Free Weekly Instant Tournament - March 15 - Board 5

Board 5
Our side vulnerable

♠ A K 8 3  ♥ A 6 2  ♦ Q 10 5  ♣ A 4 2

Two passes to me. I open with one notrump, and partner bids two hearts, a transfer to spades.

I believe one should pre-accept on almost any hand with four spades. This hand, with four trumps and four-plus honor tricks, should meet anyone's standards. 

I bid three spades, partner goes on to four, and West leads the queen of clubs.

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

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

I have two diamonds losers, so I need to hold my heart losers to one. If I can strip the hand, I might manage an endplay. There are two ways to play the heart suit in the end position. I can play a low heart from my hand, guess whether to play the ten or queen, and hope, if I guess wrong, that East has both honors and is endplayed. Or I can cash the ace and lead to the ten or queen, hoping, if I guess wrong, that East is out of hearts and must give me a ruff-sluff. For either plan to work, however, I need to have a trump left in each hand after drawing trump and ruffing two clubs. So I will need trumps to be two-two.

Should I ruff a club now while it's convenient? Let's see if I need to. If I win the second trump in my hand and trumps are indeed two-two, I can ruff one club at that point. Then, assuming from the opening lead that East has at least one diamond honor, I can always reach my hand with a diamond to ruff the second club. Since I have no entry problems, there is no need to ruff a club now. An early, gratuitous ruff might prove embarrassing if trumps don't split.

East plays the seven of clubs at trick one. I take the club ace, play a spade to dummy, and a spade back to my hand. They split.

Now a club ruff. West plays the three; East, the five.

I lead the deuce of diamonds. East hops with the king; West follows with the seven. East continues with the ace of diamonds. I play low, and West following with the eight. East continues the nine of diamonds to my queen, as West discards the nine of hearts. We've reached this position:

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

The nine of hearts is presumably count. If so, West is 2-4-2-5, and I'm cold. All I have to do is ruff a club, play a heart to my ace, then play a heart to the queen or ten. It makes no difference which, since if it loses, East has only minors left and is endplayed.

I ruff a club to dummy and play a heart. East plays the jack. I take the ace and claim ten tricks.

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

I guess East hopped with the jack to save himself the embarrassment of being endplayed.

Plus 620 was worth 82%. Strangely, quite a few players didn't pre-accept and languished in two spades.  

I see some declarers did ruff a club at trick two. Once I saw that the immediate ruff was unnecessary, I didn't bother to check if it might cost. Let's do that now.

Suppose I ruff a club at trick two, then draw trump. If trumps turn out to be three-one, I must draw three rounds. Then I drive a diamond honor, and the defense leads a third club to tap dummy, reaching this position:

	NORTH Robot ♠ -- ♥ Q 10 5 4 ♦ 4 2 ♣ --
	SOUTH Phillip ♠ 8 ♥ A 6 2 ♦ Q 10 ♣ --

I drive the other diamond. Now they tap my hand with a fourth club and I'm out of trumps. Even if I guess hearts correctly, I'm still going down if the hand with the heart king has the long club. So an immediate club ruff is an error. I could go down when I'm cold if I guess hearts.

Ruffing a club at trick two is the kind of error an expert can easily fall into when he's being lazy. Stripping the hand looks like a good idea. So why not ruff a club now, when you have the chance? Stopping to work out whether you're short of entries and need to ruff a club early is too much work.

Sometimes playing by instinct is unavoidable. You don't always know enough about the layout to tell whether or not you need to make some preparatory play, such as taking an early ruff or ducking a trick to prepare for a squeeze. So you have to rely more on instinct than on analysis. But this deal isn't one of those cases. If you bother to check, you can see easily enough that you aren't short of entries, so there is no hurry to ruff a club. 

Incidentally, I did misbid this hand, because I was unfamiliar with the robots' methods. I discovered later that they play two notrump over the transfer as a maximum with four trumps and "4333" distribution. So that's what I should have bid. It might allow partner, with a different hand, to choose three notrump rather than four spades.

Free Weekly Instant Tournament - March 15 - Board 4

Board 4
Opponents vulnerable

♠ K 4  ♥ K Q 8  ♦ K 8 4  ♣ J 9 8 6 3

RHO opens two diamonds, weak, in third seat. I pass, LHO raises to three diamonds. Partner, despite being a passed hand, chimes in with three spades, and RHO passes.

Personally, I would never bid this way. If I had a suit I'm willing to introduce at the three-level, I would do something on the first round of the auction. Obviously partner doesn't agree with this approach. So what does he have? Why is he willing to bid three spades now when he wasn't willing to bid on the first round?

I suspect he has a two-spade opening, or possibly a three spade opening, but was deterred by a four-card heart suit. If so, my hand is golden. I have three cover cards for him. (The king of diamonds is probably opposite his singleton, so I'll ignore that card.) Still, if three cover cards were enough for game, partner would have a six-loser hand. A six-loser hand with ten cards in the majors is an opening bid. Another concern is that his fourth heart may be an unexpected loser, since he won't be able to ruff it in dummy. Despite the fact this is quite a good hand on the auction, it doesn't appear to be enough to raise.

I pass, as does LHO. RHO leads the heart six.

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

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

I called it! A weak two-spade bid with four hearts and seven losers. So my three cover cards are just enough to make three. Fortunately, partner has the heart jack, so the fourth heart isn't a problem. Although a heart ruff by an opponent might be. This lead looks suspiciously like a singleton. If so, is there anything I can do about it?

I could try winning the heart in dummy and leading a low spade from the table. But what if East hops with the ace, leads another heart, and West follows? Then there was no heart ruff after all. But now spades are blocked. I can't get to my hand to draw the last trump. So if West has it, I've gone down in a cold contract.

In fact, if West has three spades, the ploy can't work anyway. Even if East ducks the spade ace, he can still give his partner a ruff on the next round. So the ploy works only when West is specifically 2-1-6-4 and East choses to duck the spade ace. And I go down in a cold contract whenever West is three-two in the majors and East hops. The swindle is clearly a bad bet.

I win with the heart king; East plays the deuce. I lead the spade king--eight--deuce--ace. Oh. Somehow I didn't think of the pre-empter's holding the spade ace. The swindle is worse than I thought. It works only if West is 2-1-6-4 and East holds the spade ace and chooses to duck it.

West continues with the heart four. I have three unavoidable losers left. Making three.

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

Everyone played three or four spades and almost everyone took nine tricks. Plus 140 was worth 61%.

One declarer tried a ploy I didn't think of. He won the first heart in his hand with the ace and played a spade toward dummy. If East holds five hearts, this leaves open the possibility from his perspective that the opening lead is from jack-nine-six and declarer holds ace doubleton. Unfortunately, declarer's imaginative play was punished. West ducked the first spade, won the second, and played another heart. Declarer had no way to get off dummy to draw the last trump, so he went down one.

This might have worked if East had the spade ace. But even then it seems unlikely. If declarer has ace doubleton of hearts, why wouldn't he cash his hearts and pitch his stiff diamond before driving the spade ace? Still, I like the idea of trying to convince East the lead isn't a singleton.

Perhaps there's a better way to accomplish that: Play the heart king from dummy and overtake with the ace. You can always hook against the ten later, and this sequence might make it appear to East that you have ace-jack third and are retaining an additional hand entry.

Again, it seems unlikely this will work. It's not as if East has anything better to do than to try to give his partner a heart ruff. But it can't hurt to try. Unlike the other two ploys, there is no risk if the six is an honest card. If West unexpectedly has the ten, you will find out in time, since he will play the seven on the second round. So why not? I wish I'd thought of it.

Free Weekly Instant Tournament - March 15 - Board 3

Board 3
Opponents vulnerable

♠ K Q 5  ♥ Q 8 6  ♦ A K 9 7  ♣ J 8 7

I open one notrump in first seat and buy it. LHO leads the three of hearts.

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

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

I play low from dummy and West wins with the king. What should I do if East continues with a low heart at trick two? A priori, East is twice as likely to have the jack as to have the ace by restricted choice. Yet one could argue that I should go up with the queen anyway, since East would lead the jack if he had it to smother dummy's ten.

But would he? He certainly would if he had the nine. But if he doesn't, then I might have it and leading the jack takes my guess away. True, leading low from jack-empty risks letting me take a trick I'm not entitled to. But if I'm going to hop whenever he leads low, leading low from jack-empty doesn't cost. 

But if I decide East will reach this conclusion and will therefore lead low from jack-empty, it becomes wrong for me to hop. I should go with the a priori odds and duck. But if I'm going to duck, East can no longer afford to lead low from jack-empty. But that means it is right for me to hop. And so on ad infinitum.

How do you escape this vicious circle? What's the right answer? It so happens I wrote a Bridge World article about this suit combination years ago. If you're interested, you can find my solution there. In this case it's moot, since East continues with the ace at trick two, and West follows with the nine.

At trick three, East leads the jack of hearts. I win with the queen, and West follows with the seven. I still haven't seen the deuce. Hearts could be four-four or either opponent could have started with five hearts.

I have six tricks. I need one more. If East has the spade ace, my contract is safe. I can lead a spade toward my hand. If East ducks, I'm home. If he hops, there is no scenario where the defense can take seven tricks. If East has five hearts, they can take four hearts and two aces. If West has five hearts, they can't cash them unless East leads a club to West's ace, solving my club problem. And if hearts are four-four, the best they can do is to take three hearts, a spade, and two clubs.

If West has the spade ace, however, I could have a problem. Say I play a spade to my hand, and West wins, cashes two hearts, and leads a low club. I'll need to hope West has a club honor and will have to guess which one in order to make my contract.

I could run all my diamonds before playing a spade to maximize my chance of guessing clubs. But then I won't be able to lead up to my spades twice. I'd like to do that, since if East has both aces and no more hearts, I can make an overtrick by taking two spade tricks.

It's not clear how much I will learn by running all my diamonds anyway. So I'll compromise by cashing three diamonds before playing a spade toward my hand. If the spade wins, I'll finish the diamonds and play another spade. If it loses, at least I'll have some extra information from having cashed three diamonds.

I pitch a club from dummy on this trick and cash the ace and king of diamonds. On the second diamond, West pitches the five of clubs. There are two lower clubs out. I can't tell whether that's a high club or a low one.

I play a diamond to dummy, and West pitches the ten of spades. That one's high. The robots like pitching count cards. So it appears West is 4-5-1-3 or 4-4-1-4. If he turns out to be 4-5-1-3, I'm going to play him for the club ace. I doubt his first discard would be a club from queen third.

We've reached this position with the lead in dummy:

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

I lead a spade from dummy. East plays the jack, and I play the queen. West takes the ace and cashes the five of hearts. I pitch a spade from dummy. East pitches the six of clubs. I'm happy to see that card. If East had both club honors, he wouldn't be pitching clubs. He would be hoping to run the club suit. So I'm sticking with my assumption that West has the club ace. Presumably this is the current layout.

	NORTH Robot ♠ 7 ♥ -- ♦ J 6 ♣ K 9
WEST Robot ♠ x x ♥ 2 ♦ -- ♣ ? ?		EAST Robot ♠ x x ♥ -- ♦ -- ♣ ? ? ?
	SOUTH Phillip ♠ K ♥ -- ♦ 9 ♣ J 8 7

West cashes the last heart. I pitch a spade from dummy, and East pitches the club three. East's coming down to a doubleton club was an error. I can now pitch a club from my hand safely. Even if I misguess clubs, I'm down only one. East would have done better to hold all four clubs. Then, if I think East has both club honors, I might decide to pitch a diamond from my hand and concede down one. Pitching a club retains the possibility of making but risks going down three.

I pitch a club, intending to play West for the club ace if he leads a low one. But he doesn't put me to the test. He shifts to a spade, and I claim three tricks. Making one.

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

Plus 90 is worth 61%. Most declarers ran all their diamonds before playing a spade. I think that's a mistake, though it didn't matter this time.

West's spade exit at the end was strange. That was simply giving up. But I see what he was "thinking." Since robots assume you are double-dummy, they will never put you to a guess if they have another option. West was hoping his partner had the last diamond and I had no way to get to dummy except to lead a club to the king, in which case he could win and cash a spade. In the robot's opinion, I'm more likely to have completely butchered the play earlier than I am to misguess a queen now.

Free Weekly Instant Tournament - March 15 - Board 2

Board 2
Our side vulnerable

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

RHO passes. I open with one heart. Partner responds one spade. I rebid two clubs. Partner bid two diamonds, artificial and game-forcing. I bid three clubs, and partner leaps to four hearts.

The tooltip says this shows heart support and 13 to 14 total points. That makes no sense. It's classic Eastern Science Fiction. 

You need some way to show slam interest in hearts. If three hearts promised extra values, then you could play fast arrival: Bid three hearts with slam interest and four hearts with a minimum. But three hearts can't promise extra values, because you haven't established the strain yet. If you have heart support but are willing to play three notrump if partner suggests it, you need to be able to bid three hearts even with a minimum. Since three hearts can't promise extras, playing four hearts as fast arrival would leave you with no way to show slam interest below game. In general, fast arrival should apply only when strain has already been established. In a game-forcing auction, jump preferences, like jumps in notrump, should show about a king more than you have already promised.

One might argue that this auction should be an exception. After opener has shown five-five in hearts and clubs, it's wildly unlikely he will suggest three notrump over three hearts. But making exceptions is dangerous. The rule as stated above makes sense most of the time. A partnership will be less apt to have an accident if it applies such rules consistently.

With this hand, I have a pass whether four hearts shows extras or not. I pass, and LHO leads the diamond ace.

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

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

East encourages with the eight. West continues with the diamond nine, and East follows with the six.

Whatever heart losers I have are unavoidable. But I might be able to do something about my club loser if clubs are four-one. I could cash the spade king, then, if I reach dummy with the heart king, pitch my clubs on the ace and queen of spades. That runs the risk of having my spade queen ruffed when clubs were three-two all along.

A priori, a five-two break is less likely than a four-one break. But I have reason to believe clubs are splitting. West might have led a singleton club. And, if he has the heart ace, he might have shifted from at least some four-card holdings, since he would know from the auction that his partner had a singleton. Given that inference, I'm inclined to play for clubs to break rather than risk a spade ruff.

Of course the inference isn't 100%. So if I can cash spades safely, I'd prefer to do that. Can I? Let's assume trumps break. To cash spades safely, I would need to reach dummy with the heart king after trumps are drawn. If West has the heart queen, I can't manage that. He can cover the first or second heart hand and force to me play the king early. If West has the heart ace, however, I can. If he takes the ace early, I can win the third round of hearts with dummy's king. If he has ace third and ducks twice, I can win the second round with the king, and the only heart outstanding will be the ace, which I don't mind his ruffing with.

I play a spade to the king. East plays the six; West, the four. Should I lead the heart jack or a lower heart? I don't see that it matters. I choose the jack as a discovery play. If West has the queen, I'd like to see what holding he does or doesn't cover from for future reference.

West covers my jack with the queen. I play dummy's king, and East wins with the ace. OK. Cashing spades is out. I have to rely on a club break.

East shifts to the club six. I take the ace, and West follows with the five. Everyone follows to the heart ten. This is the position with one trump outstanding:

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

If clubs break, I have the rest. What if they don't break? If the hand with club singleton is out of hearts I can cash two clubs and ruff one in dummy to make five. It costs nothing to try. If the club king gets ruffed, I still make four. I'm simply trading a club loser for a trump loser. 

I lead the club king. Everyone follows, and I claim. Making five.

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

Plus 650 is worth 61%.

West covered with queen doubleton, apparently worried I would lead the jack from something like J107xx. I'll keep that in mind.

Some declarers led the heart eight rather than the jack and found themselves with an interesting problem. West played low, and East took the ace and switched to the club six. Declarer won and played a heart to the queen and king, reaching essentially the same position as above except that the lead is in dummy. Now what?

If East has the last trump, declarer can guarantee his contract by playing spades. If East doesn't ruff, he gets his clubs away. If East does ruff, he overruffs and has a trump in dummy to ruff a club with. The only time cashing spades fails is if West is short in spades and has the last trump. On the other hand, the only time you need to cash spades is if clubs aren't breaking, and it seems likely they are. If East had shifted to the ten of clubs, it would be a different matter. But when he leads the six, how can clubs be four-one? Did West really chose to lead the diamond ace holding either a stiff club or J1095?

Most declarers who reached this position played on spades. I think I would have played for clubs to break. Since both lines work, it's hard to say who's right. Although perhaps I did make a mistake in leading the heart jack rather than a lower one. Ensuring West doesn't play the queen on the first round does give you extra options, even if you decide not to take them.

Free Weekly Instant Tournament - March 15 - Board 1

Board 1
Neither side vulnerable

♠ K Q 2  ♥ J 7  ♦ A J 10 7 5  ♣ K Q 5

RHO opens with one spade. I overcall with one notrump. Partner bids two clubs, Stayman. I rebid two diamonds and partner invites game with two notrump. With 16 HCP and a good five-card suit, I have an obvious acceptance. I bid three notrump, and West leads the spade ten.

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

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

If clubs come home, I have nine tricks. Can I do better? If East has all the high cards (the queen-ten of hearts and the king-queen of diamonds), I can triple squeeze him. After I cash my black-suit tricks, I'll be down to

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

To keep three hearts and the king-queen of diamonds, East must throw all his good spades away. I can then duck a diamond to take a tenth trick. I have no reason to believe East has all the high cards, but I'll keep this ending in mind as a possibility.

I play a low spade from dummy, and East encourages with the five. East can be pretty sure I have the spade king, but he may be less sure about the queen. So I win with king, the card I'm known to hold.

I lead the king of clubs--three--deuce--ace. East cashes the spade ace, and West drops the nine. East continues with the spade four, and West discards the heart deuce. This is probably from a five-card heart suit.

Here is the current position:

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

West is out of spades. So I can develop a diamond trick if he has a diamond honor and I can arrange to lose a diamond to him. I can cash the club queen, lead a club to dummy, and play a diamond. No, I can't. East simply puts up his diamond honor, forcing me to take the ace, and I have no way back to my hand after I drive the other honor. 

If I'm going to develop a diamond trick, I have to do so while I still have a club entry to my hand: Heart to dummy immediately. Diamond. East rises with his honor. I win with the ace and play the diamond jack. That works if the diamond honors are split. But if East has both honors, I go down. It's not all that unlikely East has both diamond honors. In fact, there is a slight inference that he does. Clearing the spades suggests he has an entry. So I like playing for the triple squeeze better.

Maybe I can improve my chances for the squeeze, though. Suppose I lead the heart jack. If West has the queen, he will probably cover. Now all I need for the squeeze to work is for East to have both diamond honors and the heart ten. If West doesn't cover the jack, no harm done. I'll go up with the ace and play East for everything.

I lead the heart jack. West covers. Great! I take the ace, and East plays the four. 

Let's take stock now. How likely is the squeeze to work? If East is balanced, he needs at least the diamond king to come up to 12 HCP. Both diamond honors would bring him up to 14. Either is possible, so the squeeze isn't necessarily working even if East has the heart ten. But I now have another option. I can simply finesse West for the heart ten. I'll run the clubs first, then decide which line to take.

I lead a club to the queen. East plays the ten; West, the eight. Now a club back to dummy. West discards the diamond six. If I'm right about his holding five hearts, that gives West 2-5-4-2 and East 5-3-2-3. The doubleton diamond does not bode well for East's having both diamond honors. There are four ways for him to hold Kx but only one way to hold KQ. The diamond queen is four to one to be on my left.

I cash the nine of clubs, and East pitches the heart five. A good player might be stiffing his heart ten here. But I don't think my robot opponent would do that. I suspect the heart ten is onside. I pitch the five of diamonds. West pitches the heart six.

On dummy's last club, East pitches the four of diamonds. West, the nine of diamonds. If I've read the deal correctly, we are down to this position:

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

I lead a diamond. East plays the king. I take the ace and lead a heart to the nine. It holds. Making four.

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

Plus 430 is worth 86%. I thought it would be better, but quite a few players made four, which surprises me. It takes a bit of foresight to make four, and the field doesn't often have foresight.

It turns out at most tables, East, after taking the club ace, cashed the spade ace then shifted to the king of diamonds, making it easy to make four. Why was the defense so soft at the other tables?

Most other declarers won trick one with the spade queen. It shouldn't matter. Either way declarer knows I have the remaining honor after he cashes the ace, since West would unblock from honor-ten-nine. But robots don't draws inferences from the play. So my East must have thought his partner had the queen left. At the other tables, East thought it unlikely his partner had the king left, since that meant South had overcalled one notrump with queen doubleton of spades. Looking at no entries, they gave up on spades and shifted to the diamond king.

As declarer, I almost always try to play the card that is most apt to keep the defense in the dark. But that's lazy of me. Sometimes you don't want to keep the defense in the dark. Here, I would welcome any shift, so I should be advertising my spade strength, not trying to hide it. Winning with the spade queen at trick one is the correct play. By playing routinely, I made the deal harder for myself than it should have been.

Free Weekly Instant Tournament - January 18 - Board 8

Board 8
Neither side vulnerable

♠ --  ♥ A K Q 8  ♦ A J 10 8 7 3  ♣ A J 6

The auction begins one spade--pass--two spades to me.

I have two options. I can double, intending to follow with some number of diamonds if partner can't bid hearts. Or I can bid three diamonds, intending to double on the next round. As a general rule, you should time your auctions so that they end with double. That way, you aren't committed to offense. If you bid then double, partner can pass if the hand is a misfit. If you double then bid, partner doesn't have the option of defending. 

With this hand, however, there are problems with the bid-then-double approach. For one thing, if I bid three diamonds, I can't be sure of getting another chance to act. I may buy it in three diamonds cold for four hearts. For another, even if I do get a chance to double on the next round, we may still miss a heart fit. Partner may be worried I have only three hearts and may elect to support diamonds rather than bid a weak four-card heart suit.

I do have quite a good hand for offense: four losers and a good suit, so I'm not too worried about taking away partner's option to defend. I'll go for the double-then-bid approach.

I double, LHO passes, partner bids three clubs, and RHO bids three spades. I bid four diamonds as planned. To my surprise, LHO doubles. Everyone passes. and LHO leads the ten of hearts.

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

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

LHO probably has all the outstanding diamonds for his double. And RHO has four spades for his three-spade bid. So LHO is either 5-2-4-2 or 5-1-4-3. He probably would have led a spade from ace-king, so I'll assume East has a spade honor. With his diamond void, East doesn't need any other high cards. So West could have one or both club honors.

With the bad trump break, I have five losers, not four: three diamonds and two clubs. So I can't see making this. But if I can get West to break clubs for me, I'll avoid one of those losers and get out for down one.

I unblock the nine of hearts from dummy. East plays the deuce, and I win with the queen.

I need to ruff a heart in dummy, so I cash the heart ace. If West ruffs, I don't mind. It's with a natural trump trick. He doesn't ruff. He follows with the heart seven; East, with the five. So West is 5-2-4-2.

Now a low heart. West declines to ruff in front of dummy. He pitches the spade deuce instead. I ruff in dummy and lead a diamond. East shows out as expected, pitching the spade seven. I play the ten, losing the the queen. Here is the presumed position:

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

West can't afford to play a diamond or a club. So he perforce switches to a small spade, the three. I play the jack from dummy. East covers with the king, and I ruff. Now the seven of diamonds endplays West again. He wins with the nine as East discards the eight of clubs. We've reached this position:

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

Again, West can't afford a trump or a club, so he exits with the ace of spades. I ruff. Now ace and jack of diamonds endplays him a third time:

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

West must lead either a club, giving me a club trick, or a spade, giving me dummy's spade queen. He chooses a spade. I pitch one of my club losers on the spade queen and finish down one.

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

Most players in four diamonds doubled went down two. Some got higher. Minus 100 is worth 68%.

The reason this result isn't better is that some doubled two spades, then doubled again over three spades and played it there. That worked out fine this time, but it strikes me as an awfully dangerous way to live. We can argue about whether it's right to bid diamonds now or later, but not bidding them at all makes no sense to me. How can you expect partner to make an intelligent play-or-defend decision when you have good six-card suit you haven't told him about?

Be sure to play this week's Free Weekly Instant Tournament by Thursday. We can start comparing results next week.

Free Weekly Instant Tournament - January 18 - Board 7

Board 7
Both sides vulnerable

♠ A Q 4  ♥ 9 6 3  ♦ 10 8 6 3  ♣ A Q 5

I open with one diamond in first seat. Partner bids one heart and I rebid one notrump. Partner raises to two. Even though I have only 12 HCP, I do have three honor tricks, which is a maximum by some standards. Still, 4-3-3-3 is a minus, and I have no fitting card in partner's suit. So I suppose I should decline the invitation. I pass, and LHO leads the spade eight.

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

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

I can take three clubs, two spades, two hearts, and a diamond. Eight tricks unless the opponents can take six first. The spade eight looks like top of a doubleton. So I must duck the first spade to maximize the chance that I can keep the opponents from establishing and running the suit. The diamond suit does represent a danger. But that's the suit I opened, so it may be hard for the opponents to attack that suit.

I play low from dummy, East plays the king, and I duck. East continues with the six of spades. I win with the queen (the card West knows I hold) and West drops the jack. The jack? Apparently West led low from jack-ten-eight rather than top of his sequence.

I play the six of hearts, concealing the three, to dummy's king. West plays the four; East, the seven. If the club king is onside, I've made this. I can take three clubs and establish another heart for my eighth trick. What if the club king is offside?

Let's say I ride the jack of clubs and it loses to the king. West switches to a diamond. I duck one round and win the second round. Since clubs are blocked, I can cash only two club tricks, reaching this position:

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

I need three of the last five tricks. I lead a heart. The opponents win the heart ace, cash whatever diamonds they can, and I have the rest. If they can take only one more diamond trick, I've made my contract. If they can take two, I'm down one. If they can take three, I'm down two.

If I don't block the clubs, I can cash three club tricks, ensuring I can't go down more than one. Maybe floating the jack of clubs is a bad idea.

What happens if I lead a club to the queen? If the king is onside, it makes no difference. I can repeat the finesse later. If the queen loses to the king, I'm in good shape. The clubs are no longer blocked. I either make or go down one depending on what happens in diamonds. 

The problem comes if the king is offside and they duck. If I assume the king is onside, then I might find myself in some precarious predicament later on. But I don't think my robot opponent is up to ducking. If the club queen holds, I think I can safely assume East has the king. 

I wouldn't do this against opponents I trust. But I decide to play a club to the queen. East plays the deuce; West, the king. See? I told you he wouldn't duck.

West shifts to the four of diamonds. I duck in dummy. East takes the king, and I play the six to disguise whether West's four is low or high. East continues with the nine of diamonds--three--seven--ace. It appears West had QJ74 and East had K92.

If so I'm down. The defense has taken three tricks and can take three more when they get in. Maybe West started with five diamonds, QJ742, and East has the heart ace. That seems unlikely. Why would the defense set up the suit in the hand that has no entry? East probably has the long spade. If he had the heart ace and only one more diamond, he would have shifted back to spades after winning the diamond king.

Still, it doesn't hurt to try. If that's the layout, I don't need to knock out the heart ace early. I can cash all my tricks, reaching this position:

	NORTH Robot ♠ -- ♥ Q J 2 ♦ -- ♣ --
	SOUTH Phillip ♠ -- ♥ 9 ♦ 10 8 ♣ --

I need one more trick. If East has the heart ace and is out of diamonds, I can play a heart to the queen. East can win and cash a long spade, but he will have to concede a heart trick to dummy at the end.

I play a club to the ace and a club back to dummy. Both opponents follow. I cash the club ten, and East pitches the spade seven. That confirms my suspicion that the heart ace is on my left. East wouldn't be pitching his spade winner if he held the heart ace.

The ten-eight of diamonds may prove useful if I've misread the position. But my hearts are worthless. So I pitch the three of hearts. West pitches the heart eight.

I play a spade to my ace, reaching the above position. Both opponents follow. I exit with a heart. To my surprise, it's East, not West, who wins the trick. East then cashes the diamond jack and concedes a heart to dummy. Making two.

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

Plus 120 is worth 75%. The median result was passing it out. I briefly considered accepting partner's game try, and some thought this hand wasn't worth opening?

West played four, then seven from Q742 and the diamonds were blocked all along. It turns out I gave the defense a chance to beat me. Here was the position when I cashed the last club:

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

If I knock out the heart ace at this point, I take eight tricks thanks to the diamond blockage. When, instead, I cashed the last club, all East had to do to beat me was to pitch a loser instead of a winner. If he pitches a heart, my hand is squeezed. To hold my diamond stopper, I have to let go of a heart and now have no way to cash the heart once I establish it.

I didn't visualize the diamond blockage. I was mesmerized by the defense's carding and assumed West had the queen-jack or queen-jack-deuce of diamonds left. I should have gotten the end position right. I lucked out that East defended poorly.

This deal is a good example of how humans and robots make different kinds of mistakes. My mistake was making an assumption about the layout and forgetting that my assumption might be wrong. That's a very human mistake and a difficult one to avoid.

Most of what we think about when we play a deal is reconstructing the opponents' hands from clues. Sometimes our deductions are virtually certain; sometimes they are more speculative. It's easy to forget which ones are speculative and back off those assumptions when necessary. But robots don't have that problem. They don't play detective in the first place. So a robot would not have a blind spot in the above position and would easily find the heart play.

East's mistake was assuming I knew what I was doing. That's a very robot mistake. He could see that, if I played correctly, it made no difference whether he pitched a spade or a heart, so he chose one at random. Giving your opponent a losing option when he has a choice is something a robot doesn't even "think" about. A human, on the other hand, would see that the long spade might come in handy but the low heart could not and would be unlikely to make this mistake. 

Free Weekly Instant Tournament - January 18 - Board 6

Board 6
Opponents vulnerable

♠ Q 9 2  ♥ 8 7 2  ♦ A K J 9  ♣ K 5 4

RHO passes. I open with one diamond. Partner responds one spade, and I rebid one notrump. LHO chimes in with two clubs.

The tooltip confirms what I suspect: LHO has no idea what this auction means. He thinks it shows five or more clubs and ten or more HCP. He probably has a hand where he wanted to overcall on the previous round but he considered his hand flawed in some way. Possibly the suit quality is below standard.

This kind of bidding makes no sense at all. If you're going to make an overcall you consider unsound, why let the opponents exchange information first? Not only is it more dangerous to bid now than it was on the first round, it is also less productive. An immediate two club overcall would have taken the one level away from us. Passing allowed responder to get his suit into the auction cheaply and allowed me to limit my hand with a one-notrump rebid.

That's not to say this auction doesn't exist. But it should show at least a sound opening bid with primary diamonds and secondary clubs. Clubs might even be a four-card suit. Just because your opponent opened with one diamond doesn't mean diamonds isn't your side's best strain. And it can be hard to get there without the agreement that unsolicited belated actions show primary length in opener's suit. It is certainly a more useful agreement than playing that such actions announce to the opponents that you are making a questionable call.

Over two clubs, partner bids two spades and buys it. RHO leads the club queen.

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

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

Note that an immediate two club overcall would have worked much better. Partner would bid two spades, which I would raise to three. With his diamond fit, partner would probably decide to bid on and we would reach a hopeless game.

East plays the club three at trick one, and I win with the ace. I could play a diamond to dummy and take a heart pitch on the the club king. But the opening lead suggests East has seven clubs, and West's silence suggests East has at least two hearts as well. So the chance East has a singleton diamond is quite high. If he does, breaking diamonds may enable him to get two diamond ruffs when the defense takes the spade ace. I'll be trading one heart loser for two diamonds losers, which is not a good trade. On a bad day, East might even be void in diamonds. Then I could go down trying to take my pitch.

What if I play a spade instead? If West has the ace and ducks, I'm in dummy to take my pitch. Will he duck? Almost surely. He's not looking at my hand and doesn't know my problem. From his point of view, I might be intending to insert the spade nine, losing to East's jack. Or hopping might drop his partner's stiff king.

And even if the spade ace is offside, a spade lead doesn't necessarily cost. East may ask himself why I seemed uninterested in taking a pitch on the club king. He might conclude that his partner is the one with the singleton and might try to give West a club ruff rather than cash hearts. 

Since a spade will surely work if West has the spade ace and might work even if he doesn't, it looks like a better play than opening myself up to diamond ruffs.

I play a spade--eight--nine--ace. Will East play a club now? No. He cashes the heart king, then plays the queen. West overtakes with the ace to cash to jack. East doesn't let him cash it, however. He makes the good play of ruffing his partner's trick to lead a club. I ruff with the ten and claim. Making three.

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

Plus 140 is worth 46%. My first below average board in this set. East has a doubleton diamond, so I could have made four by crossing with a diamond to take my pitch, as some did. I stand by my choice, however. I think a spade at trick two is the better play, even though it was wrong this time.

Free Weekly Instant Tournament - January 18 - Board 5

Board 5
Our side vulnerable

♠ A 9 4  ♥ K 9 2  ♦ Q 8  ♣ A Q 8 6 3

Partner passes. RHO opens with one notrump, 15 to 17 HCP. Normally I would not double with only 15 HCP. But this is a "best-hand" tournament, so RHO is limited to 15 HCP as well. Should I double under these conditions? 

If my club suit were better, say AQ109x, I might double. But with such weak spots, I'm hesitant. If we can't run clubs, it may be hard to come to seven tricks. There is also the factor that my robot partner is no help on defense. Even if we can beat this, I'll have to figure out how all by myself. And even if I figure out how, I may have trouble getting partner to cooperate. Passing seems the wiser course. I pass, ending the auction, and lead the six of clubs.

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

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

Dummy has 5 HCP. Declarer is known to have 15. So partner must have exactly 5.

Declarer plays the jack of clubs from dummy--seven--four. Declarer would have ducked with the ten, so partner obviously began with ten doubleton. That makes it difficult to run the club suit. When I continue clubs, declarer can insert the nine, knowing that if this loses to partner's stiff ten, he will be unable to continue the suit. 

Declarer plays a heart from dummy. Partner plays the three; declarer, the queen. I have nothing urgent to do, so I see no reason to win this trick. Winning makes things easy for declarer. It not only establishes his suit, it also gives him a dummy entry with the heart jack. Ducking may be especially effective if declarer has the heart ten. He may then waste an entry repeating the finesse. There is, in fact, an excellent chance declarer does have the heart ten. Without it, he might just as well start hearts from his hand. So he might have found something better to do while in dummy. I play the heart deuce.

Declarer leads the deuce of diamonds from his hand. It could be right to duck. If declarer has ace-jack, hopping lets him hook partner for the king. If I duck, he may play partner for king-queen and lose a later finesse to my stiff queen. But it's not clear declarer has the flexibility to do that. After partner wins the king, I'm two to one to have the queen by restricted choice. Given his communication problems, declarer may elect not to take a finesse that's apt to fail. He might end up dropping my queen for lack of viable options. I may have a better chance at taking two diamond tricks if I hop and hope declarer uses his dummy entry to repeat the heart finesse.

Further, there is no guarantee declarer has ace-jack of diamonds. He might have king-jack and just be trying to set up tricks as best he can. If I duck and dummy's ten forces partner's ace, I'll certainly wish I had hopped.

I hop up with queen. Partner plays the seven. Can I place partner's high cards now? I assume he has the ace or king of diamonds. If he has the ace, he must hold exactly one jack to come to 5 HCP. If he has the king, he must hold either both missing jacks or the spade queen.

I might as well continue clubs. If I lead the club three, revealing my five-card suit, declarer will surely play the nine, as I noted previously. Perhaps if I lead the club eight, retaining the possibility that I began I with four clubs, declarer will play the king. If he plays the nine, he risks never taking a second club trick.

I lead the club eight. Declarer does rise with the king, and partner follows with the ten as expected. Declarer now, as I hoped, repeats the heart finesse. Five of hearts--eight--ten--king.

Can I deduce declarer's heart length? With AQ10 tight, he would have led the heart jack at trick two, so he must have four or five. Leading low twice make sense with AQ10x, since it guards against a doubleton king onside. If the finesse works, he can afford the jack on the first round only if the suit is three-three. What about AQ10xx? Low the first time, guarding against a stiff king onside, is the right play in isolation. But a stiff king is unlikely, and, given declarer's shortage of dummy entries, catering to it might be a luxury he can't afford. I suspect he would have led the jack with five hearts, enabling him to repeat the finesse. So I'll tentatively assume he has four.

Here is the current position:

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

Three clubs, a diamond, a heart, and the spade ace bring us up to six tricks. If partner has the diamond ace, declarer is down. So I'll assume partner has the king. When I run clubs, declarer must come down to five cards. What will they be?

If partner has the spade queen, declarer will come down to

♠ K J  ♥ A x  ♦ A  ♣ --

I'll exit with a heart. Declarer will win in dummy and must guess the spades to make his contract. He should guess right. If partner had the spade ace, I would exit with a diamond, setting up a diamond trick for partner while he still had an entry.

If partner has both jacks, declarer will come down to

♠ K Q  ♥ A x  ♦ A  ♣ --

Now we have no defense. So it appears I must hope partner has the diamond ace or that he has the diamond king and spade queen and declarer misplays.

I cash the ace of clubs. Partner discards the heart six, confirming my assumption that declarer has four hearts. Declarer pitches the spade deuce.

On the club queen, partner discards the spade six; declarer, the diamond five. Since this is partner's first spade, it is probably count, given the robots' proclivities. That means partner has four spades, giving declarer 3-4-4-2. Declarer is now down to two spades, two hearts, and ace-jack or king-jack of diamonds.

On the last club, partner discards the spade three; declarer, the king of diamonds. So declarer had king-jack of diamonds, which leaves him with king-queen of spades. This must be the position:

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

Dummy's diamond ten saved declarer from being squeezed. There is no way to take anything other than our two aces. I exit with a heart to dummy's jack. Declarer leads a spade to the king and my ace. I play a diamond to partner's ace. Down one.

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

Plus 50 is worth 86%. Continuing with the eight of clubs rather than the three proved to be critical. Everyone who continued with the three saw declarer insert the nine. The defense is much better placed if declarer rises with the club king, and he has no reason to do that if he knows you began with five clubs. 

Although it turned out not to matter, I might have defended a little better. Let's consider again the case where partner has the diamond king and the spade queen. As I said earlier, if I run clubs, declarer comes down to:

♠ K J  ♥ A x  ♦ A  ♣ --

When I exit with a heart, he wins in dummy and must the guess the spades, which he should "guess" correctly.

But what if the jack of hearts wasn't in dummy? If my heart exit tosses declarer back in his hand, he's down. So I would like declarer to lead the heart jack from dummy when he takes the second finesse. Let's back up to that point. Here is the imagined position, with the lead in dummy:

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

As the play went, a low heart now, guarding against king doubleton onside, is the correct play. And declarer should then make his contract. But what if  I had played the nine rather than the deuce when I ducked? Now it's reasonable for declarer to lead the jack for the second finesse, playing me for nine-eight doubleton. If he does lead the jack, then I can win with the king, run my clubs, and exit with a heart, forcing declarer to lead spades from his hand for down one.

Obviously at the time I ducked the heart king, I didn't know enough about the layout to see how playing the nine might gain. But I think I should have found the play anyway on general principles. The falsecard of the nine frequently gives declarer extra options. So long as these aren't winning options, gratuitously playing the nine is often a good idea. All I had to do was follow Michael Rosenberg's rule: "Always play the nine unless you have to."