Free Weekly Instant Tournament - May 30 - Board 3

Board 3
Opponents vulnerable

♠ J 6 2  ♥ K Q 4 3  ♦ 8  ♣ A K J 7 6

I open with one club in first seat. LHO doubles, partner passes, and RHO bids two clubs.

Partner can't bid at the one level, and the opponents are cue-bidding. I'm out of the auction. Bidding two hearts would be foolish. We aren't going to outbid them, and showing my shape will help declarer more than partner in whatever contract they end up in.

What about doubling? Double should be take-out of spades, but the robots don't play that way. They play it shows good clubs. Given that, there is something to said for doubling to help partner with the opening lead. But I've already bid clubs, so partner will be inclined to lead them anyway. And doubling gives West two options he doesn't have if I pass, so it may make the opponents' auction easier. There is probably more to lose than to gain by doubling.

I pass. LHO bids two diamonds, RHO bids two heart, and LHO jumps to three spades. The auction so far is:

West	North	East	South
Phillip	Robot	Robot	Robot
1 ♣	Double	Pass	2 ♣
Pass	2 ♦	Pass	2 ♥
Pass	3 ♠

What should three spades mean?

Advancer's cue-bid after a take-out double creates a force until a fit is found. So two diamonds and two hearts were both forcing. If LHO bids two spades now, that would be forcing as well. So there is no need to jump to make a forcing bid in spades. Three hearts, however, would not be forcing. Once a suit has been bid and raised, the force is over. If the doubler wants to ensure reaching game, he must bid four hearts. That means he has no way to make a forcing bid in hearts should he hold a hand too good to bid four hearts. Should three spades show that hand? Should it be what some call an "out-of-the-blue cue-bid"?

Why not bid three clubs with that hand? Because cue-bidding the opponent's suit after a take-out double shows doubt about strain. A typical hand for three clubs at this point would be a 3-3-5-2 without a club stopper. So three spades as an artificial forcing heart raise makes a lot of sense.

Still, it's one thing for an interpretation to make a lot of sense. It's another for you and your partner to be on the same wavelength in an undiscussed auction. Without a clear understanding, I can't imagine throwing this auction at partner. 

In any event, I'm pretty sure a forcing heart raise is not what my robot opponent intends. Let's see what the tooltip says. It says, "6+ spades, 3+ hearts, 4+ diamonds, and 2- clubs," leaving open the possibility of having 15 cards. I don't know how he can have six spades when he bid two diamonds. Perhaps he thinks he's supposed to bid up the line regardless of suit length.

I'll find out soon enough what he has. Partner passes, RHO bids four hearts and buys it. I lead the king of clubs.

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

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

North lost his mind. Several times. The take-out double was insane. When you have two suits, you start bidding them. Double accomplishes nothing.

Two diamonds was also insane. It does appear North thought he was supposed to bid his suits up-the-line. Even so, any time you double offshape with an independent suit, you must jump at your next turn to advise partner you did something foolish. Unless you jump, partner is entitled to assume you have three-card support for his suit. So the proper continuation over two clubs is three spades.

North did try to catch up by bidding three spades at his next turn, but South didn't get the message. He still assumed his partner had heart support.

North's final action, passing four hearts, was suicide. Or perhaps fratricide, since partner has to play it. True, it's going to be impossible to get intelligent cooperation from partner now. But simply blasting six spades has to be better than passing four hearts. It might make. And even if it doesn't, it's going down less than four hearts.

What is South's hand? He should have five or six hearts. But he didn't open with a weak two bid. And he might have bid four hearts earlier with six of them. So I'll assume he has five hearts and around 10 HCP, leaving partner with around 3 HCP.

Partner plays the ten on my king; declarer follows with the three. According to the BBO system notes, the robots might encourage at trick one with an ace, king, or queen but won't encourage with a doubleton. So apparently two of partners HCP are the queen of clubs. If declarer is 2-5-2-4, I can underlead to partner's club queen, win the club return, and let partner pitch a spade on the fourth club. Then I can give him a spade ruff.  Or I can play declarer for 1-5-3-4. If he has that hand, I can play five rounds of clubs, letting partner pitch two spades, then give him a ruff when I win a trump trick.

No need to worry yet about which hand to play for. First let's see if declarer has four clubs. I lead the six of clubs. Declarer pitches the three of spades from dummy. Partner wins with the queen, and declarer follows with the four. Partner returns the five of clubs--eight--jack--four of spades from dummy.

I cash the club ace. Dummy pitches the diamond six, and partner pitches the seven of spades.

OK. Which layout do I play for? If that was a stiff spade, I can give partner two ruffs by leading a spade now. But if I lead a spade and partner follows, I've allowed declarer to score a spade trick he wasn't entitled to.

I don't see any way to resolve this other than play the odds. Spades are just as likely to be two-one as to be one-two. But if declarer has two spades, he has a doubleton diamond. With seven diamonds missing, declarer is more likely to have three than two. Much more likely if I assume declarer has the king-queen of diamonds, as seems likely. There is only one way for him to hold king-queen tight and seven ways to hold king-queen third.

I go with the odds and play a fifth club. Dummy pitches the eight of spades, and partner pitches the spade ten. Yay! I got it right.

Declarer ruffs with the five of hearts and plays a spade to dummy's ace. What's that all about? Why isn't he drawing trumps? Perhaps he's trying to score trump tricks by ruffing spades in his hand. Partner beats him to it. He ruffs with the six of hearts. Wait. Who has the deuce? Why did neither of them ruff with the deuce?

Partner leads the seven of diamonds--three--eight--ten. Declarer plays a diamond back to his king and I ruff with the three. We are down to his position with me on lead:

	NORTH Robot ♠ K Q 9 ♥ -- ♦ A 4 ♣ --
WEST Phillip ♠ J 6 ♥ K Q 4 ♦ -- ♣ --

Declarer presumably has four hearts and one diamond, leaving partner with three hearts and two diamonds.

Declarer will score the heart ace and whatever low hearts we allow him score with spade ruffs. If partner's trumps are good enough, we might hold him to one ruff. Let's say partner has 109x of trumps. When I lead a spade, he can ruff with the nine, forcing declarer's jack. When declarer plays a diamond, I ruff and play another spade. Now partner can ruff with the ten, forcing declarer's ace. My king and queen are now high.

I lead the six of spades. Partner ruffs with the eight and declarer overruffs with the ten. If partner has the heart nine, then the position must be as follows, with declarer on lead:

	NORTH Robot ♠ K Q ♥ -- ♦ 4 ♣ --
WEST Phillip ♠ J ♥ K Q 4 ♦ -- ♣ --		EAST Robot ♠ -- ♥ 9 x ♦ J x ♣ --
	SOUTH Robot ♠ -- ♥ A J 7 ♦ Q ♣ --

We can't stop declarer from scoring two more tricks.

Declarer surprises me by leading the jack of hearts. I take the queen, and partner follows with the nine. The nine? If partner is playing the nine, his last heart must be the seven, so the diagram above is wrong. I don't know why partner didn't ruff with the seven rather than the eight on the previous round. Lowest from equals when playing third hand, partner. In any event, if lead a spade, partner can ruff with the seven, forcing declarer's ace, and I'll take the last two tricks. 

I lead the jack of spades. Partner ruffs with the seven, and declarer pitches the jack of diamonds. The jack? OK. My construction was wrong again. Partner shifts to the five of diamonds. Declarer plays the queen and I ruff it. Declarer has the trump ace left. Down six.

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

Declarer had only four hearts? That never occurred to me. So North wasn't the only one who lost his mind. I'm not sure what South should bid over three spades, but I'm pretty sure his bid should have the word "diamonds" in it.

In the end position above, we were actually down to,

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

Declarer should have exited with the queen of diamonds instead of the jack of hearts. I can still beat it six by ruffing and leading the heart king. But if I carelessly return my last spade, declarer will score a ruff with his jack of hearts for down five. I should be able to work it out. But who knows? The hand wasn't making any sense. It's easy to make a mistake when you don't know what's going on.

Plus 600 when the opponents are cold for two slams can't be a bad result. In fact it's worth 100%. Most of the field was defending four hearts, but we were the only pair who took all our tricks.

No one reached six spades, but a few pairs did reach six diamonds when West decided to act at his second turn. Hats off to the guy who salvaged the board by doubling five diamonds. Going minus 950 instead of 1370 was worth 43%. Lowenthal (who invented that maneuver in case you didn't know) would have been proud.

Free Weekly Instant Tournament - May 30 - Board 2

Board 2
Our side vulnerable

♠ 9 3  ♥ A Q 9 8  ♦ A 10  ♣ A K 10 9 4

RHO passes.

2-4-2-5 is an awkward pattern with 15 or 16 HCP. Take away the heart queen, and I would open with one notrump, since if I open with one club, I would have no good rebid after a one-spade response. But with 17 HCP, I have enough to reverse, so there is no reason to treat this hand as balanced. And evaluating this hand as 17 HCP doesn't even do it justice. Prime values. Good spots. One notrump is not only a misbid but an underbid as well.

I open with one club and partner responds one heart. I bid four hearts and everyone passes. RHO leads the four of diamonds.

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

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

This is a rather poor contract. Unless West has led from the diamond king, I have three fast losers and no easy way to get to my hand to take the heart finesse. In addition to managing a successful heart finesse, I need to establish the clubs. And I need to avoid a four-one heart break, since the defense can tap dummy to promote a heart trick if West has king fourth. 

Perhaps it's not so surprising this is a bad contract. Partner doesn't have much. Some would pass one club, though I agree with partner's decision to respond.

I play low from dummy. East takes the king. It's good technique to conceal the deuce. If the four is fourth best, playing the deuce lets East know that his partner doesn't have five. So I play the diamond eight.

East shifts to the deuce of spades. It might be right to play the queen just in case East is being tricky. But I doubt my robot opponent is leading low from ace-king. And if trumps break badly, retaining a spade stopper might prove useful. So I play low.

West wins with the ten and cashes the ace. East follows with the seven. West continues with the nine of diamonds to dummy's ace. East plays the jack. Here is the position, with the lead in dummy:

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

West surely would have tapped dummy if he had king fourth of hearts. So if I can reach my hand and the heart king is onside, I'll make this. I'll ruff a club high and hope West follows. If clubs are three-three, I can lead a heart honor for a finesse. If West has four clubs, I can lead a low heart to the eight, ruff another club, and repeat the finesse. If East has four clubs, I'm down. Or maybe not. If West doesn't overruff, I can try to drop a stiff king of hearts offside.

I play ace and king of clubs and ruff a club with the seven. They're three-three. I lead the jack of hearts and West covers. Making four. Nice one-heart bid, partner.

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

Plus 620 is worth 86%, since not everyone got to game. Some opened with one notrump and played it there. As I said before, one notrump is an underbid. It's true we got to a poor game and got lucky. But partner had a marginal response. If his hand were a tad better, we would be getting to a good game while those who opened with one notrump would still be playing it there.

Others missed game by raising one heart to three. That's a clear underbid. 19 support points. Or, if you prefer, four and half honor tricks. Or five losers. I can't think of a method that values this hand as less than a raise to game.

If you don't like counting points, honor tricks, or losers, you can always apply an extended version of Culbertson's Rule. The original Culbertson's Rule is for slam bidding: 

If partner's perfect minimum makes slam cold with normal breaks, then you are worth an invitation. 

The idea is that, if partner has a maximum and accepts, perhaps his maximum will subsume this perfect minimum. And, even if partner has the wrong cards, slam may still be a favorite, since it was cold opposite the hand you envisioned.

While the rule was meant for slam bidding, it's a reasonable rule for game bidding at matchpoints as well (though it's too conservative for vulnerable games at IMPs). The problem is that the rule tells you when you have invitation, not when you have a game or slam drive. So I recommend this extension:

If partner's perfect minimum makes you cold for an overtrick on normal breaks, you should drive to game (or slam). 

Partner's perfect minimum here would be:

♠ x x x  ♥ K x x x  ♦ x x x  ♣ Q J x.

Opposite that hand, you are cold for five against normal breaks. So you are worth a four-heart bid.

Free Weekly Instant Tournament - May 30 - Board 1

Board 1
Neither side vulnerable

♠ J 4 2  ♥ A 10 8  ♦ A 6 5  ♣ K J 10 6

Two passes to me. I open with one club, and LHO overcalls with one diamond. Partner bids one spade, and RHO bids two hearts.

I double, showing three-card spade support. RHO bids three diamonds--pass--pass back to me. I have shown my hand; I have nothing further to say. I pass, and partner leads the king of spades.

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

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

The spade ace is declarer's last dummy entry. If he has the ace-queen of clubs, he will probably use it to take a club finesse. 

He does. He wins with the spade ace. I encourage with the four, and declarer plays the five. He then leads the nine of clubs from dummy. Double-dummy, I must cover this, since declarer could let the nine ride. But if he has AQ7x, covering might expose me to some kind of end position. Perhaps that's not possible. But there is no need for me to figure that out. Declarer isn't looking at my hand, so he isn't letting the nine ride. From a practical standpoint, there is no reason to cover. I play the six, and declarer wins with the queen. Partner plays the seven.

I expect declarer to play ace and ruff a club. But he plays the deuce of diamonds to the king, partner following with the seven. Why didn't he ruff a club? Does he have a doubleton? He has at most two spades, since partner has at least four. He has at most two hearts, since he didn't raise them. Unless he's 2-2-7-2, he has a club to ruff. Perhaps he knows the ruff will cost a trump trick. If he has QJ10xxx or QJ98xx, a ruff rates either to gain or to break even. So his diamonds must be worse than that.

Should I win this trick? It's often right to duck a stiff honor, since it gives declarer communication problems. Say declarer has this hand, for example:

♠ x  ♥ Q x  ♦ Q J x x x x  ♣ A Q x x

If I win, declarer has an easy nine tricks. If I duck, declarer may be afraid to ruff a spade to his hand for fear of tapping himself out. Instead, he may lead a heart. Then I can hop with the ace and lead the club king. Declarer will win and lead the queen of diamonds. Now I can take my ace, cash clubs, allowing partner to pitch a heart, then give partner a heart ruff, holding declarer to eight tricks.

Ducking does have a risk. If declarer has, say, 

♠ x x  ♥ J x  ♦ Q J x x x x  ♣ A Q x

he may continue with the five of hearts from dummy. Now my plan of hopping with the ace will not be a success.

Since he can place me with the heart ace for my opening bid, that's not a hard play from him to find. Still, that hand looks more like a two-diamond overcall than a one-diamond overcall. So I take my chances and duck.

Declarer continues with a low heart from dummy. I hop with the ace--deuce--six. I shift to the king of clubs--ace--five--eight.

Declarer leads the queen of diamonds, pitching dummy's seven of hearts. I take the ace, reaching this position with me on lead:

	NORTH Robot ♠ 8 6 3 ♥ K 9 4 3 ♦ -- ♣ --
		EAST Phillip ♠ J 2 ♥ 10 8 ♦ 6 ♣ J 10

I cash two clubs. Unfortunately, partner follows to both of them, declarer pitching the seven of spades on the last club. Declarer was 2-2-6-3, so I can't give partner a ruff. Declarer has the rest. Making three.

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

Minus 110 is worth 79%.

The support double turned out to be important. Some chose to pass two hearts, either because they didn't know they were playing support doubles or because they didn't wish to make one with a "4333" shape. When they pass, South passes also, and partner competes with three clubs. Now, knowing his partner has tolerance for hearts, North competes to three hearts, scoring 140.

South should have passed even after my support double. Perhaps he was anticipating that the auction would go two spades--pass--pass back to him and felt that, if he was going to balance with three diamonds, he might as well bid it now to take away our bidding room.

Often it's a good idea to bid immediately to the level you're willing to compete to. But I'm not so sure I would want to compete to three diamonds over two spades. If I did, surely it would be better to pass now, showing heart tolerance, so that partner can correct back to hearts if he has a singleton diamond. 

In retrospect, I'm not sure I did the right thing in ducking the diamond king. It's hard to say. Partner's seven of clubs at trick two should be count. If I trust him, declarer can't be 1-2-6-4, so there is nothing to gain by ducking the diamond. Even if I think it's unlikely declarer has jack doubleton of hearts and will lead a low heart from dummy, there is no need to take that risk if I'm not gaining anything. On the other hand, the robots don't always give accurate count when following suit. So I'm not sure I should trust the seven. Defending with robots is difficult.

Challenge Match - Jazlene vs. Phillip - Board 16

I'm up 12 imps going into the last board of the match.

Board 16
Opponents vulnerable

♠ A J  ♥ A 5 3  ♦ A Q 5  ♣ Q 9 5 4 3

Three passes to me. I open with one notrump. Partner bids two clubs, Stayman. I bid two diamonds. Partner bids two notrump and I go on to three. West leads the deuce of spades.

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

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

If East plays a spade honor on this trick, I don't like my chances of making this. I could try to drop a stiff king of clubs on my left. Or lead the queen, hoping to find a stiff jack on my right. Or I could hope both red-suit finesses are on. If I win the spade and run the heart suit, then lead a diamond to the queen, I'm down to this position:

(A)

	NORTH Robot ♠ 10 ♥ -- ♦ J 8 ♣ A 10 8 7
	SOUTH Phillip ♠ J ♥ -- ♦ A 5 ♣ Q 9 5 4

I've taken six tricks. The two aces make eight, so I need to find one more. East, who presumably began with five spades, must hold all four of his remaining spades, else I can afford to concede a club trick. East must also hold two diamonds, else I can drop his king. So he was squeezed down to a stiff club. If it's the stiff jack or king and I can guess which, I'm home.

And there's a fourth option. I could play West for honor-nine-seven-deuce of spades, in which case the suit is blocked and I can try to set up clubs. 

I'm not sure yet which line I'll go for. I play the eight of spades from dummy, and East plays the nine. This deal just got easier. All I have to do now is avoid two club losers.

In isolation, the right way to play this suit is to play ace and another. The alternative of taking two finesses is correct with eight clubs but not with nine. Taking two finesses loses to king-jack tight or third offside. Ace and another loses to king-jack third or fourth offside. The king-jack thirds cancel out, and king-jack tight is more likely than king-jack fourth.

We aren't in isolation, however. West led the deuce of spades. If we assume he would have led a five-card suit if he had one, then the only way he can hold a singleton club is if he is specifically 4-4-4-1. That makes king-jack third on my right unlikely and tips the scale in favor of the double finesse. The assumption that West would have led a five-card suit if he had one is less certain against a robot than against a human, since robots like passive leads. But, given West chose to lead aggressively, I think it's safe to assume he would have led a five-card suit in preference to king-queen fourth.

Accordingly, I lead the three of clubs. No finesse is necessary, since West plays the jack. I win with dummy's ace as East plays the six. I continue with the seven of clubs. East pitches the six of diamonds and West wins with the king. West split with king-jack third? That was a poor play. I was intending to finesse, but he didn't know that. Splitting takes my guess away. Plus, for all he knows his partner had a stiff queen and splitting costs a trick by force.

West continues with the king of spades. East plays the six, and I take the ace.

West apparently began with king-queen fourth of spades and East with nine fifth. Since West has 9 HCP already and passed in first seat, the diamond king must be on my right.

I lead the nine of clubs and play low from dummy. East pitches the nine of hearts. The robots pitch count cards, so East appears to be either 5-2-5-1 or 5-4-3-1. The former seems more likely, since I doubt East would pitch down to a doubleton king of diamonds at his first opportunity.

When I cash the club queen, West pitches the three of diamonds; East, the diamond seven. That's a bit unexpected. If East is true to form and pitched his lowest diamond from five at his first discard, he must have K10976, leaving West with 43 doubleton, which means West pitched low from his doubleton. While the robots like to pitch count cards from length, I have noticed that they don't always pitch high from doubletons, especially from equals. So I'll assume I'm still right about the shape. On the last club, West pitches the four of spades; East, the deuce of hearts. If I've read the deal correctly, this should be the position:

(B)

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

East will show out when I cash the heart ace, and I can take the rest of the tricks.

I cash the ace of hearts--eight--four--five of spades. Now a heart to the jack on which East pitches the three of spades I lead the jack of diamonds. East covers with the king, but I was finessing anyway. I take the ace and claim. Making six.

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

Whoa! I was wrong about the spade queen. East played the nine at trick one holding queen-nine, apparently playing me for king-jack third. Had he played the queen, I would have a problem. As it happens, none of the four lines I contemplated works. But which one is right one?

It's hard to calculate the chance that West has a stiff club. But, given the opening lead, it's small. Let's assume it's zero for now to make our calculations easier. We can come back and revisit that assumption if necessary.

That means Line 1 (playing West for a stiff king) is out. Line 2 (playing East for a stiff jack) works in one out of four cases when the suit is 3-1 and in zero out of six cases when the suit is 2-2. That's 10% of the time. Line 3 (the squeeze) needs two finesses plus East having whichever club honor I choose to play him for. That's essentially three finesses, or 12.5% of the time.

What about Line 4 (playing for the suit to block)? There are six critical spot cards, so fifteen ways for West to hold two of them for his middle spot cards. That means he will hold specifically K972 one time in fifteen. And even if the suit is blocked, I still have to be able to establish a club trick, so the line is worse than that.

The squeeze is the winner in our rough calculation. What happens if we revisit our assumption that West can't have a stiff club? That assumption overstated the odds of dropping the stiff jack but had no bearing on the squeeze. So the squeeze is still the winner.

[Jazlene is good at these calculations, so I had her check them over before I published. She points out that my one-in-fifteen calculation for the spade suit's being blocked assumes West has the spade king. In fact, I don't know that he does. He's two to one to have the spade king by restricted choice, but East might have both honors. So Line 4, which was already in last place, falls even further behind.

She also pointed out that my statement after Diagram A, "So he was squeezed down to a stiff club," is incorrect. If East began with a doubleton king of diamonds, he wasn't squeezed. He's now down to a stiff king of diamonds and two clubs. So I should try to drop the diamond king before making my guess in clubs.]

Jazlene took 11 tricks on this board, so I pick up another imp, winning the match by 13.  In her post mortem, she also pointed out that ace and another club was right in isolation but concluded that, because of the opening lead, it was right to take two finesses. Her reasoning was slightly different from mine. You can hear her argument at JazPlaysBridge.

It was a tight match. 13 of the 16 boards were pushes or small swings. Jazlene bid more aggressively than I did on two deals. She lost 5 imps on one and picked up 12 on the other. Both results were just. She overbid on the first board, and I underbid on the second. I regained those 7 imps with a series of 1- and 2-imp wins, bringing the match back to even. The match hinged on board ten, where we each faced a guess on an auction made awkward by the robots' methods. I guessed right and picked up 13 imps, the margin of victory. On a different layout, her guess would have been right. So the board--hence the match--could easily have gone the other way.

Next week, I return to the Free Weekly Instant Tournament format. If you want to compare results, be sure to play in this week's tournament on BBO. You have until Thursday night.