Zenith Daylong - Oct 14, 2021 - Board 8

Board 8
Neither vulnerable

♠ A K 6 3  ♥ 9 4  ♦ K Q 9 5  ♣ Q 9 7

Partner opens with one notrump. With 29 HCP, there is often no advantage to playing in a four-four major-suit fit. The cards you can ruff may be winners anyway. So I'm going to raise to three notrump without looking for the four-four spade fit. This has two ways to win: it might be the right contract when partner has four spades, and it might make the defense harder when he doesn't, since the opponents will have less information about declarer's shape. 

I bid three notrump. Everyone passes, and West leads the heart deuce.

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

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

I have five tricks in the majors. If I have four diamond tricks, that makes nine--ten after knocking out the club ace. What are my chances for eleven? One possibility is to take four heart tricks. I have two ways to attempt to do that. If West has led from jack-ten, I can hop with dummy's nine and win the trick. If he has led from eight third, I can play low, forcing an honor, then finesse against the other honor. 

What are my chances for an eleventh trick if I don't have four heart tricks? If either hand has four hearts and the club ace, I have a strip squeeze. I lead a club through the ace, then cash four diamonds, coming down to seven cards. The targeted hand has to keep two clubs (else I can duck out the ace) and three hearts (else my seven is good), so he must come down to a doubleton spade. Now I cash the ace and king of spades and toss him in with a heart to score my other club honor. 

That possibility solves my trick-one problem. If I play the nine and it's covered, I can go for the endplay. If I play low, I may lose that opportunity. Say East plays an honor at trick one and my later finesse loses. Now I no longer have a heart loser to throw an opponent in with. So playing the nine at trick one gives me two chances while playing low gives me only one.

I play the nine, and East covers with the jack, in principle denying the ten. It's usually right to conceal the card immediately above the one third hand plays, since that is a card that either opponent might hold from his partner's perspective. So I win with the king.

Which hand should I target for the endplay? The robots like leading from three-card suits against notrump, but ten third isn't especially appealing. Given West has the heart ten, I think it's likely he has the four-card suit, so I'll try leading clubs through him. I play the club five--ten--queen--three. He wouldn't insert the ten gratuitously. So either he has the jack also or he has ace-ten doubleton.

Now I can run the diamonds and squeeze West. All I have to do is decide which opponent is more apt to have a stiff diamond, so I can cash my honors in the right order to pick up jack fourth. As a general rule, when someone leads a four-card suit against notrump and you need to guard against a side-suit singleton, it's right to guard against the singleton on your right. That's because the only way the opening leader can have it is if he is 4-4-1-4 or if he has a five-card suit he chose not to lead. Against traditional opening leaders, playing East for the singleton diamond is clear. Robots are less inclined to lead their longest suit, so that changes the odds somewhat. But I doubt it changes them enough actually to reverse the normal play. Accordingly, I cash the diamond king--eight--deuce--four. Now the five of diamonds--seven--ace. West pitches the eight of clubs. 

Oops. And things were going so well. Eleven tricks is now out of the question. I still have nine tricks. Is there any way to find a tenth? I need to start by ducking a spade--both to correct the count for a possible squeeze and to isolate the spade stopper if spades are four-three. If East wins the spade and plays a club, I won't be happy. But why should he do that? Clubs is the suit I was attacking. If I duck a spade to him, he will probably continue hearts, his partner's suit.

I play the spade seven--four--three--nine. East, as expected, shifts to the five of hearts. I win with the ace as West plays the three. This is the current position:

	NORTH Phillip ♠ A K 6 ♥ -- ♦ Q 9 ♣ 9 7
	SOUTH Robot ♠ 8 ♥ Q 7 ♦ 10 3 ♣ K 6

To take another trick, I need to cash my winners and throw West in to lead away from his ace of clubs. Unfortunately, I don't have the communication to throw him in in hearts. I started out hoping West began with four hearts. Now I have to hope he began with three--along with at least four spades. I can cash the queen of hearts, then lead to dummy's queen of diamonds. West will be down to five black cards. If he has two spades, dummy's spades are good. If he has three spades, I can toss him in with a spade to lead away from his club ace. And if he has four spades, the club ace is singleton, so I can duck a club.

I cash the heart queen. I know West has the heart ten left. If I don't see it on this trick, I have no chance left. I do. West follows with the ten. I pitch a diamond from dummy and East follows with the heart six. I play a diamond to dummy's queen, and West discards the club eight. 

Dummy's club nine is a fortunate card. It prevents West from dropping the club jack from ace-jack third, pretending to stiff his ace. I know he has ace-jack of clubs left. If he has the long spade, I have him. I cash the ace and king of spades and lead a third one. Unfortunately, it's East who wins the trick, as West pitches the heart eight. He was just toying with me when he dropped the ten. East cashes his diamond jack and leads a club to his partner's ace. Making three. 

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

9%. My three notrump bid backfired. If I bid two clubs and let partner show his four-card heart suit, it steers West off the heart lead. He chooses the club jack instead. Now I can make four--or five if I pick up the diamonds--without the bother of an endplay.

But the primary blame for this result goes to my play of the diamond suit. If I play diamonds the other way and make five, I get 90%. As I think about it more, not only am I pretty sure I made the wrong play against robots, but I'm beginning to believe my statement, "Against traditional opening leaders, playing East for the singleton is clear" was wrong as well. One thing I didn't consider at the time was that I know something about West's club honors. I know he has specifically ace-ten doubleton of clubs or some holding headed by ace-jack-ten.

For the sake of argument, let's take it as given that West won't have a five-card suit lurking. Let's also assume East doesn't have six spades. (He might have opened a weak two-bid if he did. And a six-one spade break is unlikely even without that consideration.) So West's possible patterns are 4414, 2443, or 3442.  If those patterns were equally likely, the odds would be two to one in favor of playing East for the stiff diamond.

Often similar patterns are close enough to being equally likely that assuming they are is sufficient for a rough, at-the-table calculation. But this time our constraints in the club suit make a big difference. There is only one way for West to hold a doubleton club or a tripleton club. But, a priori, there are four ways for him to hold four clubs, since he can hold any one of four small cards along with his ace-jack-ten. So 4414 is roughly four times as likely as either 2443 or 3442, making the odds roughly two to one in favor of West's having the stiff diamond.

We could make a more accurate calculation by taking into account the spade distribution. But since it isn't close, there is no need to do so. Even against traditional opening leaders, West is the overwhelming favorite to hold a stiff diamond. And against robots, who might easily have a five-card black suit, he is an even bigger favorite. I played by rote and didn't stop to consider that the general rule might not fit this specific problem. It was a costly error.

At least I judged correctly to risk my contract by ducking a spade. East could now beat me by shifting to a club. But going down isn't much worse than making only three. Having misplayed diamonds, I had to go all out to try to find another trick