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

Match 2 - Board 31

Board 31
Our side vulnerable

♠ J ♥ K 10 3 2 ♦ A K 8 7 4 3 ♣ 9 3

I open one diamond, LHO overcalls one spade, partner bids two clubs, and RHO cue-bids two diamonds, showing a constructive raise.

What should opener's rebids mean on this auction? Passing should show better defense than offense, in other words, either a balanced hand or an unbalanced misfit (such as a 3-4-5-1 pattern). Doubling should show a better hand of the same type and should establish a force. Jack thinks I should pass with this hand because I have a minimum, but that's nonsense. You can't pass with an offensively oriented hand, since this may be your last chance to describe your hand at a relatively low level. The idea that a free bid in a competitive auction shows extra values was debunked back in the 60s. It's hard to imagine passing with any hand that includes six diamonds. I bid two hearts.

If RHO had passed, I would have rebid two diamonds. Two hearts, as a reverse, would establish a game force opposite partner's two-over-one. In this auction, two hearts does not create a game force, because it is cheaper than rebidding diamonds. Accordingly, minimum rebids by responder (two notrump, three clubs, or three diamonds) are all passable. If responder wants to set up a game force, he has a cue-bid available.

I should point out that not everyone would agree with what I've said here. Some, like Jack, would pass over two diamonds, thinking any action should show a better hand. Others would go ahead and bid two hearts but would consider it a tactical overbid and would still play responder's rebids as forcing. Neither approach makes sense to me.

Over two hearts, LHO bids two spades, and partner bids three spades. Obviously partner agrees with me that two hearts does not establish a game force. Otherwise he would just pass rather than consume a full round of bidding without saying anything useful.

RHO passes. Interesting. If RHO isn't doubling the cue-bid, I wonder if my singleton jack of spades is enough for me to bid three notrump. Maybe. But I'm too chicken to try it. I bid four diamonds, and partner raises to five. LHO leads the ace of spades.

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

West	North	East	South
			1 ♦
1 ♠	2 ♣	2 ♦1	2 ♥
2 ♠	3 ♠	Pass	4 ♦
Pass	5 ♦	(All pass)
1Constructive raise

I don't understand the cue-bid. If partner thinks two hearts establishes a game force, then a forcing two notrump bid seems like the right call. And if he thinks two hearts does not establish a game force, then a non-forcing two notrump seems like the right call. What's the point of three spades? To my mind, the auction should have proceeded two notrump--three diamonds--pass.

Of course, the cue-bid might have worked out if I had had the courage to bid three notrump. If LHO has ace-queen of spades and leads a low one, I would make it. At the very least, I have a better chance of making three notrump from my side than I have of making this.

RHO plays the five of spades, and LHO shifts to the six of hearts. RHO plays the ace, and I drop the deuce. RHO continues with the queen of hearts. Really? Why are the opponents so sure I don't have a singleton club? Shouldn't they be cashing the club ace?

Is there any way I can possibly take advantage of the opponents' carelessness? Not that I see. The best I can do is to make the opponents feel stupid by creating the illusion that I have a singleton club.

I ruff the heart in dummy, cash the spade king, pitch a club, and snicker. (An advantage of playing against the computer. I couldn't snicker against humans. That would be coffeehousing.) East ought to be feeling a surge of panic right now. Is he panicked enough to make another mistake if he has the club ace? I lead the club king--seven--nine--ace. Down one.

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

I see I wouldn't have made three notrump. The one pair who played three notump did make it, but I suppose they played it from the North side and either West never bid spades or his partner chose to lead his own suit anyway. One pair actually passed the board out. The rest were down one in five diamonds. Since one of those pairs was doubled, we get five matchpoints.

I think partner bid too much. He, of course, thinks I bid too much. Would we have stayed out of game if I had passed at my second turn as partner wanted me to? I rebid the hand with Jack to find out. If I pass, LHO bids two spades, and partner bids three diamonds. After my pass on the previous round, I can hardly pass that. With six diamonds and a singleton spade, I have a much better hand for play in diamonds than partner expects me to. I bid four diamonds. Partner might suspect we're off three key cards and pass.  But he doesn't. He continues on to five diamonds. I guess once I open, we are destined to get to game. Hats off to the pair who passed this board out!

Score on Board 31: -100 (5 MP)
Total: 250 MP (67.2%)

Current rank: 1st

Match 2 - Board 30

Board 30
Neither vulnerable

♠ A J 6 4 3 ♥ A K J 6 ♦ J 9 8 2 ♣ --

RHO opens one club. I bid one spade, hoping I will be able to double some number of clubs at my next turn. I get my wish. LHO bids two clubs, partner passes, and RHO bids three clubs. I double, partner bids three hearts, and RHO bids four clubs. I don't have anything further to say. This is about what partner should expect for this auction. I pass, and partner bids four hearts.

This makes no sense. If he couldn't bid four hearts the first time, how can he bid it now? If this makes, I owe RHO a thank-you for his four club bid, giving partner a chance to reconsider his decision. Everyone passes, and RHO leads the queen of clubs.

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

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

Partner certainly should have bid four hearts a round earlier. An eight-loser hand with a known double fit? Of course, the fact that he should have bid it doesn't mean I'm going to make it. West rates to have six clubs and a singleton heart for his four club bid. His likeliest pattern, then, is 3-1-3-6, in which case I'm going down unless his singleton heart is the queen.

Is there any way I can endplay East if my construction is correct? What if I pitch a diamond on the club ace, play a spade to the ace and ruff a spade, then a heart to the ace and ruff another spade. Now a club ruff to dummy and ruff a fourth spade. I'm down to this position:

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

I play a diamond. East wins with his singleton honor and is endplayed. He leads a club, and I can ruff in my hand, discarding a diamond loser from dummy. All very nice. But to acheive this endplay, I've tapped dummy out. I need two more tricks, and there is no way to take them.

I'm not entirely sure I would adopt such a committal line even if it were going to work. But I'm certainly not going to adopt it if it isn't going to work.

It seems my only chance to make this if everything is breaking badly is to trick West into crashing diamond honors. Too bad he doesn't know I have five diamonds. If he did, and if I played a diamond from my hand, he might hop with ace-king or ace-queen third to give his partner a ruff.

Maybe I should ruff a spade to my hand to clue him in to my spade shortness. What if I ruff the club in dummy, (I can't afford to let him know I have the club ace. That would tip him off that I don't have any red-suit honors.) then play ace and ruff a spade? Now I play a diamond. Since he now knows I have long diamonds, he might hop. Is there any risk in this line? Possibly. What if West is 2-1-3-7 with a singleton queen of hearts. Now I'm cold on a staightforward line. But I go down on my tricky line, since East can lead a third round of spades for his partner to ruff with the queen.

I suppose I can guard against that by drawing one round of trumps before ruffing a spade. I find it hard to believe that trumps are two-two, so I'm willing to take the risk of not drawing a second round. That's the plan I settle on. I ruff the club in dummy and cash the heart ace. If everyone follows low, I intend to ruff a spade to my hand and lead a diamond.

My ruse proves unnecessary. West drops the heart queen under the ace. I draw the remaining trumps and play a diamond. Diamonds are two-two, so I wind up making five. There was never anything to worry about.

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

This result is worth seven matchpoints. The only result other than plus 450 came from the pair who defended five clubs doubled and collected 300. I must apologize to partner. Had he bid four hearts over my double, West would surely have bid five clubs. We could compete to five hearts, but, in practice, we would probably double and score one matchpoint. Sorry I criticized your bid, partner. (But it's a hollow apology. I still think three hearts is insane.)

Score on Board 30: +450 (7 MP)
Total: 245 MP (68.1%)

Current rank: 1st

Match 2 - Board 29

I usually publish my weekly post on Sunday, but I need to publish early this week, since it is going to be a busy weekend. Hartford Opera Theater is premiering my latest opera, Fall Back.  If you're going to be anywhere near Hartford Sunday night, stop by.

Board 29

Both sides vulnerable

♠ K J 4 3 ♥ K 10 8 6 5 2 ♦ -- ♣ K 8 5

Two passes to me. I open one heart, and LHO overcalls one notrump. Partner passes, and RHO bids five diamonds. If he isn't remotely interested in three notrump, there is a good chance he has a heart void. My best guess as to his shape is 4-0-7-2. I'm crediting him with four spades because of his unwillingess to pre-empt at his first turn. Partner probably has enough in high cards to raise to two hearts, since the opponents aren't sniffing at slam, so I suspect he has a doubleton and that there are five hearts on my left.

I pass, LHO passes, and partner doubles. Doubling five of a minor at matchpoints is seldom a good move, since some pairs will play in three notrump. If three notrump makes, the double has little to gain. And if three notrump makes four, a failed double could flip a top to a bottom. So partner must be fairly sure of his ground. He is probably doubling on natural trump tricks, assuming that if diamonds aren't running, three notrump won't be making either.

Unless partner has three tricks himself, I'm going to have to contribute something, and that something is probably a spade trick. One thing I'm not leading is a heart. The risk that declarer is void and a heart lead will allow him to take a finesse he can't otherwise take is too great. A spade lead seems inadvisable as well. Let's say I'm right that declarer is 4-0-7-2, and let's give dummy a 3-5-2-3 pattern, as seems likely. If I give away a spade trick on the opening lead, declarer may be able to pitch one spade on the heart ace and another on the third round of clubs. If I give away a club trick on opening lead, however, that may not be fatal. Suppose declarer has jack doubleton of clubs opposite ace-queen third. A club lead gives him a third club trick, but he still can't dispose of all his spades. As long as the ace and queen of spades are not both behind me, I still have a spade trick. Of course, if dummy has the spade ace, partner must find a spade shift at some point to break up the squeeze. But that should be easy for him to see.

Which club should I lead? The eight seems like the best choice. If declarer thinks I don't have the king, he may hop with the club ace and pitch his club loser on the heart ace. He might even follow with a ruffing finesse in clubs against partner. I don't see how it can hurt to mislead partner. I want a spade shift when he gets in anyway, so misleading him may even prove to be productive. The eight of clubs it is.

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

West	North	East	South
		Pass	Pass
1 ♥	1 NT	Pass	5 ♦
Pass	Pass	Double	(All pass)

Aha! 3-5-2-3. I called it! It looks as if my construction is correct. Declarer plays low from dummy. Partner wins with the jack; declarer follows with the nine. Declarer must have ten-nine doubleton and was hoping I had led from king-jack-eight third or fourth.

Partner switches to the deuce of spades. The deuce? Unless partner is getting into the act with funny spot card leads of his own, it looks as though I'm wrong about declarer's having four spades. Declarer takes the ace, and I encourage with the four. Declarer plays the seven of hearts. Yes, I was indeed wrong about the spade suit. It now appears declarer is 3-1-7-2. That means he may be able to avoid a spade loser. He can play the heart queen, ruff a heart, club to the queen and ace, and pitch his last spade on the heart ace as partner ruffs in with what may be a natural trump trick.

I play the heart eight, declarer plays the jack, and partner follows. Instead of a low heart, declarer plays the heart ace. Partner ruffs with the seven and declarer overruffs with the nine. I play the six to reassure partner about the spade king. It appears my spade trick is now safe. Declarer plays the deuce of diamonds to the queen. I play the heart five. Partner wins with the diamond ace and shifts to the queen of spades. I overtake with the king and cash the jack. Annoyingly, but not surprisingly, partner follows.

Partner really should have led a low spade. On this particular deal, I can't think of any reason I would need to overtake the queen if I don't have the jack. But leading low from doubleton honors when there is no future in any other suit should be a matter of routine. It would inspire confidence to know I could trust partner to do that.

Anyway, we're out of tricks.  Declarer finishes down two.

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

Obviously declarer could have finessed the club queen, either at trick one or at trick five, and held it to down one. Ducking at trick one seems right. He might have made this if I had led from king-jack of clubs. But he should have taken the finesse later. It's true that he would go down three if the finesse lost. But I doubt there is much difference between minus 500 and minus 800. He was apparently mesmerized by the eight of clubs. And it was an expensive mistake. Five diamonds doubled down one was the normal result. We would have received only seven matchpoints for plus 200. Plus 500 is a top. And it seems partner was right to double. Plus 100 would have been worth only three matchpoints.

Professor Jack (Jack's post-mortem commentator) wishes to inform me of a possible "misunderstanding" in the card play. I ask him to explain. "Leading the club eight is not right," he says. "From king-eight-five the systemic lead is the five." OK, Jack. Sorry.

It occurs to me that if declarer had held jack-nine of clubs instead of ten-nine, a club is the only lead (other than a bizarre king of hearts) to let him make it. That's a little too close for comfort. I can't imagine either major is really the percentage lead. But I have a feeling the field doesn't know that. It's scary to think how close we came to having a disaster.

Score on board 29: +500 (12 MP)
Total: 238 MP (68.4%)

Current rank: 1st

Match 2 - Board 28

Board 28
Our side vulnerable

♠ K 3 ♥ A J 9 8 6 4 2 ♦ 9 5 2 ♣ K

One diamond--two clubs--pass to me. I bid two hearts. This bid isn't forcing, but so what? If partner has heart support, he'll raise. If he has a solid opening bid, he'll try to bid something. If he has neither, two hearts is probably high enough.

At least I hope it's high enough, because two hearts ends the auction. West leads the king of diamonds.

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

West	North	East	South
1 ♦	2 ♣	Pass	2 ♥
(All pass)

East plays the four of diamonds. I'm not sure what the opponents' lead conventions are, so I'm not sure whether West can have the diamond ace or not. Perhaps West has ace-king-queen and East is discouraging, or perhaps East is encouraging with honor-four-three. I "discourage" with the deuce, hoping to induce a spade shift. West shifts--but to the four of clubs. This shift doesn't make much sense unless it's a singleton. I play the club jack, East plays the queen, and I win with the king. I guess it's not a singleton. Why would East cover with queen fifth?

I'm tempted to play a diamond. Perhaps I can ruff the third round of diamonds in dummy and pitch a spade on the club ace. If so, then I'll make three if I have to lose a heart and four if I don't. Might I go down on that line? Suppose East wins the diamond and plays a spade. West takes the queen and ace and plays a third diamond. If I ruff with the king, I could lose two trump tricks. So I ruff low. East overruffs and leads a club. That would be awkward.

I've stayed nice and low. I'd hate to give up my edge by going minus, so I decide to play it safe. I play the heart ace--five--ten, then the four of hearts (As always, hanging on to those deuces on principle)--seven--king--five of spades. I can now pitch a diamond on the club ace and try a finesse against the queen of spades.

Actually, I can't. West ruffs the club ace. His club shift was a singleton after all. He can now play two rounds of diamonds, tossing me in my hand and holding me to eight tricks. But, for some reason, he cashes the spade ace. Making three.

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

It turns out the overtrick is immaterial. We are the only North-South pair to go plus on this board. One pair went down two in four hearts; two went down one in three hearts; the rest defended three spades making four.

The opponents have a double fit, yet they didn't locate either one. What went wrong? For one thing, I believe West should double two hearts. This double should show shortness in clubs, not shortness in hearts. In fact, it should promise three or four hearts so that responder can pass with an appropriate hand.  Using double to show something like a 4-1-5-3 pattern makes little sense. Opener should avoid re-entering the auction with club length when responder couldn't act over two clubs.

Also, although I don't expect a lot of people to agree with me, I think East must take some blame for his pass over two clubs. He knows the opponents have at least eight hearts, he knows from his club length that his partner rates to have long diamonds, and he knows this may well be his last chance to support the suit. I think he should bid two diamonds. The three-card competitive raise of a minor is routine in the style I'm used to playing: weak notrumps with four-card majors.  It is almost unheard of in Eastern Science Fiction, but don't think it's a bad idea in that system either. Of course, if you bid two diamonds on awkward hands with three- or four-card support, you must avoid it when you have good support.  I don't see that as a hardship. With five trumps, you can usually muster up a raise to three or a cue-bid.

If East does bid two diamonds, West will compete with three diamonds over two hearts. It's not clear what will happen after that, but East-West should at least wind up with a plus score.

Score on Board 28: +140 (12 MP)
Total: 226 MP (67.3%)

Current rank: 1st

Match 2 - Board 27

Board 27
Neither vulnerable

♠ 7 4 3 ♥ K 9 7 ♦ K 9 8 4 ♣ K 10 4

I pass in first seat. LHO opens with one spade, and RHO bids two diamonds. I pass. LHO rebids two spades, and RHO raises to four. Partner leads the deuce of hearts (third and lowest).

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

West	North	East	South
		Pass	1 ♠
Pass	2 ♦	Pass	2 ♠1
Pass	4 ♠	(All pass)
1Forcing

The first thing I do when dummy hits is to take note of and memorize the outstanding diamond spots: the three, six, and ten. I once complimented a player for his table presence. Whenever he held a suit like this and played low to the queen, winning the trick, he always seemed to know without any doubt whether the king was onside or whether his RHO had ducked. "That's easy," he told me. "The guy who has the king is the one who glances at dummy's spot cards after his partner plays."

Partner seems to have five hearts. I'm not sure what the opponents' style is with regard to the two spade bid. But I'll assume that South has either six spades or five spades with a side club suit. That makes South's likeliest patterns 6-3-1-3, 6-3-2-2, or 5-3-1-4.

Declarer plays low from dummy. That's a revealing play. If declarer has ace-jack third of hearts, he would normally play the queen as a discovery play. It gains to play low only if I have a singleton king (which seems unlikely) or if declarer needs to win the first trick in his hand (which does not seem to be the case here). The advantages of playing the queen are: (1) declarer finds out where the king is, which will help him in constructing the defenders' hands, and (2) it conceals the location of the jack from both opponents. So I assume declarer has ace-ten third of hearts.

If I'm right about that, then partner probably has the club ace. Leading from the jack is not particulary attractive, and there is no instrinsic reason from the auction that partner should lead a heart rather than a club. The likeliest reason for choosing a heart over a club is that he has the club ace.

If I'm right that partner has the club ace, then I can draw the further conclusion that declarer probably does not have a doubleton club. With ace-ten third of hearts and two small clubs (or queen doubleton), declarer would want to guess whether partner has led from the jack or from the king and play accordingly. Since defenders are more likely to lead from a king than from a jack, the queen is the normal guess. With ace-ten third of hearts and three small clubs (or queen third), however, it would be logical to play low to ensure taking a second heart trick. Declarer doesn't have the tempi to ruff both the third round of hearts and the third round of clubs. So guessing hearts doesn't gain anything. Declarer would be unlikely to go down in this contract if he plays low at trick one. He might well go down if he plays the queen and it gets covered.

I play the nine, and declarer wins with the jack. Poof! The entire chain of conclusions I reached above has now gone up in smoke. Playing low from dummy with ace-jack third in your hand is such an unusual play that, opposite some partners, I would be virtually certain that partner had underled the heart ace. In this case, however, I will just assume that Jack doesn't appreciate the value of information. On purely technical grounds, low is the correct play, so Jack chose it.

Declarer plays the deuce of spades--six--jack. I play the four. Offhand, this play doesn't appear to make any sense. If declarer intends to take ruffs in dummy, he shouldn't be playing trumps. And if he intends to establish diamonds, he shouldn't be wasting dummy entries.

Declarer leads the queen of hearts. I can't imagine he's going to let this ride, so I play low. If declarer didn't want to make a discovery play at trick one, I'm not going to help him out now. Declarer plays the ace, and partner follows with the three. Now declarer attacks diamonds: six--three--ace. I guess partner wasn't sure he could afford the ten. I've seen him give away tricks in the past with his count signals. I'm not sure why he's being more careful this time, but I'm happy to see it. I play the four and follow with the eight when declarer leads a low diamond from dummy.

Declarer ruffs with the five of spades, then plays the eight of spades to dummy's nine as partner pitches the five of hearts. Two mistakes in a row. With king-queen-ten-eight-five of spades, there is no reason not to ruff the diamonds high (with at least the ten). He should then led the five of spades to the ace, not the nine. Even if he can't imagine why he would want to win the third round of spades in his hand, what does it hurt to keep his options open? Sometimes the reason doesn't occur to you until later, for example, a half a second after you call for the nine.

Declarer leads the queen of diamonds from dummy. I play the nine, and declarer ruffs. With diamonds not breaking, all declarer can do now is ruff a heart in the dummy and lose three club tricks. Making four.

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

As I thought, leading a spade to dummy at trick two was an error. If declarer had started diamonds right away, he would have had enough dummy entries to make five. You might think that making five would be the normal result, but no one acheived that. One pair made six. Everyone else made four. Presumably the declarer who made six chose to take a ruffing finesse against the king of diamonds. Perhaps his West got into the auction and tipped off his two-suiter.

Score on Board 27: -420 (7 MP)
Total: 214 MP (66.0%)

Current rank: 1st

Match 2 - Board 26

Board 26

Both sides vulnerable

♠ A 6 ♥ A 10 9 7 2 ♦ A 6 4 3 ♣ K 10

RHO passes. I open one heart. LHO overcalls one spade, partner bids two diamonds, and RHO bids two hearts, showing a constructive spade raise.

I have enough to force to game opposite partner's two diamond bid, and three diamonds isn't forcing in this style, so I cue-bid two spades. Partner bids three diamonds. Since my two spade bid did not guarantee support, partner probably has six diamonds. Jack thinks I should bid five diamonds at this point. That might be right if partner has a singleton heart. In that case, I might be able to hold my losses in five diamonds to a spade and a club when three notrump has no play. But any time partner doesn't have a singleton heart, it seems unlikely that I would be making five diamonds unless I'm also making three notrump.

I could punt with three spades, asking partner to bid three notrump with either solid diamonds (which I know he doesn't have) or help in spades. But I'm not so sure I need help in spades. Why can't partner have the club ace or the heart king or a seventh diamond? Even the heart queen may be enough for me to make three notrump on a strip squeeze. I bid three notrump, and everyone passes. West leads the ten of spades.

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

West	North	East	South
		Pass	1 ♥
1 ♠	2 ♦	2 ♥1	2 ♠
Pass	3 ♦	Pass	3 NT
(All pass)
1Constructive raise

Well, I hope I was right about that strip squeeze. I cover the ten with the jack to isolate the spade stopper in West's hand. East plays the queen. I have no particular reason to win this. Maybe if I duck, East will find something clever to do. I play low. No clever antics are forthcoming. East simply continues with the seven of spades--ace--three--deuce.

Given the auction, the heart king and club ace are surely split. Probably East has the club ace, since he the heart king will not look like a particularly good card to him, and he seems to be light for his two heart bid as it is. If so, West can't defend the end position. He must come down to five cards. If he discards a spade, I can simply drive the club ace. So he must come down to three spades and two hearts, throwing all his clubs away. I can now toss him in with a spade to lead away from the king of hearts.

If the heart king and club ace are switched, I can still make this provided West has the heart jack. To hold all his spades and the club ace, he must stiff the heart jack. I can now lead the heart queen to pin it.

I play a diamond to the queen and play the seven of diamonds back to my ace. (I doubt very much if I'm going to need that deuce of diamonds. But what does it hurt to hold on to it? One of these days this habit of routinely retaining deuces is going to pay off.) West plays nine-jack of diamonds. East follows once, then discards the club deuce.

It's a good idea in these situations to make an initial guess about how the cards lie, then modify that guess as you go along if the opponents' discards are inconsistent with your picture. If you wait until you're through running the diamonds before you try to reconstruct the unseen hands, it's easy to overlook an inference. Reading the ending on this deal could be difficult. The defenders already knows they have to come down to five cards. So West knows his objective. He must either stiff the heart king while making it appear that he hasn't, or he must retain king doubleton of hearts while making it appear that he has stiffed it. It's East's job to figure out what hand West is trying to represent and to cooperate.

For my initial guess, I'm going to place West with 5-2-2-4 and East with 3-4-1-5. That seems like the single likeliest pattern.

I play a diamond to dummy. West discards the heart three; East the club three. Possibly West is being tricky and stiffing his heart king right away. But Jack isn't usually so deviousl. So I'm inclined to doubt that he began with a doubleton heart. I'm going to revise my guess. I'm now guessing that West started with 5-3-2-3; East, with 3-3-1-6. Having a six-card side suit is perhaps more consistent with his aggressive two heart bid anyway. On the next diamond, East plays the club four; West, the heart five. This doesn't look good. Could West have started with three small hearts? If so, I'm not making this. Perhaps he has jack third of hearts and is hoping his partner has king-ten (or the ace).

On the penultimate diamond, East plays the heart four. I pitch the heart seven, and West pitches the five of spades. Not a good move, West. Now I'm cold. Both opponents pitch clubs on the last diamond. I drive the club ace and claim my nine tricks.

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

West had a golden opportunity to mislead me. I wasn't expecting East to have seven clubs. West should have represented 5-3-2-3 and pitched two clubs and two hearts. I might then play him to have stiffed one honor or the other and go down. We again see the difficulties in teaching a computer to play bridge. Jack can tell that there is no defense, so he gives up. Since he can't look at the deal from his opponent's point of view, he has no way to see that pitching a spade offers declarer no realistic opportunity to make a mistake, whereas pitching two hearts and two clubs does.

Only one other pair reached three notrump. That pair was also plus 600. Every other pair was down in five diamonds, so we get 11 matchpoints.

Score on Board 26: +600 (11 MP)
Total: 207 (66.3%)

Current rank: 1st