Free Weekly Instant Tournament - October 28 - Board 2

Board 2
Our side vulnerable

♠ A K 9 2  ♥ J 5 4  ♦ 10 8 4  ♣ A K 8

RHO opens with one notrump. I have a one-notrump opening myself, so I could double. Some players don't care for penalty doubles of one notrump--so much so that they give double some other meaning. But I think the penalty double of one notrump is a useful call.

Perhaps, though, "penalty double" is not the best description. It's true that if partner has a flat hand, he will pass and you will defend one notrump doubled. But that's not the main reason you double. You double because it might be your hand, and if partner has a long suit and some shape, you want to encourage him to bid it. The double, paradoxically, tends to work out better when partner pulls it than when he passes.

You do, however, have to be prepared to defend if partner is flat, and with this hand, I have poor defensive prospects. I have four tops tricks and possibly a long spade trick, but no place to look for tricks beyond that. If I knew partner had some shape and was going to pull the double, I would double. It might be our hand and doubling now might be the only way to get into the auction. But if partner passes the double, I won't be happy.

I pass and am quite pleased with my decision when I hear LHO raise to three notrump. Everyone passes, so I must find a lead.

If the opponents have 25 HCP, partner is broke. If one of the opponents has counted a five-card suit as a point, partner might have a jack. My best chance to beat this is to find partner with the spade jack. Either I can lead a low spade, hoping to find dummy with queen-ten, or I can lead the king, hoping to drop a doubleton queen. The latter is more likely, so I lead the spade king.

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

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

Queen-ten of spades were in dummy after all. And, since dummy has only nine HCP, partner could have a jack, so I might wind up regretting my opening lead. But it's too late to do anything about that now. Partner plays the three; declarer, the six. Now what?

If I continue spades, declarer can take five diamonds, one spade, and anywhere from three to five hearts, making anywhere from nine to eleven tricks. Since I can't beat this, perhaps I should just cash out to ensure holding declarer to nine tricks.

One thing to consider is that declarer might not know diamonds are running. Partner might have the jack and declarer might have ace doubleton. But even if that's the case, what choice does he have but to try to run the suit? If I'm the one with spade length, I must have a club honor, since I would have led low from ace-king and length with no side cards. Even if declarer doesn't draw that inference, three-three diamonds is a priori more likely than both club honors in the short-spade hand.

So playing on diamonds is declarer's best chance to make this. But will he necessarily try to make it? It's a normal contract, after all. Might declarer drive the clubs anyway, conceding down one to avoid going down more?

If I concede a spade, declarer can count three diamonds, one spade, and three hearts. If he has five hearts, he can cash the ace and king and discover the suit is running. But if he has four hearts, cashing the ace and king doesn't help. When the jack doesn't drop, he doesn't know whether the fourth heart is good or not. In that case, it's possible he will wind up down two if he tries to run diamonds, so he might decide to play on clubs and concede down one.

Still, for me to continue spades hoping for that to be the case is playing for a parlay: Declarer must have ace-small doubleton of diamonds, he must have fewer than five hearts, and he must have two or three spades (else I can't set up a spade trick anyway). And, even if he has all that, he must judge to concede down one rather than try to make it--hardly an obvious decision. It's clearly right for me to cash my four tricks.

I cash the spade ace, then king-ace of clubs, then play another club on the off chance partner has the queen. Making three.

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

Minus 400 is worth 46%. Nine defenders did continue spades at trick two and found declarer with the magic hand where he has a decision to make. Three times, declarer cashed out and made an overtrick but six times he attacked clubs and conceded down one. Presumably there is some randomness build into the program to account for this.

I notice some defenders chose to lead the spade ace rather than the king. The standard approach against notrump is to lead the king from ace-king or king-queen, reserving the ace as a request for partner to unblock an honor (or to give count if he has no honor). The queen also requests an unblock of the jack, so you lead the queen from king-queen-ten-nine but the king from king-queen-ten-small.

Someone--I don't know who or when--came up with the idea to reverse the ace and king leads. In this method, you lead the ace from ace-king and lead the king to request an unblock. This makes absolutely no sense to me. It means you can't afford to lead the king from king-queen unless you can stand an unblock. Perhaps the method makes some sense if you play Rusinow leads against notrump, but it seems unplayable otherwise. Yet I see that several websites for beginners suggest it.

If someone can point me to an article providing a cogent argument for this method, I'd love to see it. Perhaps I'm missing something. Until then, I'm sticking with the standard approach.

Free Weekly Instant Tournament - October 21 - Board 1

Board 1
Neither vulnerable

♠ K J 9 8 6  ♥ A 10 2  ♦ A K  ♣ A 10 3

Two passes to me. I open with one spade, intending to raise one notrump to two. I don't get the chance. LHO bids four clubs, which is passed back to me.

I can hardly pass, since partner could easily have a hand that will produce game. While I'm not a fan of offshape take-out doubles, they are less of a problem at a high level, since partner is freer to pass the double without a clear direction. Let's hope that if partner bids diamonds, he won't be disappointed with ace-king doubleton for support.

I double, and partner bids four hearts. Everyone passes, and RHO leads the club seven

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

West	North	East	South
Robot	Phillip	Robot	Robot
			Pass
Pass	1 ♠	4 ♣	Pass
Pass	Double	Pass	4 ♥
(All pass)

If I pick up the trump suit, I have six hearts, one club, and two diamonds for nine tricks. I should be able to find a tenth trick in either diamonds or spades.

How should I play trumps? Since East has at least seven clubs and probably eight, West is a favorite to hold the heart queen. So my best play is a low heart to the king then a heart to the ten. Even if this finesse loses, all is not lost. At least I'll have a trump left in dummy to ruff a diamond with.

I play the heart deuce from dummy--seven--king--five. Now a low heart--nine--ten--club eight. On the heart ace, East pitches the club five.

I'm up to nine tricks. I can set up a diamond trick on most layouts and two diamond tricks on some. The only danger is that East has a small singleton. Is there anything I can do if he does?

Suppose I cash the ace and king of diamonds and East shows out. Now what? The spade ace is surely onside, but setting up the spade king does me no good, since I no longer have a dummy entry with which to reach it. Perhaps I should cash one diamond, then ruff a club to my hand and play a spade. Now I have an entry to the spade king, and I still have two trumps left, so I still have enough entries to my hand to make five if the diamonds behave.

But what if I'm wrong about the spade ace? What if West plays low on my spade play and the king loses to East's ace? Now I'm in trouble. East will tap me and, with only one trump left, I can no longer establish a diamond trick. So I'm down one. It's embarrassing to go down with normal breaks by trying to guard against bad ones.

I could take the position that West will always hop with the ace if he has it and play the jack if he ducks. But if I'm wrong about that and the jack loses to the queen, I again get tapped out and go down. In fact, even if the jack loses to the ace, I could get a poor result. I make four, but if the diamonds lie favorably, declarers who unimaginatively cash the ace and king will be making five.

Cashing only one diamond doesn't seem to be a good idea. Is there another way to handle a bad diamond break? Let's say I cash both diamonds and East shows out. I ruff a club to my hand, ensuring West is out of clubs, then lead the diamond ten. West wins and, if he has the spade ace, he must give me either a diamond trick or the spade king for my tenth trick. So long as West has the spade ace, there is no need to lead a spade toward the king early.The need to retain a dummy entry was an illusion.

I cash the ace of diamonds. East plays the deuce; West, the eight. Maybe I should have cashed one diamond before doing all that thinking. Now that I've seen the eight, I have no further problems. I cash the king of diamonds, and East drops the jack. Good. Now I'm making five. I ruff a club to my hand as West pitches the spade three.

But hold on. Maybe I can make six. I still have two trumps left, so I can afford to lead a spade before driving the diamond queen in case West sees a reason to duck. Actually he might have a very good reason. What if I held a second spade instead of the diamond ten? From West's perspective, this might be the end position.

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

If West hops when I lead a spade, the defense can take only one diamond trick. If he ducks, they get two. It's worth a shot. Let's hope West thinks of this layout.

I play the spade deuce, and West plays the seven. Did this actually work? Or was East overstrength for his pre-empt? I play the king, and East takes the ace. He taps me with a club and I claim eleven tricks.

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

96%! This board should be average. Even if you take "eight ever, nine never" too seriously and cash the top hearts, you still make five. You can ruff out the diamond queen, trading a diamond loser for a trump loser. It's strange that this is such a good result.

Incidentally, I don't care at all for East's four-club bid. He could easily be missing three notrump. Pre-empts are supposed to be bad hands.

Free Weekly Instant Tournament - October 14 - Board 8

Board 8
Neither vulnerable

♠ A 6  ♥ 10 9 5  ♦ K 6 5  ♣ A Q J 9 8

LHO passes, partner opens with two spades, and RHO passes.

Playing opposite myself, I would pass. While game is possible, it's remote enough that I wouldn't want to risk going minus at the three-level. With three trumps, going minus at the three-level isn't so bad, since you have the protection of the Law: If you go minus, chances are the opponents can make something. With only two trumps, that is less apt to be true, so it pays to be conservative.

Playing opposite robots, however, passing is less clear. Robots often pre-empt with hands I would open at the one-level, so the chance of game is greater. I have missed games passing robot weak two-bids with worse hands than this.

Ron Klinger, in The Modern Losing Trick Count, recommends that, when holding a doubleton in support of partner's weak two-bid, you should invite game with three and half or four cover cards. My aces and king provide three cover cards, and the club queen provides a half. So this hand is worth an invitation by that standard. Since my record opposite robots is poor in these situations, I'll follow Ron's advice.

I bid two notrump, and partner bids three clubs, showing a maximum with a club feature. If spades are solid, we have eleven tricks. The question is whether the opponents can cash four first.

Let's hope not. I bid four spades and everyone passes.

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

West	North	East	South
Robot	Phillip	Robot	Robot
		Pass	2 ♠
Pass	2 NT	Pass	3 ♣
Pass	4 ♠	(All pass)

Do you want to be in four spades with these cards? Against best defense, game is worse than a finesse, since we might have a trump loser. But in practice it's better than that, because the opponents might lead a black suit or might fail to solve the cash-out problem. It's not clear whether that consideration boosts the odds to better than fifty percent. But I don't mind being in game, so I have no quarrel with Klinger's rule.

Unfortunately, the opening lead is the diamond queen, so the ace is offside. And, since my auction revealed my club king to the defense, they know they must cash four red cards immediately. My only chance to make this contract is to convince the opponents I have a singleton in one red suit so they will try to cash three tricks in the other one. 

What's the best way to do that? Since the opponents know they are facing a cash-out problem, all their signals should be count. If I duck this trick, East should play a count card. If that card happens to be higher than the four and is intended as low, I can obscure the message by dropping the ten. But most of the time his card will be readable. Perhaps it's better to cover the queen, forcing East to take his ace and preventing him from signaling.

The defense should be able to solve their problem even after I cover, but it will be more difficult and the opponents might not be on the same wavelength. Of course, robots aren't on any wavelength. They don't signal at all nor do they draw inferences from the play, so this whole discussion is moot. But, just for practice, I might as well pretend I'm playing against real bridge players.

I  play the king and East takes the ace. Should I drop the ten or the four? The ten tells East I have a singleton or doubleton diamond, since I would have ducked the queen with ten third. The four leaves open the possibility that I have one, two, or three diamonds. The more possible layouts I give East to defend against, the harder it will be for him to find a defense to cater to all of them, so the four is the correct play.

I play the four, and East shifts to the heart ace. So far, so good. I play the six; West, the deuce. East now shifts to the diamond deuce. It's all over. West, seeing my ten, isn't going to try to cash a third diamond, since I can hardly have ten third. And indeed he doesn't. He takes the jack and cashes the heart king, as East follows with the seven.

West continues with the heart jack. East follows with the four, and I ruff. My only chance for a good board is to hope that other declarers will be minus in a partscore. Does it makes sense to finesse the spade, hoping East has jack fourth? Could I conceivably get back to average that way?

That might make sense if I thought the field was in three spades. But it's hard to see three spades being a popular contract. Either you make a game try and get to game or you don't. So the contract will be either two spades or four at most tables. I can neither beat nor tie anyone in two spades, so I'm competing only against other pairs in four. That means I should simply take my percentage play. I play a spade to the ace and back to the king. They split. Down one.

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

East's heart ace at trick two was a poor play. If I had three hearts and a stiff diamond, West would have to unblock his heart king to beat me. A better play would be to shift to the heart three (showing an odd number of hearts). West would now know what to do.

This works if West has two or three hearts, but what if he has four? How will he know whether West's odd number of hearts is five (in which case he must cash two diamonds) or three (in which case he must cash two hearts)? He will know because East shouldn't lead low with three hearts. He should cash an honor, allowing West to play a count card. Then he will know himself what tricks to cash. An interesting wrinkle: From ace-queen third, East should lead the queen. If West has king sixth, he knows only one heart is cashing, so he can overtake and play diamonds.

The defense must cater to three critical cases: declarer's holding a singleton heart, a singleton diamond, or two red doubletons. Since signals are binary, you can't cater to three cases by signaling alone. (That's why it was important for declarer to play the diamond four at trick one.) But you can often cater to three cases by combining signaling with logic.

I get 4% for this result, which seems a bit harsh for bidding a decent game. Only two other players reached game, and they both made it. One raised two spades to four and got a club lead. Yes, my auction was revealing. But if I was afraid to invite for fear of tipping off the defense, I think I would prefer passing to blasting a game.

The other player bid two notrump, then three notrump over three clubs and also got a club lead. Given the robots' preference for passive leads against notrump, there is some merit to this decision. I did briefly consider it but decided it was too much of a gamble.

Free Weekly Instant Tournament - October 7 - Board 7

Board 7
Both vulnerable

♠ --  ♥ 9 3  ♦ A K Q J 7 6 5  ♣ K Q 10 4

I have seven tricks in diamonds and a trick and a half plus in clubs--just shy of nine tricks in total. One diamond followed by three diamonds shows seven and a half to eight tricks, so this hand is too good for that sequence. It isn't worth a game force, however. So my plan is to start with one diamond and rebid two clubs.

I open with one diamond, LHO passes, partner bids one heart, and RHO doubles. Two clubs may not be my best choice anymore. LHO is probably about to bid some large number of spades, so I want to get as much information across as possible with this call. Perhaps an underbid of three diamonds is best now. At least it lets partner know that I have excellent diamonds and a good hand, a message two clubs would not convey.

One problem with three diamonds is that it both understates my offense and overstates my defense. If I bid three diamonds and partner doubles three spades, I would have to pull. The whole point of a limit bid is to leave further decisions to partner. If I'm not willing to do that, then perhaps the limit bid is the wrong choice.

Another problem with three diamonds is that it forces the opponents to act at a high level. I won't be sure whether they are happy to act at that level or whether they are stretching because they are under pressure. Often that's a good thing. If you are want the opponents to make the last guess and are willing to make them live with their decision, then by all means take as much bidding room away from them as you can. But if you might be making the last guess yourself, you want as much information as possible. With this hand, I may find myself considering a sacrifice over four spades. So I want to give the opponents room to tell me what they think they can make.

Perhaps, then, two clubs is the right bid after all. It avoids surrendering captaincy, and it keeps the auction low.

I bid two clubs, LHO bids two spades, and there are two passes to me. I'm glad I chose two clubs. Had I bid three diamonds, LHO probably would have bid three spades. This way, I know West doesn't have a hand worth jumping to three spades voluntarily. If the opponents bid game now, I'm not sacrificing.

I bid three diamonds, LHO bids three spades. Two passes to me. I might make four diamonds opposite as little as the jack of clubs, so I have to compete. I bid four diamonds and buy it. West leads the diamond three.

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

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

Partner's hand isn't much help. I'm probably going to lose two hearts and three clubs for down two.

I play the nine of diamonds from dummy, and East plays the four. Well! Now I have a dummy entry to hook against the club jack. If East is smart enough to duck his diamond ten holding ace-empty fifth of clubs, he's entitled to his good result. I underplay the nine and lead the deuce of clubs--six--ten--ace. West shifts to the deuce of spades--ten--jack--diamond six.

The opponents can't possibly mis-discard, so I will have to lose a club trick in the end. I play it out anyway just in case. I run all the diamonds but one, then exit with a heart. Nothing good happens, so I finish down one.

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

Three spades should go down. (Three rounds of diamonds, partner pitching both his clubs. Now declarer doesn't have the entries to pick up the spade suit.) But, of course, almost everyone competed to at least four diamonds. Some reached five diamonds. And some in four failed to take advantage of the favorable opening lead and went down two. Minus 100 was worth 82%,

Free Weekly Instant Tournament - September 30 - Board 6

Board 6
Opponents vulnerable

♠ Q J  ♥ A K 8 3  ♦ A 10 3  ♣ A 10 8 3

RHO passes. I have a balanced hand with 18 HCP, so I open with one club, intending to rebid two notrump.

LHO overcalls with one diamond, partner bids one spade, and RHO raises to two diamonds.

Two notrump, with only a single diamond stopper, looks less appealing now than it did when the auction started. If partner has no help in diamonds, I may need to take nine tricks off the top in order to make game in notrump. On the other hand, as little as jack doubleton of diamonds gives me an extra stopper. And there is still room to investigate other strains. Besides, what else can I do? I can hardly pass. And bidding two hearts suggests more shape. So I bid two notrump.

Partner bids three diamonds, which the tooltip says promises a fifth spade. I show my four-card heart suit, and partner bids three notrump.

With three spades, I would usually make a support double over two diamonds. If I chose to bid two notrump instead, my hand should have a heavy notrump orientation. So partner needn't check back for spade support just because he has five spades. If he has a flat hand with help in diamonds, he should simply raise to three notrump. This auction suggests he has some reason to believe notrump is the wrong strain.

If partner thinks notrump might be the wrong strain, I'm inclined to agree. Queen-jack doubleton is decent support opposite for a five-card suit, and my honor dispersion is perfect for spades: fast tricks outside the spade suit, slow tricks in the spade suit. Opposite a reliable partner, it is clear to correct to four spades. It is less clear opposite a robot, whose judgment isn't always reliable. But the opponents did bid and raise diamonds. Unless partner can contribute a second stopper, I suspect we can take more tricks in spades than we can in notrump.

I bid four spades, ending the auction. West leads the six of diamonds.

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

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

Wow! Partner drove to game with this hand? I'm touched by his confidence. At least I was right to correct to four spades. Partner has no side entries, so on most layouts the opponents could hold me to two spade tricks in notrump.

To have any chance, I'm going to need to run spades. Five spade tricks and four cashing tricks on the side will bring me to nine. I have a shot at a tenth trick in either clubs or hearts.

I see no reason to win this trick. I might as well duck to cut the opponents' communications. I play low from dummy, East wins with the queen, and I play the five.

East shifts to the four of hearts--five--nine--ace. Perhaps East didn't continue diamonds from the king for fear I had the jack. Still, if he wanted to make a passive shift, he could have led a trump. The heart shift suggests he is afraid the club suit is a threat, and he needs to go after heart tricks before I can take a pitch.

I lead the spade queen--five--deuce--nine. I continue with the jack, and East covers with the king. I take the ace, and West follows with the six. Obviously spades are three-three. West would not have dropped the nine from nine fourth, and East would not have covered with king fourth.

What is my plan now? My best chance for a tenth trick is in the club suit. I can lead a club to the eight, playing West for the nine and one of the high honors. If that fails, I still have the option of playing for three-three clubs or for someone to have king or queen doubleton. Of course that would require the hand with the club entry to have short hearts, else the defense could establish a heart trick and cash it upon winning the second club trick.

What should I pitch from dummy on the third round of spades? Obviously I must keep a long club. I would like to keep a long heart as well to give myself an extra chance. Say, for example, I lead a club the the eight and queen and East continues hearts. My main chance is to hook West for the club king. But I can give myself an extra chance by winning the heart and continuing the suit. If hearts are three-three, I don't need the club finesse anymore.

I draw a third round of trumps, pitching a diamond from dummy. As expected, everyone follows. This is the position.

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

I now lead the club deuce--six--eight--nine.

That's disappointing. If East plays another heart, I have a decision to make. Do I play for three-three hearts? Or do I go after a club trick, hoping the opponents can't cash their heart? Fortunately, East doesn't play a heart. He shifts to the four of diamonds.

I win with dummy's ace and cash the club ace. West drops the king, so I claim. Making four.

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

Plus 420 is worth 100%.  A fair number of players were down in three notrump. But, surprisingly, half the field played a partscore. They opened with one notrump and their partners transferred to two spades.

Presumably those who opened with one notrump counted the queen-jack of spades as only two HCP. I have some sympathy for this decision, since I am not a fan of slavishly counting high-card points. But you do have two tens to compensate. Besides, honors in short suits are not so bad in notrump as they are in a suit contract. While I might count queen-jack doubleton as only two points in an unbalanced hand, I count them at full value for determining my notrump range.

In retrospect, I'm I think my diamond pitch on the third round of spades was a mistake. Since the club finesse lost to the nine, it made no difference. But suppose it loses to an honor? The layout might be something like this:

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

If I play a club to the eight and queen and get a heart continuation, I can still make it double dummy. But if I play as I said I would (exit with a heart, playing for hearts to break or for the club king to be onside), I go down. Had I kept a diamond in dummy, I could ruff a diamond back to my hand to take the club finesse. Even though the club finesse loses, I still make my contract because East is out of hearts.

I think the above scenario is more likely than three-three hearts. A small doubleton makes for a more attractive heart shift than any three-card holding. So I should have pitched a heart on the third trump and held on to my entry.

Note, by the way, that if East had king-queen-nine of clubs in the above layout, he should win the club eight with an honor, not with the nine. Winning with the nine gives me no chance to go wrong.