Challenge Match - Jazlene vs. Phillip - Board 11

After the last board, I'm back in the lead. I'm up 11 imps going into

Board 11
Both sides vulnerable

♠ 9 6 5 4  ♥ 7 4  ♦ A K J 3  ♣ K Q 8

I open with one diamond, partner bids one notrump, and RHO overcalls with two hearts. I know they have an eight-card heart fit, so I don't want to sell out. Ed Manfield suggested that double here by either side should show precisely two hearts. That way, we won't sell out at the two-level when they have an eight card fit and we will sell out if each of us has three hearts.

Unfortunately, this is too sophisticated an agreement for mere robots. In their methods, any call I make shows a much better hand than this. I have no choice but to pass and hold my breath.

I pass, and LHO raises to three hearts. Thanks. Now that they're at the three-level, I can breathe easily. This is passed around to me. I pass and lead the diamond king.

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

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

Partner plays the four of diamonds; declarer, the seven.

If declarer has the ace and king of hearts, we will need to take four tricks in the black suits to beat this. Any club tricks we have aren't going away, but spades might get pitched on dummy's clubs. Say declarer has

♠ x x x ♥ A K J 10 x  ♦ x x x  ♣ A x

If I don't switch to a spade right away, declarer can set up clubs for a spade pitch. Is that the only layout where I need to switch to a spade? How about this one:

♠ Q x x ♥ A K J 10 x  ♦ x x x  ♣ x x

I must lead spades twice from my side before his clubs are set up. I don't have to switch to a spade now, since partner can let me win let both clubs. But it makes the defense easier if I do.

What if declarer has a stiff club, so the club suit isn't a threat? He must have at least three spades, since partner bypassed spades to bid one notrump. Suppose declarer is 3-5-4-1. The club suit is no longer a danger. The danger now is that he can ruff three diamonds in dummy. If we lead trumps twice, we can hold him to two ruffs. Maybe we can then take three black-suit tricks and another diamond. 

Let's give declarer

♠ Q x x  ♥ A K J 10 x  ♦ x x x x ♣ x

If I lead a spade, partner must duck it to declarer's queen. Declarer then ruffs a diamond and plays a club. We can win and play one round of trumps, but declarer scores eight trumps on a cross-ruff plus the spade for nine tricks. But if I shift to a trump now, we can lead trumps twice and hold him to seven trumps and one spade.

How about

♠ x x x ♥ A K J 10 x  ♦ x x x x  ♣ A ?

Now nothing works. Since declarer doesn't need to duck a club, we can't lead two rounds of trumps.

How about

♠ Q x x  ♥ K J 10 x x  ♦ x x x x  ♣ A ?

Again, if I lead a spade, partner must duck. Declarer can take a spade, a club, and seven trump tricks. If I switch to a trump, partner can play ace and a trump and beat it.

Once again, I wish robots know how to signal. As on Board 9, I would know what to do opposite a reliable partner. Partner's diamond four can't be his highest affordable spot, so it should be his lowest and should suggest that a spade switch looks right to him.

And by "a spade switch looks right," I mean exactly that: Shifting to a spade looks like the right defense. That means partner doesn't just look at his spades. He also considers whether our spade tricks are apt to disappear. If he has the club suit under control, he should encourage to let me know there is no rush to lead spades. I would then switch to a trump.

As I've mentioned before, attitude signals are holistic. Partner's holding in dummy's potential source of tricks should influence whether he encourages or discourages as much as his holding in the suit led or in the suit I'm apt to shift to.

And, as readers of Gargoyle Chronicles know, I don't subscribe to the theory that partner should give suit preference when dummy has a singleton in the suit led. The idea that you don't need to be able to encourage in diamonds just because dummy has a singleton is nonsense. For starters, you might want a diamond continuation to tap dummy. And, even if that makes no sense in context, you might want to encourage diamonds to suggest that's where your tricks are coming from and partner should shift to a trump to protect them.

A discouraging attitude signal suggests attack; an encouraging one suggest a strategy of containment. Most of time, that's what I want to know. I could care less about suit preference.

I suppose one could answer the "attack or containment" question with suit preference. Partner can't really want you to play clubs, so if partner shows suit preference for clubs, perhaps he's saying, "I've got clubs under control. Don't worry about pitches," in which case a trump shift is called for. But what have you gained other than potential for confusion? Playing attitude, a low diamond suggests a spade shift. Playing suit preference, a high one does. Using opposite signals to mean the same thing in different scenarios is asking for a misunderstanding. Since attitude works just fine, play it safe and stick with it at trick one--no matter what dummy holds in the suit led.

Playing with a partner I trusted, then, I would shift to a spade. Opposite a robot, however, I'm on my own. I must make the play I think works most often.

Partner is going to need good spades whichever defense I go for. If we can't take at least two spade tricks, beating this will be an uphill battle. The determining factor seems to be declarer's shape. If he's 3-5-4-1, I want to shift to a trump to stop ruffs. If he's 3-5-3-2, I want to shift to a spade before he can set up the club suit. Since 3-5-3-2 is a priori a likelier shape for declarer than 3-5-4-1, I'll go with the spade shift.

I shift to the six of spades--deuce--jack--queen. Partner's jack means declarer has the spade ten, so I assume nothing would have worked. It turns out declarer has four diamonds and the club ace, so partner's spade ace is the only trick we get. Making five.

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

Jazlene chose a trump shift and also went minus 200 for a push. You can listen to her reasons here: JazPlaysBridge.

In retrospect, I think my spade shift was a mistake. While it's true 3-5-3-2 is a priori likelier than 3-5-4-1, it's also true South chose to overcall with two hearts. It's not clear South would have overcalled with either of the 5-3-3-2 examples I gave. At least I wouldn't. If you're making two hearts, with those hands, you are probably beating one notrump, so there is little upside to bidding. With a balanced hand, it's almost always better to defend one notrump than to overcall in a five-card suit. So if I'm going to play declarer to have only five hearts, as I must, I should play him for an unbalanced hand. I should play declarer for 3-5-4-1 and shift to a trump.

Challenge Match - Jazlene vs. Phillip - Board 10

I've picked up small swings on the previous two boards, so I'm down only two imps going into

Board 10
Both sides vulnerable

♠ Q 9 8 5 3 2  ♥ A 9  ♦ A 9  ♣ Q 8 2

RHO passes. I open with one spade and partner bids two hearts. I bid two spades. This is the catch-all rebid in the robots methods. It doesn't promise six.

Partner bids three clubs. Hearts, spades, and notrump are all possible strains. Three hearts is the right bid, since it keeps all those strains in play. Strangely, the tooltip says the bid shows three hearts. That makes no sense. With three hearts, I would have raised on the previous round.

Even if my robot partner actually believes it shows three hearts, three hearts still may be the best bid. Without the spade jack, I don't want to emphasize spades. If partner has five good hearts, a five-two heart fit may be better than a six-two spade fit. The weak spades also make notrump unappealing, as do my aces and my single diamond stopper. Besides, on many deals where three notrump is right, partner would have bid notrump himself on the previous round. If I bid three hearts and partner's hearts are weak, maybe he will take into account that I failed to raise hearts immediately, so I must have some doubt that hearts is the right strain. Perhaps he will continue exploring with three spades or three notrump if appropriate.

It can be frustrating trying to have an intelligent auction with a robot. But sometimes they surprise you. I have no idea what the right strain is, so I'm not prepared to make a unilateral decision. I'll bid what I would bid opposite a human and hope partner does something sensible.

I bid three hearts. Partner bids four hearts, and everyone passes. RHO leads the jack of spades.

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

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

I seem to have survived the auction. This looks like a fine contract. I can afford to lose two hearts and the club ace.

I play low from dummy, East plays the seven, and I take my ace. Now deuce of hearts--eight--ace--three. And a low heart--king--four--ten. East shifts to the four of spades.

I'm pretty sure the opening lead was from shortness and East has the spade king. If so, I'm cold if I pitch a club. But I'm not that sure. I'm more likely to be wrong about the lead than I am to have a club loser, so I ruff small. West overruffs and shifts to a club. I claim ten tricks.

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

Jazlene chose to bid three notrump over three clubs and went down two, so I pick up 13 imps, putting me back in the lead. 

Three notrump makes for a more challenging play problem than four hearts did. I'm envious. Let's give it a try. But first, let's turn the table around. I find it confusing to have South dummy.

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

West leads the deuce of diamonds, and East covers dummy's jack with the king. Since we have to knock out the club ace, we need diamonds to be blocked. The deuce was presumably fourth best, so we need West to have Q1082. Even so, we have only seven tricks. The only legitimate line I see is for both kings to be singleton. 

Let's see how the play will go if that's the case. Suppose we win the diamond ace and start on clubs. The opponents win the third round and cash their three diamond tricks. But then they can exit with the king of hearts to our ace, reaching this position, where we need the rest of the tricks:

	NORTH ♠ A ♥ Q 7 ♦ -- ♣ K J
	SOUTH ♠ Q 9 8 5 ♥ 9 ♦ -- ♣ --

Even if the king of spades does drop singleton, we have no way to get back to our hand to cash the queen. To make our contract, we must think ahead and cash the spade ace before playing clubs. It would be embarrassing to be lucky enough to find the only layout where we can make this contract and still go down.

Potential embarrassment notwithstanding, I don't think cashing the spade ace is the right play. In addition to its being wildly unlikely to work, we go down at least one trick more than necessary if the king doesn't drop. This is not an easy hand to bid opposite a robot, so there is no guarantee the other table is going plus. Extra undertricks could be costly.

We do have another chance to make the contract that doesn't risk losing oodles of tricks: Play for one stiff king and careless defense. Win the diamond and drive the club ace. If the opponents win, cash three diamonds and exit with a black card. Then we cash the spade ace and run clubs, coming down to this position:

	NORTH ♠ -- ♥ Q 7 6 ♦ -- ♣ K
	SOUTH ♠ Q 7 ♥ A 9 ♦  ♣ --

If West had the singleton king of spades, then the queen is good. Furthermore, East has the only spade stopper. If he has the heart king as well, he is squeezed on the last club.

If the king of spades didn't fall under the ace, we still have the chance that the heart king is singleton. If whichever hand has the long hearts also has the spade king, then the last club squeezes him.

Of course, this line requires misdefense. The opponents can stop the squeeze either by not cashing diamonds or by cashing them and leading a heart to kill our communication.

Now go to JazPlaysBridge for Jazlene's perspective on Board 10.

Challenge Match - Jazlene vs. Phillip - Board 9

I picked up 2 imps on Board 8 when Jazlene played a lower-scoring partial. I'm down 5 imps going into

Board 9
Opponents vulnerable

♠ K Q 10 8  ♥ K 9  ♦ A J 5  ♣ Q 7 5 3

Partner passes, and RHO opens with one club. I overcall with one notrump. This is passed around to RHO, who balances with two clubs. I pass, and LHO bids two spades.

That's a strange call. He should have some game interest. If not, he would pass two clubs. Or, with a good spade suit, he could have bid a non-forcing two spades on the previous round. But if he does have a good hand, why didn't he double one notrump? 

RHO is having none of this. He goes back to three clubs, which ends the auction.

Leading LHO's best suit doesn't appeal, but every other lead looks worse, so I lead the king of spades.

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

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

Interesting. He has neither a good hand nor a good spade suit.

One of my partners liked to play that a raise of partner's minor after a one-notrump overcall showed five-five or better in the majors. In essence, it's Michaels in partner's suit. The idea was that you are unlikely to want to raise partner's minor to the two-level. If you have a fit and a good hand, you would prefer to double. If you have a fit and a bad hand, you would prefer to make a pre-emptive raise to the three-level. This would be a good agreement to have with this hand. Maybe South will suggest it after the deal is over. ("If you're so determined to bid with that hand, partner, why don't we play...?")

Declarer plays the jack from dummy. Surely that's not a congratulatory jack. Do the robots play that convention? Partner plays the nine; declarer, the four,

I continue with the eight of spades. Partner plays the ace and declarer ruffs with the club eight.

Assuming my club queen is our only club trick, we'll need to find three tricks in the red suits to beat this. If declarer has queen-jack third of hearts, we'll have to find our tricks in the diamond suit. That means when I win my club queen, I will need to switch to a low diamond, playing partner for the king. If partner has a heart honor, however, I'd rather defend passively and let partner lead diamonds from his side.

In my regular partnerships, I would already know that a diamond shift from my side can't be right. Partner played the spade nine at trick one from ace-nine-deuce, so can't have the king of diamonds and nothing in hearts. If he did, he would have discouraged to suggest we need to go after diamond tricks.

What would he do with the queen of diamonds? After all, if I have king-jack instead of ace-jack, it might be nice to let me know I can play the suit. The answer is, it depends on his heart holding. If he has the heart suit bottled up, he would encourage in spades. There is no rush to attack diamonds from my side if declarer isn't getting discards on dummy's hearts. But if the heart suit looks like a potential source of tricks, he might decide to encourage with just the queen. 

The bottom line is: if he encourages, a shift from the ace can't be right. If discourages, it's less clear what to do. With the king, I can shift. But with the ace, I must use my judgment. If my own heart holding suggests there is no urgency in shifting to diamonds, then I won't. I must also take into account that he might have overtaken my spade king and shifted himself if it appeared safe to do so. 

Attitude signals at trick one are not just about the suit led or even just about the obvious-shift suit. They are a holistic statement, offering partner's opinion on the overall defensive strategy. Partner may encourage because he wants you to continue the suit led. He may encourage because he doesn't want you to make the obvious shift. Or he may encourage because he knows dummy's suit is not a source of tricks and there is no need for an active defense. That's why I shake my head when I hear the comment, "How can my card be attitude when you know what I have?" Well, maybe I know what you have in the suit led, but that's only a small part of the picture. Attitude, if played with intelligence and flair, conveys much more than that.

My robot partner's nine, however, probably just meant he had the spade ace if it meant anything at all. So I'll have to use other means to decide what to do.

Declarer cashes the ace and king of clubs. Partner plays deuce-six. Declarer leads the club jack to my queen and pitches the eight of hearts from dummy. The eight? There seems to be a theme here with discards from dummy.

Partner pitches the four of hearts. He has a perfectly safe spade discard available, so the four of hearts should mean that partner can offer no help in the heart suit. Since robots pitch count cards, the four should be low from three small, in which case I must shift to a low diamond.

Robots don't discard to help partner, however. I suspect if partner was 3-3-5-2, he would be pitching from his five-card diamond suit. The heart four is probably the dreaded bloodless count signal from xx43. If so, then declarer has a doubleton heart, which means he can't run the heart suit. 

At least not right away. What if he has

♠ x  ♥ Q J   ♦ K x x x  ♣ A K J 10 x x ?

If I get out passively with a spade, declarer can draw my trump, then lead the queen of hearts and duck when I cover. Now the heart suit is good, but declarer is tapped out. I can cash my last spade and the diamond ace for five tricks. As long as I'm right that declarer has only two hearts, it can't hurt to tap him with a spade.

I lead the queen of spades, and declarer ruffs with the club nine. He draws my last trump, and partner pitches the eight of diamonds. That's looks like another count card, so my construction seems to be correct. Partner was 3-4-4-2. We've reached this position with declarer on lead:

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

Declarer leads the queen of hearts. I cover with the king, and he ducks in dummy. Partner plays the six. Declarer is out of trumps, so I can cash my spade winner. Partner pitches the four of diamonds; declarer pitches the nine of diamonds.

The diamond ace is the setting trick, but it isn't going away. Even if declarer has the jack of hearts, dummy has a diamond loser after he runs the suit. I might as well exit with a heart in case partner has the jack and can lead diamonds through declarer.

I exit with the nine of hearts. Somewhat to my surprise, declarer finesses the ten and loses to partner's jack. Partner shifts to the queen of diamonds. Declarer covers and I score my ace and jack of diamonds, but I have to concede a diamond to declarer at trick thirteen.

I see. The heart finesse was free. Declarer lost the heart ace but got a diamond trick at the end instead. Down three.

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

Declarer made a mistake in pitching dummy's fifth spade. If, in the diagrammed end position, dummy had two spades instead of a spade and a diamond, I would be in trouble after winning the heart king. If I cash my spade, I set up a spade winner in dummy. If I exit with a heart, declarer rises with the ace and tosses me in with a spade to force a diamond return. Either way, he gets out for down two.

North's weird two-spade bid worked out quite well for a strange reason. If he passes two clubs, partner should double, showing a doubleton club, support for the other suits, and 7 or 8 HCP. (Perhaps the robots don't play that way. I don't think it's come up before, so I don't know. But that is my agreement with my human partners.) I will pass the double, knowing we have the balance of power and the opponents are in a seven-card fit. Then we collect 500 if declarer plays the same way. North's clever two-spade bid allowed them to escape for 300. Maybe the spade jack at trick one was a congratulatory jack after all.

It may seem odd that it's easier to double two clubs than three clubs. But if North passes two clubs, partner should double to compete--to find a playable partscore ourselves or to push them up to three clubs. He's not trying to penalize them. The fact that I can pass and collect a number is just a lucky consequence. When the opponents reach the three-level on their own steam, our work is done. Partner certainly has no desire to compete at the three level, and he has no particular reason to believe they are overboard by three tricks. So he has no reason to double.

Jazlene chose to pass over one club, and her auction proceeded one spade--pass--two clubs--all pass. So she collected only 200. As a result, I pick up 3 imps on this board, reducing my deficit to 2.

I'm not sure why Jazlene didn't overcall one notrump. I do know she plays raptor with her regular partner, so perhaps she has a philosophical dislike of natural notrump overcalls. I quite like them myself. In fact, I go out of my way to overcall with one notrump, frequently overcalling offshape with I hand I wouldn't open one notrump. I can't imagine giving them up. At least not at IMPs. When you have a strong notrump behind an opening bid, partner doesn't need much to produce game. In fact, it's normal for him to bid game with about a point less than he would after a one-notrump opening. How are you supposed to get to game with this hand opposite a flat nine-count if you don't overcall one notrump?

On this deal, we don't have a game, but the overcall had the secondary benefit of making it easy for partner to compete for the partscore. The opponents took the push all on their own. But, even if they hadn't, partner wasn't selling out to two clubs after my overcall.

For Jazlene's analysis of Board 9, see JazPlaysBridge.

Challenge Match - Jazlene vs. Phillip - Board 8

I'm still trailing by seven imps. Next board:

Board 8
Neither side vulnerable

♠ A 7 6 2  ♥ A 10  ♦ A J 7 2  ♣ J 7 4

LHO opens with one club, partner passes, and RHO bids one heart. I prefer to have at least nine cards in my suits for a two-suited take-out double. But it's now or never. If I pass, I'm probably out of the auction for good. And what fun is that? I double.

LHO redoubles to show three-card heart support, and partner bids one spade. This bid does not necessarily show four spades. Partner must bid one spade any time he doesn't want to hear me bid two diamonds if he passes. So he could easily have only three spades.

RHO bids two hearts. I now know they have an eight-card heart fit, and so does partner. If two hearts is passed around to him, he should compete to two spades on almost any hand with four spades. Since I have no game interest and no fifth spade, there is no reason for me to bid two spades in front of him.

No reason opposite a reliable partner, that is. The robots are not always Law-abiding citizens, so there is a serious danger we will defend two hearts if I pass. I bid two spades. Even if partner has only three, maybe this won't be too bad. Or maybe we'll push them up a level.

LHO passes, and partner bids three diamonds. I was trying to push the opponents up a level, partner. Not us. Presumably partner is making a game try. Or maybe he's getting even with me for bidding his hand for him. Anyway, I'm below minimum for my auction, so I sign off in three spades. Everyone passes, and RHO leads the three of diamonds.

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

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

West chose to lead our second suit in preference to his partner's suit or the suit they bid and raised. So this is probably a singleton. The robots open one diamond with four-four in the minors, so the only way this can be a singleton is if East is 1-3-4-5. But how can that be? With four trumps, West wouldn't be going for ruffs. He would be leading one of their suits to start a tap. I've changed my mind. I suspect West is leading from length, trying to give his partner a ruff rather than going after one himself. In any event, I don't think he would lead from the diamond king. Maybe he has four small and the king is singleton offside.

I hop with the ace of diamonds. East plays the eight. No stiff king. The fact that East played the eight, however, is convenient. It means if I'm wrong about the diamond suit and West did lead from king-ten fourth, I haven't saddled myself with two diamonds losers. I can lead the queen to drive his king, then lead low to the seven, finessing against his ten.

I don't think that's the case, however. I suspect West led from three small, hoping his partner had a singleton and that the defense has a trump entry. Catching his partner with king doubleton as he did may be just as good. If I take a trump finesse and it loses, East can cash the king and put his partner in with a club for a ruff. 

I'm off three top tricks in the minors. I can afford to lose a spade trick so long as I don't lose a diamond ruff as well. Should I play ace and a spade in an attempt to stop the ruff? If East has king third of spades, that does no good. He still gets his ruff. Ace and a spade stops the ruff only if East has king doubleton. If West has king doubleton, ace and a spade lets East get a ruff he wasn't entitled to. 

Which layout is more likely? If East has king doubleton of spades, he holds six clubs. If West has king doubleton of spades, East holds five clubs. The latter is more likely. In addition, choosing to go after a diamond ruff in the first place is a more attractive defense if West holds a potential trump entry. So the diamond lead itself suggests West has the spade king. It looks right to finesse the spade.

I lead the ten of hearts from dummy. East covers with the jack. I play the king, and West follows with the deuce. I lead the spade queen, and West covers with the king. I win in dummy with the ace and play a low spade. East follows with the ten, so I have no further problems. I win, draw the last trump, and drive the diamond king. The defense cashes two clubs and I claim. 

Making four. I guess I should have accepted partner's game try.

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

The right play in the spade suit is trickier if queen-jack-nine are in dummy where the defense can see it. Suppose this is the layout and our goal is to take four tricks:

	NORTH ♠ Q J 9 3
	SOUTH ♠ A 7 6 2

The only four-one break where we can take four tricks is if East has the stiff king. We aren't going to play for that, so let's ignore four-one breaks.

There are seven cases where our play matters. East can hold king-ten (1 case), king-small (3 cases), or king-third (3 cases). We have four possible strategies. If we lead the queen and it holds, we can continue with a low card or we can continue with the jack. If the queen is covered and we win the ace, we can hook the nine on the way back or rise with jack, playing to drop the ten. Our four strategies are the four combinations of these decisions, which we will call Low-Hook, Low-Rise, Jack-Hook, and Jack-Rise.

What strategies does East have? He must cover the queen with king-ten, and he must duck with king-third. If he doesn't, we have no losing options. So his only choice is whether to cover or play low when he holds king-small. 

First, we'll figure out our best strategy the long way. Then we'll discuss a shortcut that leads to the same conclusion.

Since we don't know what East will do with king-small, we'll consider each of his strategies separately. The table below shows the number of cases where each of our strategies succeeds if East covers.

	Low- Hook	Low- Rise	Jack- Hook	Jack- Rise
K 10	0	1	0	1
K x	3	0	3	0
K x x	0	0	3	3
Total	3	1	6	4

As we can see, if East covers with king-small, our best strategy is Jack-Hook, that is, continue with the jack if East doesn't cover and finesse the nine on the way back if he does. This wins six times out of seven.

The next table shows the number of cases where each strategy succeeds if East ducks with king-small.

	Low- Hook	Low- Rise	Jack- Hook	Jack- Rise
K 10	0	1	0	1
K x	3	3	0	0
K x x	0	0	3	3
Total	3	4	3	4

If East ducks, the winning strategy is to rise with the jack if East covers (no surprise, since he covers only when holding king-ten). It's a toss-up what to do if he ducks.

Overall, our best strategy is Jack-Rise: If the queen holds, lead the jack. If it's covered, take the ace and lead to the jack. This guarantees four wins out of seven. Since East has available a strategy that holds us to four wins out of seven perforce, we can't do better than that. Jack-Rise ensures that we do as well as we are entitled to.

What's the best strategy for East? If South plays correctly, what East does with king-small makes no difference. His play matters only if South adopts one of the inferior strategies. Since East doesn't know which inferior strategy South will adopt, he can hedge his bet by adopting a mixed strategy. If the covers with king-small one sixth of the time, the payoff matrix is as follows:

	Low- Hook	Low- Rise	Jack- Hook	Jack- Rise
K 10	0	1	0	1
K x	3	2.5	.5	0
K x x	0	0	3	3
Total	3	3.5	3.5	4

Covering one sixth of the time ensures a South who misplays can't do better than three and a half wins out of seven whichever mistake he makes.

I promised you a shortcut. Since this theme occurs in a variety of suit combinations, a shortcut is useful. Here is a quicker way to come up with the best strategy:

There are seven cases we are concerned with. There is no strategy that is guaranteed to pick up both king-small and king-third. So the best we can possibly do is to pick up four cases: one of the major combinations plus king-ten. If we pick up king-ten, then we can't guarantee picking up king-small. So we give up on king-small. We resign ourselves to losing a trick to king-small no matter how East defends. We don’t play mind games and try to guess what East will do. We simply play to ensure we never lose a trick when East has king-third or king-ten. That way, we always win in four cases out of seven.

We stipulated earlier that our goal was to take four tricks. What if our goal is to take maximum tricks? We would like to take four tricks as often as possible, but not at the risk of losing two unnecessarily. So we can no longer ignore four-one breaks. Specifically, we must worry about king-ten fourth offside. If we lead the queen and it holds, then we continue with the jack and East shows out, we won’t be happy. 

Let’s add that layout to our list. Now we have ten cases to consider: King-ten onside (1 case), king-small onside (3 cases), king-third onside (3 cases), and king-ten fourth offside (3 cases). For the first three scenarios, a "win" consists of taking all four tricks. For the fourth scenario, a "win" consists of losing only one trick. We could add a row to our tables above, but let's use our shortcut instead.

Our goal is to find a strategy that wins in two of the three major cases. If it happens to win for king-ten doubleton, great. If not, six wins out of ten is the best we can do.

We know that no strategy wins for both king-small and king-third onside. So if there is a strategy that wins in two major cases, it must include king-ten fourth offside. The strategy that meets our criterion is Low-Hook. It wins against both king-ten fourth offside and against king-small onside. So, if our goal is to take maximum tricks, we continue low if the queen holds and hook against the ten if it's covered, winning in six cases out of ten.

Now see what Jazlene does on this board at JazPlaysBridge. Be sure to watch until 21:34. Don't stop when Board 9 shows up, since Jazlene circles back to Board 8 for some afterthoughts.