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.

Challenge Match - Jazlene vs. Phillip - Board 7

No surprises on Board 6. I'm still trailing by seven imps.

Board 7
Both sides vulnerable

♠ A 7 6 4 3  ♥ K J 6  ♦ 3  ♣ K Q 9 4

I open with one spade in first seat. LHO overcalls with two diamonds. Partner passes, and RHO bids two spades, showing at least a limit raise in support of diamonds.

We discussed doubles of artificial bids back on Board 2, so you know I think double here should be take-out of diamonds. With a singleton diamond and support for the other suits, I should act. And a double of two spades, which partner can pass if he has nothing, is the safest way to get back into the auction. Passing, then making a balancing double of three diamonds is considerably more dangerous. Unfortunately, the robots play this double shows rebiddable spades, so I have to pass.

LHO bids three diamonds--pass--pass back to me. This is why I wanted to double two spades for take-out. It could easily be right to compete. But forcing partner to act at the three-level when both opponents have shown good hands is too dangerous. I have no choice but to sell to three diamonds. Fortunately, Jazlene and I are forced to play the same methods, so I'm not at a disadvantage as I would be in a normal field.

Partner leads the king of spades, and the following dummy appears:

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

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

Declarer plays the spade jack from dummy. Sure. Why not? He has the ten in his hand.

My agreement in a regular partnership is that discouraging suggests a heart shift. (When dummy's side suits are of equal length, discouraging suggests the suit with fewer honors. Clubs has two honors; hearts has one.) If I encourage, I'm saying I don't want a heart shift. Partner must use his judgment in deciding whether continuing spades or shifting to a club makes more sense. On this hand, I think he would decide to shift to a club, which is the suit I prefer. So I would play an encouraging seven.

Note there is no need to play suit preference here, as I'm sure some would. If you have well-defined rules for which suit a discouraging signal calls for, attitude works just fine. If you want the obvious shift (defined here as hearts), then you play low. You don't have to stop and ask yourself whether this is an attitude situation (where low asks for a heart shift) or a suit preference situation (where high asks for a heart shift). If you want the non-obvious shift, you encourage. If it's so clear that continuing the led suit makes no sense, partner will make the right shift, since he knows you don't want the obvious one.

There is nothing to gain by playing attitude sometimes and suit preference at other times, so why risk confusion? Even if it's clear this time which signal applies, there will always be borderline cases where you and partner won't agree. So why switch ever? If your card is always attitude, you can't have an accident.

Robots, however, play neither attitude nor suit preference, so it makes no difference which card I play. I choose the three.

Declarer plays the five, and partner continues with the spade eight. I wonder if declarer played the spade jack at trick one as a clever ploy to make West think I hold ace-ten over dummy's queen. Robots don't draw inferences, so partner won't realize I can't possibly hold the ten. Who better than another robot to understand that? I'll have to remember that trick.

Dummy plays the deuce. I win with the ace, and declarer plays the ten.

In bridge, as in many games, there are two general strategies of defense: Containment and Attack. The goal of Containment is to deprive declarer of tricks. The goal of an Attack is to take tricks ourselves before declarer can take his. The fundamental task of defense is deciding which strategy is better on a given deal. The reason for making this distinction is that we analyze differently depending on which strategy we adopt. For Containment, we focus on declarer's tricks. For Attack, we focus on our tricks.

On this deal, it may be easier to count declarer's tricks than ours, so let's start with Containment. What high cards does declarer have? It's hard to see his having less than ace, ace-king in the red suits for his two-level overcall. And if he's missing one of those cards, we might beat him whatever we do. So let's assume he has them.

What's his shape? If he has six diamonds, then he has eight top tricks (six diamonds and two aces), and we can't possibly stop him from eventually taking a spade trick. So we need to assume he has only five diamonds.

Ace-king fifth of diamonds and the heart ace gives him four or five diamond tricks (depending on who has the jack), the heart ace, the club ace, and two spades: eight or nine tricks in all. If we return a spade for partner to ruff, we eliminate one of his spade tricks, reducing him to eight tricks. (The diamond jack now becomes irrelevant. After partner ruffs, declarer will always have five diamond tricks.) Can declarer find a ninth trick somewhere? If he has the heart ten, he can. If not, I don't see where a ninth trick is coming from.

The next step is to double-check our plan by constructing a concrete layout. Sometimes an abstract plan has a flaw that is difficult to see unless you play through it. Let's give declarer

♠ 10 x  ♥ A x x  ♦ A K x x x  ♣ x x x

If we return a spade, declarer will pitch a club as partner ruffs. Partner will then shift to a club. Declarer will win his ace, draw trump ending in dummy, and pitch his last club on the fourth spade. If one of those heart x's is the 10, he can develop a heart trick and make his contract. If not, he's down. Yes, our analysis seems correct. 

We now have a provisional plan. The next step is to try to improve on it. Can we defeat the contract if declarer has the heart ten?

Perhaps an Attack will do better. A successful Attack requires us to establish and cash five tricks. If partner has the club jack and declarer has three clubs, we can shift to the club king and establish two club tricks. That gives us two spades, a heart, and two clubs. Again, we need to test our plan against a concrete layout. Let's add the heart ten to declarer's hand above so that the spade return will fail:

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

We shift to the club king. Declarer wins and draws trump, ending in dummy. They don't split, so he can't take his spade pitches. He must lose two clubs and a heart. Possibly a diamond as well if partner has the jack.

So Containment (returning a spade) works if partner has the heart ten, and Attack (shifting to the club king) works if partner has the club jack and declarer has three clubs. Since Attack requires two assumptions instead of one, Containment is more likely to be right.

Or so it appears at first glance. Let's confirm we're right about declarer's needing three clubs for the club shift to work. Give declarer:

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

If we shift to the club king, his best play is to win and cash a spade, pitching his club loser and letting partner ruff. This won't hurt if diamonds split, but it saves a trick (compressing his diamond and club losers) if partner has jack fourth. Partner will now try to cash a club. Declarer will ruff, draw trump ending in dummy, pitch a heart on the last spade, then play a heart toward his ten. We get only four tricks: two spades, a heart, and a ruff.

Yes, a club shift fails if declarer has a doubleton club. What about our assumption that partner needs the club jack? If declarer has jack third of clubs, we can take only one club trick. But maybe that's enough. If partner has jack fourth of diamonds, perhaps we can take two spades, one club, one heart, and a diamond.

Let's check it out. Give declarer

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

We already know a spade continuation fails on that layout. What happens if we shift to the club king? Declarer wins in dummy and leads a second club. If we hop, declarer unblocks his jack. We continue with a club to dummy's ten to kill the entry. Now what? Declarer cashes a spade, pitching one heart as partner ruffs, then draws trump ending in dummy to pitch his last heart. We get our club trick, but we don't get a heart trick.

Perhaps, instead of hopping with the club queen, we should duck and let declarer win his jack. This deprives him of using the club ten as a dummy entry. If we do that, declarer can continue with a third club. We win and find ourselves in this position:

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

We're endplayed. A heart or a club shift gives declarer a trick, taking care of one of his small hearts. He can then cash a spade, pitching his last heart as partner ruffs. He loses only four tricks: two spades, one club, and a ruff. Our only safe return is a diamond, and that gives declarer two dummy entries. Declarer can now pitch one heart on a spade as partner ruffs, and eventually pitch his last heart, again losing two spades, a club, and a ruff.

Yes, a club return does indeed require finding partner with the jack and finding declarer with three clubs while a spade continuation requires only finding partner with the heart ten. So a spade continuation is the better play.

I return a spade. Declarer pitches the three of clubs, and partner ruffs with the nine of diamonds. Partner shifts to the eight of hearts.

Hearts? Why are we breaking hearts, partner? Oh, I see. He's hoping I have the ace, so I can play another spade and kill that trick as well. Let's hope the shift is from ten-eight-seven. If so, we still have a heart trick coming.

Declarer plays the deuce from dummy, and my jack forces his ace. Declarer draws three rounds of trump, ending in his hand, and leads the nine of hearts--ten--queen--king. I return the six of hearts. Partner overtakes with the seven. Down one.

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

Partner had both the heart ten and the club jack, so either Containment or Attack would have worked.

Jazlene and I don't agree on this one. She initially played as I did but later decided later that a club shift was better. Watch her play on Jaz Plays Bridge, then watch her post mortem.

Challenge Match - Jazlene vs. Phillip - Board 6

Board five was a push, so I'm still down seven imps.

Board 6
Opponents vulnerable

♠ J 7  ♥ K Q J 6 4 3  ♦ K 2  ♣ K Q 10

Six heart tricks, half a trick in diamonds, a trick and a half in clubs. Seven in all, not quite good enough to open with one heart and rebid three hearts.

I bid heart, LHO overcalls with two diamonds, partner passes, and RHO bids two notrump. I have a pretty good hand, but partner couldn't act over two diamonds, and RHO's two notrump suggests hearts may not be breaking. So I pass, as does everyone else.

What should I lead against two notrump? Should I try a heroic low heart in case declarer has ace-nine fourth and partner has the ten? LHO might have removed two notrump if he had a stiff heart, so if declarer does have four hearts, partner probably has a singleton. Hoping it's a stiff ten is a bit much. I'm better off hoping declarer has only three hearts. But at least, if a low heart lead turns out to be right, I can say I thought about it.

I lead the king of hearts and see the following dummy:

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

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

Declarer plays a curious ten of hearts from dummy. Partner plays the eight; declarer the six.

If diamonds are running, we aren't beating this. Can we beat it if partner has jack third of diamonds? Declarer then has five diamonds and two aces. The tooltip says two notrump show 11 HCP. There are 15 HCP missing, so even if declarer has stretched a point, partner has at most five. That means he can't have both the club ace and the spade king. Declarer must have one of those cards, so he has eight tricks even after losing a diamond.

One possibility is to switch to clubs, playing partner for ace fourth. But if he has that, we can always cash clubs when partner wins his diamond trick.

What if partner has jack fifth of clubs? In that case, I must switch to clubs now to knock out the ace, giving us a heart, four clubs, and a diamond. Is that possible? That gives declarer a 6-3-2-2 shape. I don't think so. My best shot is to continue establishing hearts and hope partner has jack-ten fourth of diamonds, so that the diamond suit isn't a threat. 

I continue with the queen of hearts. Oops. That was a mistake. I'm supposed to lead the jack, since I want a club return when partner wins his diamond. Good thing partner pays no attention to my signals. Partner follows with the deuce of hearts and declarer wins with the ace.

Declarer plays the three of diamonds--deuce--nine--ten. Declarer can't have a stiff diamond. If he did, he would be finessing the queen, not the nine. So dummy's diamonds are now good. 

Partner shifts to the deuce of clubs, and declarer takes the ace. This is the position:

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

We're not beating this. So it's all about stopping overtricks now. After declarer runs the diamonds, I'm left with four cards. What should they be? If declarer has king-ten of spades, I must keep both spades, else declarer can cash the ace and finesse against partner's queen. So my last four cards will be

♠ J 7  ♥ J  ♦ --  ♣ K.

Actually that might not work. If declarer holds jack doubleton of clubs in the end position, he can duck out my king. I can't decide what to hold until I see what declarer keeps. If he holds three spades, I have to keep both spades. If he holds two clubs, I must keep both clubs. If he holds a heart, I must keep the heart jack. If I'll have to pay attention. And here I was hoping to catch a nap. Oh, well.

Declarer has played the club ace. I follow with the ten. (In real life, this card would be face down on the table and I would now turn it over. That's how a defender can pause play to give himself time to absorb what's happened without misleading declarer into believing he is thinking about the current trick. Those who designed online play forgot about this option. There should be a "play card face down" button.)

Declarer plays a diamond to the ace and cashes the queen. Partner plays six-jack in diamonds; declarer pitches the four of club; I pitch the three of hearts.

On the next diamond, partner pitches the deuce of spades. The robots almost always discard count cards, so partner is presumably 5-2-3-3 and declarer is 4-3-2-4. Declarer pitches the nine of hearts. If my construction is correct, declarer is down to four spades and three clubs. I pitch the heart four. Since declarer is out of hearts, I can now throw all my hearts if necessary. 

On the next diamond, partner pitches the spade three; declarer, the spade eight. Declarer still has three spades left, so I can't pitch a spade yet. I pitch another heart. On the last diamond, partner pitches the five of spades; declarer, the ten of spades. Declarer is down to two spades and two clubs. I can afford a spade now, so I pitch the spade seven. We are down to this position, with dummy to play:

	NORTH Robot ♠ A 4 ♥ -- ♦ -- ♣ 7 3
WEST Phillip ♠ J ♥ J ♦ -- ♣ K Q		EAST Robot ♠ ? ? ♥ -- ♦ -- ♣ x x
	SOUTH Robot ♠ ? ? ♥ -- ♦ -- ♣ x x

Declarer leads the three of clubs from dummy. What's he doing? Why not cash the spade ace? Is he trying to endplay me? Maybe he thinks I'm now down to

♠ K x  ♥ J  ♦ --  ♣ K.

If declarer is trying to endplay me, he must have the queen of spades. So this is the position:

	NORTH Robot ♠ A 4 ♥ -- ♦ -- ♣ 7 3
WEST Phillip ♠ J ♥ J ♦ -- ♣ K Q		EAST Robot ♠ K x ♥ -- ♦ -- ♣ x x
	SOUTH Robot ♠ Q x ♥ -- ♦ -- ♣ x x

The right defense is for me to win with the king of clubs and cash my heart. Partner must stiff his spade king and hold onto a club. Now if I lead the spade jack, declarer might get greedy, duck it, and go down.

Playing with a partner I trusted, that's exactly how I would defend. Partner can see that stiffing his spade king is our only chance to beat this, so he should go for it. But robots aren't that tough. If I win the club and cash a heart, partner is going to come down to a doubleton king of spades like a wimp.

What if I win the club king and lead the jack of spades immediately, without cashing my heart? Declarer might still duck and go down. This line is a lot less convincing than letting partner stiff his king. But playing with a robot, it's the best I can do.

Partner follows to dummy's club lead with the five, and declarer plays the jack. I win with the king and play the jack of spades.

Declarer doesn't bite. He hops with the ace. Making two.

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

Maybe I was too quick to go into stop-the-overtrick mode. We still had a chance to beat it that I didn't see. My goal should be to represent

♠ K J 7  ♥ K Q J 6 4 3  ♦ K 2  ♣ K 10

and entice declarer into endplaying me. 

How would I discard if that were my hand? I would probably pitch a spade early, so that's what I should do. If I pitch a spade at my first opportunity, a good declarer would be disinclined to think I had stiffed my jack. So in the end position, he would "know" I had king-jack of spades left and might well go for the endplay. And my lucky mistake of giving the wrong suit-preference signal at trick two would reinforce that illusion. (I would, of course, tell declarer I was thinking ahead and had falsecarded with the heart queen on purpose.)

Would declarer really risk his contract for an overtrick at IMPs? He should if he thinks the odds are good enough. Yes, you are risking six imps to gain one. But if you think it's ten to one you've read the position correctly, going for the overtrick is the percentage play. Why throw that 0.36 imps away?

What if you're wrong and go down? Then you have to be philosophical about it. I once lost a Spingold match by two imps. After we compared, my teammate told me that, on the last board, he had gone down in one notrump by playing for a "sure" overtrick. When he showed me what had happened, I couldn't blame him. He had made the right play. On a different day, that overtrick might have swung the match in our favor, and I would be congratulating him on his thoughtful play. So I could hardly take issue now. Besides, it was Edgar Kaplan. I would assume he had done the right thing even without seeing the deal.

Be sure to go to Jaz Plays Bridge and see what Jazlene does on Board 6. Let's hope she doesn't bid a fearless three hearts over two notrump and pick up a couple of imps.

Challenge Match - Jazlene vs. Phillip - Board 5

Jazlene bid slam on board four and picked up 12 imps. I'm trailing by seven imps going into

Board 5
Our side vulnerable

♠ A K 10  ♥ K 8  ♦ A 10 9 8  ♣ K 9 8 7

Two passes to me.

Despite holding only 17 HCP, this hand is too good to open with a strong notrump. My HCP are all in aces and kings, and I hold two tens and no card lower than a seven. K&R point count evaluates the hand as 18.9 points. 

Still, I've never had much success opening one of a minor instead of one notrump with hands that the Work point count undervalues. Yes, sometimes you reach game or slam that you would miss after a one notrump opening. But that's aiming for a narrow target. More often, it seems, you get a poor result by letting the opponents in at the one-level, especially at this vulnerability. Since partner is a passed hand, at least I don't have to worry about missing a slam. So I decide to make the tactical underbid of one notrump and hold my breath.

LHO passes, and partner bids four hearts, a transfer to spades. I can let my breath out now. I bid four spades, and everyone passes. LHO leads the deuce of diamonds.

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

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

If the lead is from jack third or fourth, I'm taking four diamond tricks. But the robots don't like leading from honors, so it's likely the lead is a singleton. I play low from dummy, East plays the jack, and I take my ace.

I can pick up four-zero trumps in either hand if I cash the ace first, so I cash it. West plays the five; East, the six. I continue with the spade king and both opponents follow. West held the jack.

It looks as if I'm losing the diamond king and the club ace to make five. If East has the ace of clubs, is there any way to convince him to duck when I lead the club jack from dummy? Maybe. If East thinks I'm missing the heart king, then dummy's heart is a loser. If he hops with the club ace and I have the club king, then the heart loser goes away. So he might duck, hoping I have king-ten and misguess.

At least a human East might. Robots never play for a misguess; they assume you're double dummy. But even if I'm double dummy, it could be right to duck. Say I have queen-ten of clubs. Then hopping allows me to take a ruffing finesse against West and pitch my heart loser.

This means if I want to make it dangerous for East to hop, I must keep the heart ace in dummy. If I lead a heart to the ace and play a club, he has no reason to duck. He can simply hop with the ace and play a heart.

So leading a heart to dummy can't possibly work. What about a spade? The problem with leading a spade to dummy is I now have no fast entry to my hand. If East is worried about losing a heart trick, he can hop with the club ace and shift to a heart. I can't get to my hand in time to take my putative pitch. 

Leading a heart to dummy doesn't work. Leading a spade to dummy is better, since it requires a tad more care on East's part. But it probably won't work either. A diamond is the only option left. Let's give it a try.

I play the eight of diamonds. West pitches the six of hearts, and I play low from dummy. East takes his diamond king and returns the diamond seven. Yes! Perfect! I overtake in dummy with the queen as West pitches the four of clubs. We've reaching the position I was aiming for:

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

Now when I lead the jack of clubs, East has a legitimate reason to duck. If I have queen-ten of clubs and no heart king, he must duck to stop the second overtrick.

I lead the club jack. East hops with the ace. Oh, well. I claim the balance. Making five.

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

East had ace-queen of clubs, so he had no temptation to duck. Still, I don't understand his diamond return after winning the king. Couldn't I have the same hand with the queen of hearts instead of the king, in which case he must shift to a heart?

The only reason I can think of to play a diamond is he thought I had forgotten to draw the last trump and his partner was ruffing. A priori, playing for the ruff is probably percentage. But I can't have that hand. Until we teach robots to draw inferences, their card play is never going to get above a beginner level.

My one notrump opening did keep the opponents out of the auction, although it probably didn't matter. I'm not sure why West didn't bid anyway. Though perhaps there isn't much point playing Cappelletti, where you announce to partner that you have a suit to bid but you aren't going to tell him which one. I would certainly overcall one notrump with two hearts if it were natural.

While my swindle didn't work, this hand is an excellent example of the necessity of looking at a deal through your opponent's eyes. Sneaking a club through has a better chance to work if you sit in your opponent's seat and imagine a scenario where ducking makes sense. 

This has become my favorite type of play problem. When I was a beginner, my favorite hands were winkles. But any fool can execute a winkle. Even a robot. Seeing a deal through your opponent's eyes is hard. And fun. And often more profitable than it was on this deal.

Now take a look at the deal from Jazlene's eyes at Jaz Plays Bridge. I suspect the board is a push and she's still up seven imps. We'll see.