two. If, after taking one finesse, declarer thinks this is what is going on, he may refuse the second finesse. He may take the diamond ace, cash the heart, and play a diamond, trying to endplay me for down one. I don't know if declarer will fall for this or not, but it doesn't hurt to give him the option. Most defenders wouldn't clutch their three small diamonds. So, unless declarer has a lot of respect for my game, he might well fall for it.

Declarer plays the diamond queen--three--deuce. I play the seven. Whatever card partner plays on the next diamond will be higher than the four, so it may look as if his last diamond is the four and he is giving present count. (Hee. Hee.)

To my surprise, declarer abandons diamonds. He plays the seven of spades--six--nine--ten. Interesting. For whatever reason, declarer has decided I have the spade ace and he has no chance to make this. He's found a way to hold it to down one no matter who has the diamond king. I clear the hearts. Declarer plays a spade to my ace. I cash the heart and declarer takes the last two tricks for down one.

	NORTH ♠ J 7 4 ♥ 4 3 ♦ Q J 10 6 ♣ K J 7 2
WEST ♠ A 10 5 ♥ Q 7 6 5 2 ♦ 8 7 4 ♣ 8 5		EAST ♠ Q 8 6 2 ♥ J 8 ♦ K 9 3 ♣ A 10 4 3
	SOUTH ♠ K 9 3 ♥ A K 10 9 ♦ A 5 2 ♣ Q 9 6

Not surprisingly, almost every other pair played a notrump partscore. The only other pair who played three notrump made four, so we have another top. Why aren't real tournaments this easy?

This hand is good illustration of one of the primary themes of this blog: the importance of asking questions about what is going on and drawing inferences as the deal unfolds. If partner's duck at trick two strikes you as strange and if you stop to ask yourself why he's ducking, this becomes an easy deal. But if you wait until you win the heart queen before you start piecing the clues together, it is a very difficult deal. It is always hard to draw inferences from things that happened several tricks ago. This is why I spend so much time in this blog drawing inferences about what is going on even when I have no decisions to make.

Score on Board 32: +50 (12 MP)

Total: 274 MP (69.2%)

Current rank: 1st

Match 2 - Board 32

Board 32
Opponents vulnerable

♠ 7 5 4 ♥ A J ♦ J 9 8 ♣ Q J 4 3 2

Partner opens one notrump (12-14) in second seat and buys it. West leads the jack of spades.

	NORTH ♠ 7 5 4 ♥ A J ♦ J 9 8 ♣ Q J 4 3 2
	SOUTH ♠ Q 3 2 ♥ Q 8 3 ♦ A Q 10 5 3 ♣ A 7

West	North	East	South
		Pass	1 NT
(All pass)

I play low from dummy, East plays the king, and I play the deuce. East continues with the eight of spades. I play the queen. West takes the ace and cashes the ten of spades, on which East pitches the five of clubs. It's hard to imagine that the club king is onside. What club holding that includes the king would East be willing to pitch from?

I'm going to have to make two discards on West's spades. What should my plan be? One possibility is to pitch down to

(A) ♠ -- ♥ Q 8 ♦ A Q 10 5 3 ♣ A.

The defense needs to take two tricks to beat me. If East discards correctly, West should be able to tell that I've stiffed the club ace and should find a club shift. After winning the club ace, I must take at least six more tricks without losing the lead. I have two choices:

(A-1) Take a heart finesse. If this wins, I'll make an overtrick if the diamond king is onside and go down one if it's not. If the heart finesse loses, I'm down. In fact, if the diamond finesse loses as well, I'm down some ridiculous number of tricks, since the defense will be able to run the heart suit.

(A-2) Lead a heart to the ace and take a diamond finesse. This gives me my best chance to make the contract. I'll make it if the diamond finesse wins and go down many tricks if it doesn't.

Another possibility is to pitch down to

(B) ♠ -- ♥ Q 8 3 ♦ A Q 10 5 ♣ A.

This has the advantage that I will never go down a lot, since the opponents can't establish the heart suit. But, against best defense, it reduces my chance of making the contract to 25% (as in line A-1). Assuming West finds the club shift, I will will need both red kings onside to make it. If the heart finesses loses, I'm down one if the diamond king is onside (losing a trick to the heart king and club king) and down two if it's not (losing a trick to each king). As an interesting aside, note that if West somehow fails to find a club shift, I still make two when both red finesses are on. Assuming I'm right that West holds the club king, he is caught in a criss-cross squeeze on the run of the diamonds.

A third possibility is to hold a club, thus preventing West from establishing his club king. For this to gain, however, I need some place to pitch the club later. That means I must hold

(C) ♠ -- ♥ 8 ♦ A Q 10 5 3 ♣ A 7,

and the heart king must be onside. But then what have I accomplished?  West will play a heart. I finesse and cash the heart ace pitching my club.  If the diamond finesse is onside, I'm no better off than I would have been adopting A-1.  And if it's offside, I'm considerably worse off. C is never superior to A-1, so I can forget about it.

That means I have three strategies to choose from. What makes it especially hard to choose is I have no idea what will happen at the other tables, so it's hard to estimate how many matchpoints each one of my possible results is worth. I must do the best I can, however, so I am going to make some guesses (assuming a 5 top to keep the arithmetic simple):

+120	5 MP
+90	3 MP
-50	2 MP
-100	1 MP
-more	0 MP

Since the opponents are vulnerable, I've made the difference between plus 120 and plus 90 greater than the difference between the other scores on the assumption that there will be plus 100s floating about. If the opponents were not vulnerable, I would make the difference between plus 90 and minus 50 greater.

Now let's construct payoff tables for each of my three possible strategies:

A-1 (pitch club and heart, finesse heart)

	♦ K onside	♦ K offside
♥ K onside	5 MP	2 MP
♥ K offside	2 MP	0 MP

A-2 (pitch club and heart, don't finesse heart)

	♦ K onside	♦ K offside
♥ K onside	3 MP	0 MP
♥ K offside	3 MP	0 MP

B (pitch club and diamond)

	♦ K onside	♦ K offside
♥ K onside	3 MP	2 MP
♥ K offside	2 MP	1 MP

Because of my assumption that there will be a significant difference between making one and making two, A-1 turns out to be the winner. At least it's the winner if I think it's 50-50 who has each of the red kings. If East's discards offer some clue about the location of the kings, then the other strategies might prove more attractive.  (If, for example, I decide that the diamond king is probably offside, then I should adopt B.) So my initial plan is to go with A-1, but I am open to changing my mind if I get more information.

West cashes another spade. I can't afford a diamond pitch from dummy. I may need to take three finesses if East has king fourth. So I pitch a club. East discards the club six. This should be present count (assuming the first discard was attitude), so East should have begun with four small, and West should know this.

Why is East reluctant to pitch a red suit? A diamond pitch would be dangerous from almost any holding. A pitch from king-seven third, for example, will cost if I have ace-queen empty fifth. (It allows me to pitch a diamond from dummy, unblocking the suit.) Even a pitch from three small might cost, since it might induce me to drop an offside doubleton queen. Jack, however, always assumes declarer is double-dummy, so he won't worry about pitching from three small. Against Jack, I think the odds that the diamond king is onside are now better than 50%, making B an unattractive strategy.

Why is he not pitching a heart? He might have the king and be hoping hearts represents a source of tricks. Or he might have ten fourth of hearts and be afraid a pitch will give me a trick if I have king fourth.

What should I pitch? A club, retaining the option of adopting strategy B is the most flexible. But I think I've pretty much decided against B on East's failure to pitch a diamond. An immediate heart pitch offers a peculiar advantage: it makes it safe for East to pitch a heart from ten fourth. If I pitch a heart now and East still refuses to pitch one, I can be fairly confident that he has the king. So I make the "discovery play" of the three of hearts.

West cashes his last spade. I pitch another club from dummy. East pitches the deuce of hearts. East's heart pitch isn't especially meaningful. There are a variety of reasons a heart might be his most attractive pitch with or without the king. But if he hadn't pitched a heart once I told him that it was safe to pitch from ten fourth, that would be significant. I would assume he had the king, and I would switch to strategy A-2. Since that didn't happen, I'm sticking with my original plan of A-1.

I pitch the club seven. West, somewhat surprisingly, fails to find the club shift. He shifts to the four of hearts. I play the jack, and East plays the deuce. The diamond king is onside, so I make two.

	NORTH ♠ 7 5 4 ♥ A J ♦ J 9 8 ♣ Q J 4 3 2
WEST ♠ A J 10 9 6 ♥ K 6 5 4 ♦ 7 4 ♣ K 8		EAST ♠ K 8 ♥ 10 9 7 2 ♦ K 6 2 ♣ 10 9 6 5
	SOUTH ♠ Q 3 2 ♥ Q 8 3 ♦ A Q 10 5 3 ♣ A 7

We are the only pair to play the hand our way. Every other table played one spade by East-West. Why didn't I think of that? I was so wrapped up in constructing my payoff tables, I didn't even stop to ask what would happen after a one diamond opening. If I had, it wouldn't be hard to predict that one spade by West would be a popular contract. Actually, I suppose I should be happy I didn't think of that. It took long enough to play this hand as it was. If I started calculating how many tricks we were apt to take against one spade in each of the four scenarios and adjusting my payoff tables accordingly, I'd still be in the tank.

Not that it's easy to tell what would happen in one spade, even looking at all four hands.  Assume the defense starts with a diamond to the queen and a heart shift. It seems natural for declarer to rise with the heart king, since, if the ace if offside, he must lose three heart tricks anyway via a ruff. But if he does rise, he gets tapped out and goes down. If he ducks, he retains control and gets to score the club king for his seventh trick. In practice, three declarers went down in one spade, one made one, and two made an overtrick.

We can now check the accuracy of my matchpoint estimates. Here is what various scores would have yielded, adjusted to a five top.

+120	5.0 MP
+90	2.5 MP
-50	2.5 MP
-100	1.7 MP
-more	0.0 MP

I was right that the biggest difference was between plus 120 and plus 90. Although it didn't occur to me that there would be no difference at all between making one and going down one. Overall, my estimates were pretty good, except that minus 100 was a better score than I thought it would be. I hadn't anticipated the minus 110s.

Score on Board 32: +120 (12 MP)

Total: 262 MP (68.2%)

Current rank: 1st