Event 3 - Match 5 - Board 5

Board 5
Our side vulnerable

♠ K Q 2 ♥ K 9 6 5 ♦ 8 6 4 ♣ 10 6 2

Partner opens one diamond in first seat, and RHO overcalls with one heart. I bid one notrump, LHO bids two clubs, and partner bids two diamonds. After my one notrump response, partner will bid two diamonds on almost any unbalanced minimum with five or more diamonds. A pass would suggest a balanced hand (and a minimum strong notrump, since our one notrump opening is weak).

RHO doubles, which is alerted as "competitive." I know these competitive doubles are fashionable, but I don't get them. If you have six hearts, you bid two hearts. If you have club support, you raise. If you have neither (and don't have enough in high cards to invite game in notrump), why would you want to act at all? Some players feel compelled to do something whenever they have more high cards than they need for their previous actions. If nothing else appeals, they like to use double to convey that message. But I've never understood what this is supposed to accomplish. Personally, I have little interest in hearing that partner has extra high cards. Whenever partner makes one of these doubles (assuming I've agreed to play this way to humor him), I find myself in one of two positions: (1) I have some extra distributional feature to show; but I was going to show it anyway, so partner's double made no difference. (2) I don't have an extra distributional feature to show, in which case I probably want to defend this contract undoubled. Unfortuately, that option is no longer available. Either I must defend it doubled when I think it's pretty much a toss up whether we beat it or not, or I must bid, fully expecting to go minus.

But this double is LHO's problem, not mine. I pass. LHO bids three clubs, which is passed back to me.

By the Law of Total Tricks, I want to compete if both sides have nine trumps, and I want to sell if both sides have eight. If one side has nine trumps and the other has eight, I'm indifferent to whether I compete or not. Unfortunately, that doesn't help on this auction, since I don't know the trump length for either side. Partner could have five or six diamonds, and LHO could have six or seven clubs opposite RHO's probable doubleton. The Law doesn't help; I must fall back on old-fashioned judgment.

My third diamond is a plus for offense. My 4-3-3-3 pattern is minus for offense, as is my lack of a diamond honor. My heart king is better on defense than on offense. In fact, it is in some danger of being ruffed out at trick two in a diamond contract. In addition, if partner does have six diamonds and a singleton club (the only time selling out is a serious error), he might have bid three diamonds on his own, provided his diamonds are good enough. All in all, selling out seems like the wisest course. I pass, and partner leads the four of spades.

	NORTH Stephen ♠ J 10 8 5 ♥ A J 10 8 4 ♦ K 10 5 ♣ 3
		EAST Phillip ♠ K Q 2 ♥ K 9 6 5 ♦ 8 6 4 ♣ 10 6 2

West	North	East	South
Jack	Stephen	Phillip	Sam
1 ♦	1 ♥	1 NT	2 ♣
2 ♦	Double1	Pass	3 ♣
(All pass)
1Competitive

North seem to have a different concept of a competitive double than most. This looks to me more like a one-suit take-out double for spades. Even if that were my agreement, I wouldn't choose it with this hand. With a singleton club and king-ten third of diamonds, I would be happy to defend any time partner doesn't want to bid on his own initiative.

Declarer has as most two hearts and at most two diamonds. He probably would have bid two spades with four. So my best guess is he is 3-2-2-6. No. That gives partner 3-2-5-3 and a strong notrump. It looks as if I need to credit declarer with seven clubs. He could be 2-2-2-7 (giving partner 4-2-5-2) or 3-2-1-7 (giving partner 3-2-6-2).

Declarer plays the spade ten. I could falsecard with the king. But declarer should get the spades wrong even without the falsecard. Both restricted choice and the fact that partner opened the bidding makes the missing spade honor more apt to be in partner's hand. So the falsecard will only make partner's job harder. I play the queen, and declarer wins with the ace.

Declarer plays the spade six--three--jack--king. See? I told you he'd get it wrong anyway. Partner appears to have led third best in spades, so declarer is 2-2-2-7.

We have one spade, one heart, and one diamond trick. We need two trump tricks to beat this. Returning a spade to prepare for an uppercut will not help if partner has only two clubs. Perhaps, if partner has ace-nine of clubs, we can get a trump promotion. If partner has the queen of hearts, I can play a heart. If declarer errs and takes the ace, then, when partner takes the club ace, he can cash the diamond ace, lead a heart to my king, and get a trump promotion.

Is there a risk in trying this? If declarer has the heart queen, a heart shift gives up a trick. But it doesn't cost the contract unless we have two natural trump tricks. So the shift doesn't cost unless partner has ace-queen or ace-jack of clubs and no heart queen. That's quite a parlay. Then again, all declarer has to do to counter this defense is to duck the heart ace. Failing to do so is a pretty bad play. Perhaps that's even less likely than the parlay.

Actually, on second thought, ducking the heart ace isn't 100%. If partner has a singleton queen of hearts instead of a doubleton queen and if I have an entry with the queen or jack of diamonds, declarer must win the trick to avoid a heart ruff. The parlay is enough of a long shot that I'm going for the swindle. I shift to the five of hearts--three--queen--ace. Yay!

Declarer leads the three of clubs from dummy--deuce--seven--ace. Seven? He hooked me for the ten of clubs? I guess he was worried I had ten fourth. From his point of view, if partner has another heart to play, he's going to wind up playing me for the club ten anyway. So hooking now in case I have ten fourth makes a certain amount of sense.

Partner cashes the diamond ace--five--four--seven. He then plays the jack of diamonds--king--six--deuce. Partner is apparently playing declarer to be 2-2-3-6 and wants to kill the diamond entry to dummy's heart winner. But, if that's the case, this is the wrong defense. Declarer could ruff out my spade exit, draw trumps, and lead a heart to my king. I will have nothing left but hearts, so I must give him his heart trick. If partner thought I had a doubleton diamond, he should play the queen of diamonds instead of ace and another to leave me with a diamond exit. (Of course, I can't have a doubleton diamond. I would have led a diamond rather than a heart at trick three if I did. But such inferences are beyond Jack.)

Declarer leads the four of hearts from dummy. I could win with the nine. But perhaps if I win with the king, declarer will think partner has the nine and will get careless. Is there a name for this maneuver? It has a vague resemblance to a crocodile coup in that I'm playing a higher card than necessary. Maybe we can call it a crock coup. I play the king--deuce--seven. Now the six of hearts. Declarer ruffs with the five. The five? Unbelievable! Declarer did get careless, but it didn't matter. Why couldn't partner have held the six of clubs instead of me? Declarer draws trumps and claims. Making three.

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

Our teammates also made three clubs, so the board is a push.

Let's back up a minute and reconsider my problem after the double of two diamonds. What should a redouble by me mean? I suspect many would play that the redouble shows a desire to penalize the opponents. In other words, it is a warning to partner not to bid again. This parallels the treatment of redouble in other auctions, for example, one diamond--double--redouble. But I don't think this treatment makes sense here. For one, thing, advancer's pass after one diamond--double--redouble is not for penalties (and, even if it were, he would rarely hold a suitable hand). But his pass of a redouble on this auction would be for penalties. And if you hold the hand where such a redouble is appropriate--a misfit with good defense against the opponents' suits--it is quite possible that your LHO was intending to pass the double and will be delighted to defend two diamonds redoubled. Accordingly, I think it makes more sense to play that redouble invites partner to bid. Specifically, I think it should be a support redouble.

Support redoubles typically apply only by opener after a one-over-one response. But I believe they should be extended to apply by either hand at the two-level under the following conditions: (1) You are not in a force; (2) you have limited your hand; (3) partner might have either five or six cards in the suit being doubled and you might or might not have three-card support. Under those conditions, your combined trump length is your primary concern, so I propose that a redouble show three-card support for partner's suit and invite partner to compete with a six-card suit if the double is pulled.

The auction above meets these requirements. Another, more common, situation occurs after a Jacoby transfer and a balancing double:

1 NT	Pass	2 ♦	Pass
2 ♥	Pass	Pass	Double
?

In this auction, I believe you should redouble automatically with three hearts, since partner has a wide range. In the previous auction, redouble is discretionary, since partner has made a limit bid. If you have no interest in competing even if partner has six diamonds, you need not redouble.

Table 1: -110
Table 2: +110

Result on Board 5: 0 imps
Total: +5 imps

Event 3 - Match 5 - Board 4

Board 4
Both sides vulnerable

♠ K Q 8 7 4 ♥ K J ♦ A J 7 5 3 ♣ 9

Three passes to me. I open one spade, partner bids one notrump, I bid two diamonds, and partner bids two spades. My rule of thumb is I bid one less on this auction than I would after one spade--two spades. If I would bid game after a single raise, then I invite. If I would invite after a single raise (as on this hand), then I pass. Accordingly, I pass. LHO passes as well and leads the king of clubs (denying the ace).

	NORTH Jack ♠ 10 3 ♥ A 7 6 4 3 ♦ K Q 6 ♣ 7 5 4
	SOUTH Phillip ♠ K Q 8 7 4 ♥ K J ♦ A J 7 5 3 ♣ 9

West	North	East	South
Sam	Jack	Stephen	Phillip
Pass	Pass	Pass	1 ♠
Pass	1 NT	Pass	2 ♦
Pass	2 ♠	(All pass)

East plays the six of clubs. Assuming he's encouraging with the highest spot he can afford, West has the eight. West continues with the three of clubs. East presumably has the deuce--both because West seems to be leading his lowest club and because West would not know the six was encouraging otherwise. So West has king-queen-?-eight-three and East has ace-?-six-deuce. I'm not sure about the location of the jack or ten, but we would have heard from West if he had six semi-solid clubs, so he can't have both of them. Clubs must be either five-four or four-five.

If I ruff this, I'm in danger of being tapped out. Can I plan on using one of dummy's trumps to keep control? How's this for a plan: I ruff the club and lead the king of spades. If it holds, I abandon trumps and run winners, conceding four trump tricks. If the defense wins and leads a club. I discard. If they play a fourth round of clubs, I ruff in dummy, come to my hand and cash the spade queen. If both opponents follow, then they have two trumps left. I lead winners and let them score two ruffs, losing five tricks: two clubs, the spade ace, and two ruffs.

This works as long as trumps aren't five-one. Can I do better? What if I cross to dummy in hearts and lead a spade toward my hand. As long has no one has a singleton heart and a doubleton trump (unlikely on the auction), I don't see how that can be any worse than leading spades from my hand. And it might be better. If East has ace fifth of spades and ducks, for example, I can win and start playing red suits, conceding four trump tricks. I'm not sure what my plan should be if East hops with the spade ace and play clubs. But I don't need to worry about that until it happens. I'm no worse off than if I had led the spade king from my hand. And that's all that matters at this point.

I play the jack of hearts--deuce--ace--five. Now the three of spades--six--queen--deuce. It appears I'm home. The opponents have four trumps, and that's all they can score. At least I think that's true. Let me make sure. What happens if East has all the missing spades? I lead diamonds until East ruffs. Say he ruffs the second one. He then plays a club, and I ruff. I have two trumps left, and East has three. I lead another diamond. East ruffs. We are down to this position:

	NORTH Jack ♠ 10 ♥ 7 6 4 3 ♦ -- ♣ --
WEST Sam ♠ -- ♥ x x ♦ x ♣ Q x		EAST Stephen ♠ A J ♥ x x ♦ -- ♣ x
	SOUTH Phillip ♠ K 8 ♥ K ♦ A 7 ♣ --

East can now cash the spade ace and lead a club, tapping me out. But that's OK provided he's out of clubs. When he ruffs in with his last trump, he must lead a heart. So if trumps are five-one, I need East to have started with only four clubs.

What if trumps aren't five-one? Then I have no problems. If East cashes the spade ace at any point, he draws one of his partner's trumps. And if he doesn't, I can ruff the fourth round of clubs in dummy to avoid being tapped out.

I lead a diamond to the king. West plays the deuce; East, the four. So the opponents don't give routine count. Nice to know for the future. I play the queen of diamonds and a diamond to my ace. West ruffs the third round with the spade five and leads the queen of clubs. East plays the deuce, and I ruff with the spade seven. I lead the jack of diamonds. West ruffs with the jack of spades. I pitch a heart from dummy, and East pitches the heart nine. Dummy is out of clubs, so, rather than offer me a ruff-sluff, West leads the ten of hearts to the queen and my king. I am down to this position:

	NORTH Jack ♠ 10 ♥ 7 6 ♦ -- ♣ --
	SOUTH Phillip ♠ K 8 ♥ -- ♦ 7 ♣ --

The ace and nine of spades are still out. I was prepared to lose a trick to each of them. But if East has the spade nine, I can exploit dummy's remaining trump to make an overtrick. I ruff the last diamond with the spade ten. East overruffs with the ace. If West was 4-2-2-5, East can lead a heart for a trump promotion. Otherwise, I'm scoring my eight of spades. East leads the club jack. I ruff and cash the spade king. Making three.

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

With the favorable breaks, I could have made five spades. In fact, they did make five at the other table. I don't know if the defense failed to tap declarer or if declarer simply took a more a dangerous line. In any event, we lose two imps.

Two imps is nothing to sneeze at in a short match. But I still think I was right to play safely. We stopped at the two level with 23 high-card points between us. They could easily get overboard at the other table, so I shouldn't do anything to jeopardize my plus score.

Table 1: +140
Table 2: -200

Result on Board 4: -2 imps
Total: +5 imps

Event 3 - Match 5 - Board 3

Board 3
Opponents vulnerable

♠ A Q 8 4 ♥ A J 5 3 ♦ -- ♣ K Q 8 6 5

I open one club, LHO bids one diamond, partner passes, and RHO bids two clubs, promising diamond support. I think the double of any artificial raise should mean the same thing as the double of a natural raise. So a double here should show a take-out double of diamonds. But I'm not sure what partner thinks. He might think it just shows good clubs. Since I'm strong enough to cue-bid two diamonds, it seems safer to do that rather than risk a misunderstanding.

I bid two diamonds, LHO bids five diamonds, passed back to me. I know people who would double. But doubling doesn't make sense to me. West thinks he's going to make it, partner agrees with him, and I have no surprises for either of them. Even if we're a slight favorite to beat it, we certainly aren't beating it more than one. So the IMP odds are stacked against us. I pass. Partner leads the jack of clubs.

	NORTH Stephen ♠ J 10 3 2 ♥ Q ♦ K Q J 4 ♣ 10 9 4 3
		EAST Phillip ♠ A Q 8 4 ♥ A J 5 3 ♦ -- ♣ K Q 8 6 5

West	North	East	South
Jack	Stephen	Phillip	Sam
		1 ♣	1 ♦
Pass	2 ♣1	2 ♦	5 ♦
(All pass)
1Constructive raise

We have at least one club trick. If declarer has a spade or a third club, we're beating this easily. So I might as well assume neither of those things is true. That gives declarer something like

♠ -- ♥ K x x x ♦ A x x x x x x ♣ A x

But then there's no winning defense. I need to find some layout where it matters what I do. I can hardly take any high cards away from declarer. Suppose I give him a 0-5-6-2 pattern:

♠ -- ♥ K x x x x ♦ A x x x x x ♣ A x

Now perhaps partner's third trump is enough to give declarer some difficulty. Say declarer wins the club ace and plays a heart to my ace. I cash the club king and lead a low club, forcing declarer to ruff high. Declarer must now ruff two hearts in dummy. So if partner has ten third of diamonds, he has a trump trick.

I encourage with the club six. Declarer takes the ace and plays the five of diamonds--deuce--jack. I pitch the club five. Declarer plays the four of diamonds. I can't afford a heart, since declarer would have to ruff only one heart if I pitched one. So I pitch the spade four. Declarer plays the ace, and partner follows with the three. Partner echoed, so he has a third trump. Declarer plays the six of diamonds--ten--king.

Declarer drew three rounds of trumps to avoid the trump promotion. As a result, he can ruff only one heart in dummy. So he has to be going down. If the spade isn't cashing and a second club isn't cashing, I have to be scoring my heart jack, provided I don't pitch one. I pitch the spade eight. Declarer leads the queen of hearts--ace--four--deuce. I play the spade ace, and declarer pitches a club. I lead the spade queen. Declarer ruffs, cashes the heart king, and leads the nine of hearts for a ruffing finesse. My heart jack is the setting trick.

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

I didn't have much to do on this deal. All I had to do was pitch spades instead of hearts, which I probably could have figured out without bothering to construct hands for declarer. Still, it gives you a warm, fuzzy feeling to construct the one hand where what you do matters, then find declarer with that precise hand.

Partner, however, had a critical decision. He had to lead a club in order to threaten a trump promotion. Nice lead, partner. I'm not sure I would have found it. Knowing we had all three side suits bottled up, I might have led a trump. But Lowenthal's Fourth Law of Opening Leads strikes again: "The lead of a short suit is an attempt to force declarer to draw trumps."

The other table managed the identical result.

Table 1: +100
Table 2: -100

Result on Board 3: 0 imps
Total: +7 imps

Event 3 - Match 5 - Board 2

Board 2
Our side vulnerable

♠ K Q 9 5 3 ♥ A Q 7 4 ♦ 3 ♣ Q 10 5

Pass on my right. I open one spade. Partner raises to three spades, and I go on to four. West leads the five of hearts (fourth best).

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

West	North	East	South
Sam	Jack	Stephen	Phillip
		Pass	1 ♠
Pass	3 ♠	Pass	4 ♠
(All pass)

Three spades? With only three trumps? If partner judges his hand to be worth a limit raise, he should temporize with two diamonds. But this hand, with nine losers, looks like a two spade bid to me.

To make this I need to avoid a heart loser or to avoid a second spade loser. I play the heart nine--ten--queen. I still don't know if I have a heart loser or not. West might have king-six-five, or he might have a singleton five or five-three.

I need to set up a club ruff before playing trumps. So I play the five of clubs--deuce--king--ace. East shifts to the six of spades. East would surely have continued hearts, trying for a ruff, if he began with ten-three. So the heart king must be onside. I play the spade queen--ace--four. West plays the three of hearts--nine--six--four.

Apparently East doesn't have the jack of spades. Well, that may be overstating it. Sherlock Holmes always got away with such bold pronouncements. But perhaps I should be more cautious: There are indications that East doesn't have the jack of spades.

Since the opponents play fourth best leads, East knows his partner has a doubleton heart. So he knows it is safe to cover the jack of hearts. If he thought I wanted to play spades from the dummy, he would not make it so easy for me to do so. He would cover the heart jack, hoping that forcing me to win this trick my hand would cause me some inconvenience. If he holds the spade jack, he knows it is likely that I would prefer to lead spades from the dummy. So his failure to cover suggests he doesn't have it.

This inference is somewhat weaker playing against a computer than against a human. Jack, with a singleton jack or with jack-ten doubleton, knows I don't need to play spades from dummy. So he might not see the point of covering. A human, however, appreciates the fact that my double-dummy requirements are not relevant. Most of the time when I am missing the jack, I would want to start spades from the dummy whether or not I need to on the actual layout.

If trumps break, I'm home. I can cash the spade queen and ruff a club. If East has all the remaining spades, however, I need to take a double finesse to avoid losing two more trump tricks. I'm not too worried about that. In addition to the Sherlockian inference above, it's unlikely East would lead the six from jack-ten-six-deuce looking at eight-seven third in the dummy. (In this layout, since I must use one of dummy's trumps to ruff a club, retaining the six guarantees a second trump trick unless I magically duck out West's ace.) But sometimes defenders do foolish things. So if I can guard against a four-one break at no risk, I might as well do so.

Can I? I certainly can't take a double finesse before ruffing a club. If West has ace-jack-ten, he can win and play a third spade to stop the ruff. Can I afford to ruff a club first? Hardly. East might overruff and give his partner a heart ruff. A bad trump break is sufficiently unlikely that I'm not willing to take either one of thoses risks.

I play the eight of spades--ten--king--deuce. Good. I ruff a club and give up a spade. Making four.

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

I see they could have beat this. All West had to do was lead a low spade at trick one. Our counterparts at the other table stopped sensibly in two spades and made three. So we pick up an undeserved ten imps.

I would have had a problem if, after winning the club ace, East had shifted to the three of hearts. Should I (A) hop, playing West for king-six-five, or should I (B) duck, playing West for a singleton five? A priori, a singleton heart is less likely than king third. But that isn't the only thing that matters. In addition to guessing hearts correctly, I must pick up trumps for one loser. If I choose (A) and I'm right, I need East's spades to be ace third, ace doubleton, or jack-ten doubleton. If I choose (B) and I'm right, I am very likely to be able to avoid a second trump loser (after West ruffs). East failed to open the bidding and has already shown up with the club ace. So, if he has king fourth of hearts, the spade ace is probably on my left. In that case, if I take my percentage play in spades, I will lose a second trump trick only if West began with ace-deuce, ace-six, or ace-jack-ten. Add to that the fact that West, if he has king third of hearts, might choose to lead something else but would rarely choose another lead with a singleton heart. All in all, (B) seems like the clear winner.

Table 1: +620
Table 2: -140

Result on Board 2: +10 imps
Total: +7 imps

Event 3 - Match 5 - Board 1

Board 1
Neither vulnerable

♠ K J 10 8 ♥ K J 8 ♦ A 9 ♣ A K 8 5

Our new opponents, Sam and Stephen, play English Acol. I open one club. Sam makes an English Acol overcall of one heart, passed back to me. I bid one notrump. Ostensibly, this shows a hand where I would rebid two notrump had partner responded, but with a maximum strong notrump I might stretch a little. Sam isn't through yet. He bids two hearts--pass--pass. If partner thinks it's right to defend, I have no reason to overrule him. I pass. Partner leads the three of clubs (third and lowest).

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

West	North	East	South
Jack	Stephen	Phillip	Sam
Pass	Pass	1 ♣	1 ♥
Pass	Pass	1 NT	2 ♥
(All pass)

Declarer plays the jack from dummy. Partner would lead the ten from ten-nine, so declarer must have at least one of those cards. Since I'm marked with oodles of high cards, declarer would probably play low from dummy if he had just the nine. So I suspect declarer has the ten--probably ten third. He is hoping partner led from the king, in which case playing an honor from dummy guarantees a dummy entry.

This is the kind of problem computers are as yet unable to solve, because they assume the defenders are double-dummy. Since I am a heavy favorite to have both club honors, it must be better to play low from dummy at trick one to give me a problem. I can prevent a dummy entry by inserting the eight. But that would be a mistake if declarer has a doubleton club.

I would like partner to shift to a spade if he gets in, so I want to make a club continuation unattractive. Accordingly, I win with the ace rather than the king. Declarer thoughtfully plays the deuce, so I now know for sure that clubs are three-three.

If I can keep declarer off dummy, I have two heart tricks, two clubs tricks, and the diamond ace. So I need only one more trick. If declarer has a doubleton spade, I have that trick, assuming I can avoid being endplayed. Can I? Say I play ace and a diamond. Declarer wins and plays the club ten, which I must duck. If he plays another club, I must win and play a fourth club. This gives declarer a ruff-sluff. But so long as partner can beat dummy's trump spot, we're OK. I think partner should be able to beat dummy's trump spot.

If declarer has a singleton ace of spades, however, I will need to score two diamond tricks. In that case, my best defense is to exit with a spade, forcing declarer to break diamonds himself. That may seem like quite a position to take. But, in fact, declarer almost surely has a singleton in either spades or diamonds. With a 2-6-2-3 pattern and a good enough hand to bid a second time, he would probably double. And a singleton diamond is unlikely. The only singleton diamond declarer can have is the queen. With any other singleton, partner would have a natural diamond lead.

Essentially, I must decide which hand to cater to:

(A) ♠ A x ♥ A Q 10 x x x x ♦ Q ♣ 10 x x

or

(B) ♠ A ♥ A Q 10 x x x x ♦ K x ♣ 10 x x

(A) is more likely, since partner might have led a diamond from queen-jack-ten fourth. So, in (B), the only plausible diamond x's are the jack and the ten. In addition, I'm not even sure I can do anything about (B). Say I lead a spade. Declarer wins and exits with the heart ten. My only safe exit is the spade king. Declarer ruffs and plays ace and a heart. Now I'm endplayed. So if I play for (B), I need partner to have the heart ten. Clearly I'm better off playing for (A). And that's just as well. If I concluded I should shift to a spade and it turned out to be wrong, I would have a very hard time explaining that play to my teammates.

I play the diamond ace. Declarer plays the four; partner, the deuce. Declarer is probably 1-7-2-3. If I'm right that partner would have led a diamond from queen-jack-ten, then declarer's remaining diamond must be the queen.

I lead the diamond nine--queen--king. There! What did I tell you? Partner plays the jack of diamonds. I might need the fourth club for an exit, so I pitch the eight of spades. Declarer ruffs with the four of hearts.

Declarer makes a futile attempt to reach dummy by playing the nine of clubs to the queen. I take my king and play the club eight back to declarer's ten. Declarer plays the five of hearts, and partner plays the nine. What's this all about? If declarer is indeed 1-7-2-3, I should overtake and play a club in case partner has queen-nine of hearts. But why would declarer give me that chance? Why not just play ace and a heart instead of ducking one? Could it be wrong for me to overtake and play a club? Yes. If declarer made a flaky two heart bid with 2-6-2-3, he could ruff my club return with the heart queen, then play ace and heart to endplay me. That seems more likely than that declarer exposed himself to a trump promotion for no reason. So I play the eight of hearts.

Partner plays the ten of diamonds. I pitch spade jack. Declarer ruffs and leads the heart ten. I win with the jack and play a club. Declarer ruffs with the queen and cashes the heart ace. Partner follows with the nine, so I guess declarer is 2-6-2-3 after all. We get a spade trick for down two.

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

West	North	East	South
Jack	Stephen	Phillip	Sam
Pass	Pass	1 ♣	1 ♥
Pass	Pass	1 NT	2 ♥
(All pass)

Nice crocodile coup, partner! Had partner failed to play the nine of hearts, I would have to win the trick with the eight. After I exit with my last club, ace and a heart would endplay me.

Declarer's two heart bid with 2-6-2-3 was foolish. Competing for a partscore shows a significant gain only when both contracts make. If that is unlikely, then the best result you can expect from competing is a virtual push: a small plus or a small minus at both tables. When the opponents are in one notrump and you have no singleton, chances are that if you make your contract, you are beating one notrump, so it usually wrong to compete without a singleton. An unbid six-card suit can be a reason to break this rule. But South had already shown his hearts, and North was unable to raise. So South knew he couldn't have a big heart fit.

Since one notrump makes and since partner didn't quite have a double, South's result is in the "virtual push" category. One notrump can be held to two on a passive defense, but it makes four after a normal heart lead (giving declarer an entry with the heart nine to play spades); so I expect to lose two imps. In fact, we lose three. Somehow declarer managed to score 210. South must have led hearts, then continued hearts out of sheer frustration when he was in with the spade ace.

Table 1: +100
Table 2: -210

Result on Board 1: -3 imps
Total: -3 imps

Event 3 - Match 4 - Board 8

Board 8
Neither vulnerable

♠ Q 10 5 4 ♥ Q 10 ♦ K J 10 5 2 ♣ 6 2

The match is a tie going into the last board. Partner opens one club in second seat; RHO passes. I bid one spade, and partner bids two clubs. That seems high enough to me, and LHO agrees. RHO leads the six of hearts.

	NORTH Phillip ♠ Q 10 5 4 ♥ Q 10 ♦ K J 10 5 2 ♣ 6 2
	SOUTH Jack ♠ K 2 ♥ A K 5 2 ♦ 9 6 ♣ K 10 8 4 3

West	North	East	South
William	Phillip	Harry	Jack
		Pass	1 ♣
Pass	1 ♠	Pass	2 ♣
(All pass)

One notrump looks like a better spot than two clubs. This board demonstrates one of the downsides of weak notrumps: Partner can't rebid one notrump over one spade, since that shows 15-17 high-card points, so he has to rebid clubs with a bad five-card suit. Of course, if you strengthen partner's hand a bit, it is the strong notrumpers who have the rebid problem--and a considerably more difficult rebid problem at that.

What do I know about the opponents' hands? They have 19 high-card points between them. East passed in first seat, so he is limited to 11, giving West at least eight. West passed over one club non-vulnerable, so he is unlikely to have a five-card spade suit. (Personally, I would be unlikely to have a four-card spade suit.)

If I play the heart ten and it holds, I won't have the fourth-round heart loser to worry about. But if gets covered, I'm poorly placed. If I win and play a heart back to the queen, I've helped the opponents in two ways: I've given the opponents a tempo by releasing two of my heart stoppers. And, if hearts are five-two, I've set up a defensive ruff. If I try to get to dummy by playing a diamond instead, I open up the possibility of a defensive diamond ruff. The heart jack is a slight favorite to be on my right (since jack third or fourth would be an unattractive lead), so I choose not to risk the ten. I rise with the queen; East plays the three.

East would presumably encourage with the jack. So, unless East has jack-three doubleton, it appears I did the wrong thing. I'd just as soon West not continue hearts when he gains the lead, so I "discourage" by playing the deuce.

I play the deuce of clubs from dummy; East plays the seven. That's a nice card to see, since it brings dummy's six into play. I play the eight. West wins with the nine and shifts to the four of hearts--ten--jack--ace. I guess I did the right thing at trick one after all. It appears East has jack-three doubleton and West has five small. The opponents lead fourth best, so six, four is consistent with a five-card suit.

It's possible hearts are two-five instead of five-two, but there are two reasons that is less likely: One, as I've already mentioned, is East's failure to encourage at trick one. The other reason involves a principle of probability that is often overlooked. Sometimes when West has a doubleton heart, his higher heart will be too high to be a plausible fourth best. So his lead from a doubleton will be ambiguous only part of the time. His lead from a five-card suit will always be ambiguous. It will always be possible for his fourth best card to be top of a doubleton. Thus the very fact that there is an ambiguity means that he is more likely to have five hearts than to have two. This is the bridge version of the anthropic principle.

I need to get to dummy to play another club, so I lead the six of diamonds. West plays the four. Finding the ace onside is not as useful as finding the queen onside. I'm going to need to do something with my fourth heart. If the diamond queen is onside, I may be able to pitch the heart on the third round of diamonds. Accordingly, I play the jack. East wins with the ace. That's a bit unexpected. If East knew I had a doubleton diamond, he would probably duck, making it harder for me to score a second diamond trick. Perhaps he couldn't read his partner's card. That would be true only if West has a doubleton. In that case, East would be unable to tell whether West has queen-four or queen-nine-four.

East shifts to the nine of hearts. So I was wrong about the heart split. Anthropic principle notwithstanding, West did have six-four doubleton, and East, for some reason, did not encourage with jack-nine-eight fifth.

That means West is 5-2-2-4. But that's impossible. Why didn't he overcall one spade? Perhaps I'm wrong about the doubleton diamond. Maybe East chose to win the diamond despite knowing I have a doubleton in order to give his partner a heart ruff. Assuming West would give honest count with queen fourth of diamonds, he must be either 5-2-3-3 or 4-2-3-4. (He might have overcalled one spade with 5-2-3-3. But that's not nearly so attractive a pattern as 5-2-2-4, so I'm not as confident in ruling that pattern out.)

Should I play the deuce or the king on this trick? In order to make this, I must dispose of my heart loser and I must avoid losing more than two trump tricks. Playing the deuce aids in the first goal but makes it harder to achieve the second. West can pitch a diamond, forcing me to ruff with dummy's club six. I will now need considerable luck to avoid losing three trump tricks. Playing the king aids in the second goal, since it forces West to ruff, but makes it harder to avoid a heart loser. If East has an entry, the opponents can now draw dummy's trump and cash a heart trick.

To decide which play works more often, general principles will not help. I must examine specific cases. I'll start by assuming West is 4-2-3-4. In that case, if East has either black ace, I must lose three trump tricks. West can ruff this trick with the queen or jack. If East has the club ace, West leads a trump to East and gets a second ruff. If East has the spade ace, West cashes the club ace and leads a spade to East for a second heart ruff.

So if West is 4-2-3-4, I must hope he has both black aces. Is there any way to make it if he does? If I play low on this trick, West can pitch a diamond, letting me ruff in dummy with the club six. He will now have three natural trump tricks. So a low heart does not work. What happens if I play the king? (1) If West ruffs low, I overruff in dummy and lose only two trump tricks. (2) If West ruffs with the queen or jack, I can lead the club king to smother East's honor and lose only two trump tricks. (3) If West pitches, I lead the spade king. Say West wins and plays the diamond queen, putting me in dummy. I can now cash the spade queen and ruff a spade to reach this position (West's side card could be either a spade or a diamond, depending on what he discarded on the heart king):

	NORTH Phillip ♠ 10 ♥ -- ♦ 10 5 ♣ 6
WEST William ♠ x ♥ -- ♦ -- ♣ A J 5		EAST Harry ♠ -- ♥ 8 7 ♦ x ♣ Q
	SOUTH Jack ♠ -- ♥ 2 ♦ -- ♣ K 10 4

When I lead the heart deuce, West is dead. If he ruffs (with the jack or low), I lose only two trump tricks. If he pitches his side card, I can ruff in dummy, then ruff a diamond to my hand. If West overruffs, he is endplayed. So, if West is 4-2-3-4, I must play the heart king and must hope West has both black aces.

What if West is 5-2-3-3? If West has the club ace, I can always hold my trump losses to two tricks. I may have some guessing to do later on, but it makes no difference which heart I play to this trick. What if East has the club ace? If I play a low heart, West can pitch a diamond. I ruff in dummy and must lose two trump tricks and a ruff. And if I play the king? West ruffs with the queen or jack and plays a club to his partner's ace. East can now cash a heart. So it makes no difference which heart I play. I'm down either way.

The king, then, allows me to make the contract whenever it can be made. Although, later on, I may have to guess whether to duck out the club ace on my left or play East to have a singleton honor. I play the heart king, and West ruffs with the jack of clubs. I pitch a diamond from dummy. West cashes the spade ace. East plays the six. It might be nice to have a second dummy entry just in case I'm wrong about three-three diamonds, so I unblock the king. West plays the nine of spades. I win in dummy with the queen as East plays the seven. As the opponents have defended, no club guess is necessary. I play dummy's six of clubs--queen--king--ace. West exits with the eight of spades; East plays the jack. I ruff and draw the last trump. I don't need to repeat the diamond finesse. Dummy's spade ten provides a pitch for the heart.

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

Not a very good defense. East could beat me by ducking the diamond ace, which seems pretty routine. Since he has no second entry and can't give West two heart ruffs, what's the hurry? In fact, it must be better to wait until dummy's club is gone before playing hearts. So ducking seems like a good idea all around. After East did win the diamond ace and play a heart, West should have pitched a diamond rather than ruff. As we saw, that doesn't beat me by force, but it makes things much harder for me. That play, too, should be fairly routine. Ruffing with a natural trump trick is seldom a good idea.

Our counterparts at the other table reached the easier contract of two diamonds and made two. So the match ends in a tie. We score 15 victory points. We are still in the lead, but by a mere three victory points.


Table 1: +90
Table 2: -90

Result on Board 8: 0 imps

Result on Match 4: 0 imps (15 VP)
Current Total: 73 VP

Event 3 - Match 4 - Board 7

Board 7
Both sides vulnerable

♠ Q 9 6 ♥ K 8 7 5 3 ♦ 10 2 ♣ Q J 2

I pass in first seat. LHO and partner pass, and RHO opens one club. I don't see much point in overcalling. I pass. LHO bids one diamond, and RHO bids two notrump (18-19 HCP, no four-card major). LHO bids three clubs (natural), and RHO bids three notrump, which ends the auction. I lead the five of hearts.

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

West	North	East	South
Phillip	Harry	Jack	William
Pass	Pass	Pass	1 ♣
Pass	1 ♦	Pass	2 NT
Pass	3 ♣	Pass	3 NT
(All pass)

Partner has seven or eight high-card points, at least four spades, and at least three hearts. Declarer plays the jack from dummy, partner plays the queen, and declarer plays the ten. Declarer would not be ducking this trick with ace-ten third, so he must have ace-ten doubleton.

It appears we are going to beat this. Since partner has five or six high card points in addition to the heart queen, I don't see how declarer can take nine tricks without giving up the lead. Partner casts a cloud over my optimism, however, by shifting to the deuce of spades. Declarer plays the ace.

What's this all about? It makes no sense for partner not to continue hearts from queen fourth. He must have made a discovery play with ace-queen of hearts at trick one. He knows hearts are running, but, for some reason, he thinks it's a bad idea to run them. Perhaps he is afraid we will be squeezed if we cash out the hearts. Or perhaps he is afraid I won't have a safe exit.

Partner would surely cash out the hearts if he knew I had five. Since the opponents play that declarer's two notrump rebid denies a four-card major, partner would know I had five hearts if he had ace-queen third. So he must have ace-queen fourth.

I'm not happy with this development. But that doesn't mean I should discourage in spades just to express my displeasure. Partner has already shifted. What matters now is: Do I want him to continue spades or not when he gets in again? If declarer can cash four diamonds (which would bring him up to eight tricks), I may be in trouble, especially if partner doesn't have the spade jack. I will need to pitch two hearts on the third and fourth diamonds. If declarer exits with a heart, trying for a fratricide squeeze, partner must win and play another spade. After that, nothing bad can happen. (Assuming I've kept a low heart as an exit. So the two hearts I discard must be the king and the eight or seven.) To clue partner in to this plan, I encourage with the nine of spades.

Declarer plays the three of diamonds--deuce--queen--ace. Ace? You mean partner doesn't have the heart ace? Apparently not. He shifts to the deuce of hearts, and declarer plays the ace. I unblock the seven of hearts to maintian flexiblity. I can reach partner by leading a heart to his six if it proves necessary.

Declarer cashes the diamond king; partner plays the five. He then cashes the spade king. I'm pretty sure partner has the jack, but there is no need to unblock so long as we have communication in hearts. I play the six. Partner follows with the four.

Declarer leads the five of clubs. If I didn't have an exit card, I would have to play low on this trick, since splitting would leave me open to an endplay. It probably won't hurt to play low. Unless declarer has seen my hand, he isn't playing the club eight. But, to guard against good peripheral vision, I play the club jack. Declarer wins with the king, as partner follows with the deuce. Declarer plays a club to his ace, and partner pitches the diamond six. Declarer appears to be 3-2-3-5. His remaining diamond must be the four, since he would not have blocked the diamonds with king-jack third. So we must have the rest. And indeed we do. Down three.

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

I'm not sure why partner switched to a spade at trick two. But we seem to have gained a trick as a result. After a heart continuation, declarer would try to run clubs and would wind up down two. After the spade switch, declarer decided it made sense to attack diamonds first. And perhaps it does. If clubs are running, it makes no difference. If he happens to get lucky and establish three diamond tricks, he might wind up making his contract even if clubs don't come home. Still, once the jack or ten of diamonds didn't appear on the first round of the suit, it seems he should have abandoned that plan. He still had time to switch to clubs and hold this to down two.

Our teammates did finish down two in the same contract, so we pick up three imps and tie the match with one board left. The VuGraph audience is going wild.

Table 1: +300
Table 2: -200

Result on Board 7: +3 imps
Total: 0 imps