Free Weekly Instant Tournament - July 5 - Board 2

Board 2
Neither side vulnerable

♠ A K 10 8 5 2  ♥ 6  ♦ Q 7 5  ♣ A K Q

RHO opens with two hearts, weak. The usual rule in bidding over a pre-empt is that you place partner with 8 HCP and bid accordingly. By that standard, I should be driving to game. I might make four spades opposite as little as a doubleton spade and king-jack of diamonds. Unfortunately my suit isn't good enough to blast four spades, and I have no convenient way to set up a force and investigate. My best choice is probably three spades. It's an underbid. But it's justified because the suit is poor. At least partner knows I have six of them and a good hand. He doesn't need much of an excuse to raise.

I bid three spades, and partner bids four diamonds. Is this bid natural? Some would argue that three spades set the trump suit, so four diamonds is a cue-bid in support of spades. Others would argue that, while three spades shows a good suit, other strains are still possible, so four diamonds suggests diamonds may be a better spot than spades.

Marty Bergen once told me that he plays that, if partner has bid a suit, you can't introduce a minor at the four level except in auctions that begin with two clubs. At least I think that's what he told me. It was a long time ago. So presumably Marty would play this as a cue-bid.

Edgar Kaplan did not agree with this approach. He liked being able to bid his suits. Even in an auction like

1 ♠	1 NT
3 ♠	4 ♦

Edgar played four diamonds as natural. I suspect most experts would play it as a cue-bid.

My own agreements are in between these two extremes. My partnership notebook states that you can't introduce a minor at the four-level if you have previously bid notrump. Thus I would play four diamonds in the previous auction as a cue-bid, but in the auction

1 ♥	1 ♠
3 ♥	4 ♦

I would play it as natural.

The idea is that if you wanted to bid diamonds on the latter auction, it's your own fault. You had your chance and you blew it.

Fortunately, playing with robots, we don't have to guess how partner intends four diamonds. If we ask, he'll tell us. And he intends it as natural.

So what could partner have? A stiff spade and ace-king sixth of diamonds seems like a likely hand. Opposite that we belong in slam. If I had to place the contract, I would probably bid six diamonds. But there is no reason not to bid Blackwood on the way. If partner has only one keycard, we can stop in five diamonds.

I bid four notrump, and partner bids five diamonds. Oh, well. Glad I checked. I pass. RHO leads the king of hearts.

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

West	North	East	South
Robot	Phillip	Robot	Robot
2 ♥	3 ♠	Pass	4 ♦
Pass	4 NT	Pass	5 ♦
(All pass)

Nicely done, partner. I suppose. I might have passed three spades with your hand. If you don't catch a diamond fit, we are propelled too high. I'm glad we were sitting in the right seats.

East plays the heart seven at trick one, and I follow with the deuce. West's best defense is to tap dummy with a heart. Now, with two heart losers exposed, I can't afford to draw trump. Cashing the ace and king of spades, pitching my hearts, will work so long as West doesn't have a stiff spade. Is there anything I can do if he does?

It depends on what heart East follows with at trick two. If he plays the queen (or lower), then West, with ace-king-jack of hearts, can't have the diamond ace. And East is out of hearts. So there is no need to take my pitches immediately. I can just draw trump and take them later.

What if East follows with the heart ace at trick two? Personally, I would open one heart with king-queen-jack sixth of hearts and a side ace. But I suspect the robots would open two, so I can't afford to play two rounds of trumps. Can I play one round? Suppose I play a low diamond from dummy to my ten. If either opponent takes the ace or if West shows out, I have no further problems. What if my ten holds? Then I've reached this position:

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

I can't afford to play another trump. So I must play a club to dummy, take my pitches on the ace and king of spades, then lead another diamond. Have I gained anything? I gain if  West holds

♠ x  ♥ K Q J x x x  ♦ A x  ♣ x x x x

since he would be ruffing the second spade with his trump ace. I don't see any downside to playing one round of trumps, so that's my plan.

My plan proves unnecessary, however. At trick two, West shifts to the six of diamonds. East takes the ace and continues diamonds, and I claim.

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

Making five diamonds is worth 85%. Quite a few players bid two spades over two hearts and played it there. Of those two bid three spades and heard partner bid four diamonds, no one else bid Blackwood. Most simply raised to five diamonds, which seems awfully pessimistic. As I said earlier, if I were barred from bidding Blackwood, I would raise to six, not five.

One person stubbornly persisted with four spades over four diamonds and went down two. (You realize you still get to play the hand even if partner is declarer, right?)

After I posted this, some suggested I should have doubled two hearts rather than bid three spades. I didn’t address that earlier, because I didn’t consider that a possibility. With a one-suited, one generally tries to get his suit into the auction as early as possible before the auction gets uncomfortably high. Sometimes one must, regrettably, double a one-bid with a strong one-suiter, since there is no other option. But there is no reason to double a pre-empt with a one-suiter. Since jumps are strong, you can simply bid your suit at whatever level you deem appropriate. Doubles of pre-empts should always show flexible hands. Accordingly, if you do double and bid spades, partner should not play you for a suit this good. He should play you for a five-card spade suit with playability in other strains.

Free Weekly Instant Tournament - July 5 - Board 1

Board 1
Neither side vulnerable

♠ 9  ♥ A 5 4  ♦ A J 10 7  ♣ A K 8 6 4

Partner passes. RHO opens with one notrump, showing 15-17 HCP. I have enough strength to double, but doubling is unattractive with a stiff spade. Partner will expect a balanced hand and will not hesitate to bid a five-card spade suit, either pulling the double if he is weak or competing if the opponents run.

You might risk doubling with a stiff spade if you have a self-sufficient suit to correct to. But encouraging partner to bid your singleton with a "5431" is not a good idea, especially when you have perfectly fine way to handle this hand: Pass, intending to double for takeout if the opponents bid spades. If the opponents don't bid spades, there is a good chance the hand is a misfit and you don't want to be in the auction anyway. 

If you play Astro, then this sequence has the additional advantage that partner will expect you to be 1-3-4-5 or 1-3-5-4, since with a 1-4-x-y pattern, you would have bid two clubs on the first round. (The robots don't play Astro. And it's probably just as well. It's too sophisticated for them.)

I pass. LHO transfers but not to the suit I was expecting. He bids two diamonds, and RHO bids two hearts. It's now highly likely partner has a spade suit, which means our hands are better suited for defense than for offense. I pass again, and two hearts ends the auction.

Some say you should never have an ace-king and fail to lead it. But I see no reason to lead a high club with this hand. I have control of all suits, so the club tricks aren't going anywhere. And if dummy has a stiff club, a club lead may kill my only entry to partner's hand for a spade ruff. So I lead my stiff spade.

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

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

Dummy and I have 22 HCP. Declarer's 15 means partner has at most three. If partner has either the heart king or the diamond king, we can take five top tricks and a spade ruff to beat this.

Declarer plays the jack of spades from dummy. Partner plays the three; declarer, the six. I'm glad partner didn't have the spade queen. That means it's still possible he has a red king. If he doesn't, he might have the club queen. In that case, we can't beat it, but I can underlead to his queen and get a spade ruff to stop the overtrick.

Declarer leads the six of hearts from dummy--seven--eight. Is declarer finessing against the heart jack with king-eight doubleton? That would be weird. The normal way to play that suit is to play low to the king, then finesse the other way. There is no reason to lose a first-round finesse to a stiff jack.

If declarer has king-jack-eight, I could duck and hope to see an informative card from partner when I hop with the ace on the next round. But I would be crashing partner's king if declarer has only jack-eight. I can't take that risk. I have to win the ace now.

My robot partner isn't much for signaling. But I suspect he's up to dropping the club queen under the king if he has queen-jack. I cash the king of clubs--three--five--deuce. So no queen-jack of clubs. We've reached this position with me on lead:

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

Partner can have the club queen or either red king. I don't see how it's possible to cater to all three possibilities. But maybe I can cater to two of them. I can try to reach partner with the diamond king and wait for him to get in with the heart king if that doesn't work.

How do I do that exactly? Suppose I lead ace and a diamond. No, that doesn't work. If declarer has king-queen of diamonds, I'll lose my club ace.

How about ace of clubs, then ace and a diamond? No, that doesn't work either. If declarer has, for example,

♠ A Q x x  ♥ J 8  ♦ K Q x x  ♣ Q J x

he can pitch both of dummy's spades and stop the ruff.

I think I have to underlead the ace of diamonds. That way partner gets in in time to give me my ruff no matter which red king he has. The problem with underleading is that if partner has neither red king, I may lose the diamond ace. Declarer can draw trump and pitch dummy's diamond on his fourth spade.

Nonetheless, I think it's worth the risk. Some people will bid with my hand, so this may not be a normal contract. Going plus is probably more important than holding the overtrick.

Is there any reason not to cash the club ace before I underlead? Not that I can see. Declarer can't pitch both of dummy's spades away on clubs. Even if he has queen-jack fourth of clubs, partner will be ruffing the first club with his heart king.

I cash the club ace--ten--jack--seven. The club jack? Partner is limited to three HCP, so he can't have the diamond king any more. Good thing I cashed the club ace. Now I know not to underlead. I play ace and another diamond. Making three.

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

Minus 140 is worth 36%. Those who acted with my hand did better. Some overcalled one notrump with two notrump, presumably showing five-five or better in the minors. I don't like that bid at all. You have too much defense to distort your pattern and risk going minus in a silly contract. The time to make a flaky bid is when you have a bad hand, not a good hand.

Others doubled and pulled partner's two-spade bid to three clubs. Partner conveniently had a second suit and conveniently chose to bid it (which is hardly clear, since West could, and probably should, have six or seven clubs for this auction). Three diamonds typically made five.

I think the doublers lucked out. Passing and hoping to double two spades offers your best chance to get to the right spot.

Free Weekly Instant Tournament - May 10 - Board 8

Board 8
Neither side vulnerable

♠ A 8 5  ♥ K J 4  ♦ K 7  ♣ A J 10 3 2

Partner opens with one diamond in second seat. I bid two clubs, game forcing, and partner rebids two diamonds. This bid does not promise a six-card suit in the robots' methods.

Three notrump should show about 16-17 HCP, a hand with mild slam interest but not enough to bid past game. Fast arrival can't apply here, because responder must be free to bid two notrump with a minimum to leave room for investigating other strains. The robots don't play this way, however. They appear to make no distinction between two notrump and three notrump.

If three notrump doesn't show mild slam interest, then there is no reason to bid it. I bid two notrump to give partner the opportunity to describe his hand. Partner, not one to squander an opportunity, bids three diamonds.

Is this a slam try? Would partner have just raised to three notrump with no slam ambitions? As a general rule, finding the right strain takes precedence over slam bidding. Until proven otherwise, we should assume partner is simply concerned that three notrump is the wrong game. He could easily have a minimum opening. So where do we stand?

To express doubt about three notrump, partner should have a singleton somewhere. And his singleton is probably in a major, since shortness in the suit I bid is of no particular concern. If he does have a major-suit singleton, he is likely either 4-1-6-2 or 1-4-6-2, since he didn't support clubs.

Why not bid his four-card major with those patterns? He should if his diamonds are weak. But if they are playable opposite a doubleton, I think three diamonds is a better choice. If we belong in a diamond slam, it will be hard to get there if partner doesn't confirm a good suit now.

It would be nice to know where partner's singleton is. If it's in spades, our hands fit quite well. Opposite as little as 

♠ x  ♥ Q 10 x x  ♦ A Q J x x x  ♣ K x

slam is virtually cold.

The best bid at this point is three hearts. This is, in essence, an anti-Bluhmer, saying, "I have stuff in hearts. If your singleton is in hearts, I've got you covered. If it's in spades, three notrump is probably the wrong contract."

I know some will say it's a waste of time to try to have a sophisticated auction with a robot. But spades is the only suit we haven't bid. How sophisticated does partner have to be to bid notrump if he has good spades and something else if he doesn't? Besides, the alternative is to give up and bid a unilateral three notrump. That seems too defeatist to me. We could easily have a slam if partner has spade shortness, so I have to make some attempt to get there.

I bid three hearts, and partner bids four hearts. The tooltip says this shows a four-card suit, presumably suggesting a final contract. If partner thinks a four-three heart fit is a better spot than three notrump, the inference that he holds a singleton spade is pretty strong. So six diamonds looks like a good bet. I bid six diamonds. Everyone passes, and RHO leads the deuce of hearts.

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

West	North	East	South
Robot	Phillip	Robot	Robot
		Pass	1 ♦
Pass	2 ♣	Pass	2 ♦
Pass	2 NT	Pass	3 ♦
Pass	3 ♥	Pass	4 ♥
Pass	6 ♦	(All pass)

I wouldn't have been so cavalier about bidding past three notrump with partner's hand. Over responder's three hearts, three spades gets the message across: "I know you're worried about spades. My spades aren't good enough to bid three notrump, but I do have some help there." With the black suits reversed, partner would be fully justified in spurning three notrump, and six diamonds would be a fine contract.

Even opposite this hand, slam is quite good on the expected spade lead. If West leads from the king, the contract is almost cold. If East has the king, I can make it if the heart queen is onside with some chances if it isn't.

The actual heart lead isn't so friendly, but at least it reveals that the heart finesse isn't working. West surely isn't leading from the heart queen in a suit we've bid and raised. He probably has three or four small. In the latter case, the queen is dropping, so I have three cashing heart tricks. In the former case, I have three tricks after I lose one. I Either way, that brings me up to eleven tricks. For a twelfth, I need to set up a long club or possibly execute a black-suit squeeze against West.

I need the heart king as an entry to ruff out clubs, so I play low from dummy and win with the ace. East contributes the ten. Now a club to the five, ace, and eight and a low club from dummy. If East has the king, he may hop. A human East would know I can't have queen doubleton when I didn't take a finesse, but robots don't draw inferences like that. If East hops with the king, then all I need is four-three clubs. I can draw trump, cross to the spade ace, and lead the jack of clubs, pitching my spade. Then I have two clubs tricks for heart pitches.

No such luck. East plays the nine on dummy's club lead. I ruff, and West follows with the seven. I play the six of diamonds--three--king--eight and another club from dummy. East plays the king. I ruff, and West follows with the four.

We've reached this position, with the club queen still outstanding:

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

I might as well test diamonds. If diamonds don't break, I can't afford to ruff the last club. I cash the diamond ace. Both opponents follow.

If West led from four small hearts, I'm home. I'll draw the last trump, lead a heart to the king, dropping East's queen, then ruff out the club queen for my twelfth trick. If West led from three small hearts, I'll need some luck. When the heart queen fails to drop, I'll find myself in this position with the lead in dummy:

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

After I ruff out the club queen, East is down to the heart queen and three spades. If he has the spade king, I'm home. I exit with a heart, and he must give me an entry with the spade queen to cash the last heart. 

I don't see anything better. I need to hope that the heart queen drops or that East has the spade king. I draw the last trump, pitching a spade from dummy. West follows, and East pitches the nine of hearts. 

The nine of hearts? Time to rethink my construction. East isn't stiffing his queen. It appears West didn't lead from heart length. The deuce must have been a singleton. I need a new plan.

What's West's shape? If he has the last club, he's 5-1-3-4. If that's the case, I can play a heart to the king, then lead the club jack, pitching a heart. When West wins, he has only spades left. If he has the king, he's endplayed. I'll take two spades and can pitch my last heart on the club ten.

I like my chances. East is five to three to have the spade king a priori, and the fact that he didn't lead a spade on an auction that screamed for it makes it even more likely he has the king.

I play a heart. West pitches the spade deuce. I win in dummy, reaching the position above. I lead the jack of clubs. East pitches the spade four. I pitch a heart, and West wins with the queen.

West switches to the jack of spades. I duck in dummy. Annoyingly, East wins with the king and cashes the queen of hearts. Down two.

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

So close. Minus 100, as you might expect, is a zero. Most players bid an unimaginative three notrump over two diamonds and played there. I certainly don't mind reaching this slam. It had excellent chances right up to the end. Sometimes luck isn't on your side.

Free Weekly Instant Tournament - May 10 - Board 7

Board 7
Both sides vulnerable

♠ A 3  ♥ A J 9 6 4 2  ♦ K Q 10 8  ♣ Q

I open in first seat with one heart. Partner bids one spade. I rebid two diamonds, and partner bids two notrump.

Three hearts by me should be forcing. If I were six-four in the red suits with a bad hand, I would rebid two hearts over one notrump, then remove two notrump to three diamonds. Bidding two diamond then rebidding hearts, sometimes referred to as an ABA sequence, should be forcing. Unfortunately, as I've discovered in the past, the robots don't understand this. To ensure we reach game, I have to guess whether to bid four hearts or three notrump. Four hearts risks catching partner with a singleton heart. But if we can't set up hearts, we may be unable to find nine tricks in notrump anyway. So I guess to bid four hearts.

Four hearts ends the auction, and West leads the four of clubs.

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

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

Partner does have a singleton heart, but at least it's the queen. It appears I will lose a club trick, possibly a spade, and one or two trump tricks. Can I pitch my spade loser on the club king? I can if East doesn't shift to a spade at trick two. But if he does, I have a problem. I must decide whether to duck, hoping East has shifted from the king, or to hop and cross to dummy with a diamond to take my pitch. The latter risks setting up a diamond ruff for the opponents when they win the heart king.

Maybe I won't have to make that decision. If East has ace-jack of clubs, he may insert the jack at trick one and let me score my stiff queen. I play low from dummy. East, unfortunately, takes the ace. The good news is he shifts to the king of spades, solving my problem. I take the ace, and West follows with the five.

There is no lie of the trump suit where I can take all the tricks. Even if East has king-ten doubleton, I will still lose a slow heart trick to West. So there is nothing to gain by finessing. I might as well lead a low heart to the queen and hope the ten drops in three rounds. If so, I'll make five. If not, I'll make four.

I lead the heart deuce. West hops with the king, and East follows with the seven. West shifts to the four of diamonds. I win in my hand with the king and cash the ace and jack of hearts. The ten doesn't drop, so I make four.

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

Plus 620 is worth 86%. Some guessed to bid three notrump rather than four hearts. With help in both black suits, that's not an unreasonable choice, but it didn't work out here. Three notrump makes only three.

What is an unreasonable choice is the way some declarers played four hearts. They crossed with a diamond to take a pointless heart finesse. When the finesse lost, East scored a diamond ruff for down one. As we said earlier, the finesse can't gain. There is no reason not to lead a low heart from your hand.

I'm still not sure what East's shift to the spade king was all about. A low spade would beat me if I hopped with the ace. Perhaps East was worried I had a stiff jack and leading a low spade would set up a ruffing finesse against his king. But so what? Even if that happens, I'm pitching a winner. 

The only thing I can think of is that East wanted to retain the lead to make sure the defense played a second spade. He was afraid if he led a spade to his partner's ace, his partner would find something else to do, like try to give him a diamond ruff. But unless the robots have been given a major upgrade lately, they don't worry about solving problems for partner, so I doubt that's it. Robots need a verbose mode, where they explain what they were "thinking."

If East does shift to a low spade at trick two, what should I do? Ducking always works if East has the spade king. Hopping might or might not work if West has it. A priori, it's fifty-fifty who has it, so if I think the location of the spade king has no bearing on East's decision to shift, the percentage play is to duck. If I think it has some bearing but isn't necessarily determinative, then I have a much harder problem.

If East has the spade king, then, from his point of view, his partner might have the ace, which could make the shift necessary. And since I'm known to have at most three black cards, a shift from the king can't cost. So I see no reason why East should be reluctant to shift from the king. Accordingly, ducking appears to be my percentage play.

But we now know that it isn't. For whatever reason, East thinks he's supposed to shift to spade king when he has it. So if he leads low, he doesn't have it. Of course, I had no way of knowing that at the time. So if East had shifted to a low spade, I suspect I would have mistakenly ducked.

Free Weekly Instant Tournament - May 10 - Board 6

Board 6
Opponents vulnerable

♠ A Q 8  ♥ A 4  ♦ A K 8 5 3  ♣ K 6 2

I open with two notrump (20-21 HCP) in second seat. Partner raises to three. Everyone passes, and LHO leads the four of diamonds.

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

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

I have nine top tricks. The best place to try for more is in the club suit. If clubs break and RHO has the queen or jack, I can float the ten of clubs, then reach dummy and finesse again to set up the suit. I lose only two club tricks and make five.

The problem with this line is the West may shift to a heart when he wins the club. Now what? I doubt my robot opponent will shift from the king (though a crafty human might). So if he does shift, my best shot is to play low, hoping East has KJx or K10x or chooses to play the jack from KJ8. If I don't get lucky in the heart suit, I still have the chance that East has the club ace and West can't get in to continue hearts. I make four if any of these chances pans out; I might go down if they don't.

Alternatively, I could just play a club to the king. If the ace is onside, I make four, and I don't risk going down. Which play is better? 

If the club ace is on my right, floating the ten makes four if West shifts to a heart and five if he doesn't (unless West has a stiff queen or jack). So it always works at least as well as a club to the king and sometimes works better.

If the club king is on my left, a club to the king might work better. But it requires a parlay: West would need to find a heart shift, and the lie of the heart suit would have to be unfavorable. It's weird that a club to the king is the better play only when it loses, isn't it?

All in all, I would have to be quite unlucky to regret floating the club ten, so that's that line I'll choose. 

The four is the lowest outstanding diamond, so West can't have all five of them. It's safe to play the queen from dummy. I do so, as East follows with the seven. Now ten of clubs--four--deuce--ace. Well! That was a success. I'm making at least four now.

West continues with the ten of diamonds. I win with dummy's jack, and East discards the spade six. The robots discard count cards, so it appears East has an even number of spades. 

If clubs split, I'm making five. I lead the club nine, and East covers with the jack. I take the king, and West discards the eight of heart, presumably from an even number.

This is the current position:

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

East has queen-seven of clubs over dummy's eight, so the club suit is dead. My only chance for a second overtrick now is to score the heart queen.

What is the layout? I know East has an even number of spades and West has an even number of hearts. East could be 4-4-1-4, making West 4-4-4-1. But would West discard from a four-card heart suit when he had a safe diamond pitch? He might if he had the king. If he doesn't have the king, then he probably has six hearts. That would make East 6-2-1-4 and West 2-6-4-1. In normal circumstances, I would consider the latter construction unlikely, since West didn't lead a heart. But robots don't believe in fourth from longest and strongest, so I can't rule it out.

So what's next? I have two ways to score the heart queen: 

(1) If West has the heart king, I can simply lead a low heart toward the queen.

(2) If East has the heart king, I can cash my winners, coming down to this position:

	NORTH Robot ♠ -- ♥ Q 9 ♦ -- ♣ 8
	SOUTH Phillip ♠ -- ♥ A 4 ♦ -- ♣ 6

East must either stiff the heart king or come down to two hearts and the queen of clubs. In the latter case, I toss him in.

In essence, I have a two-way finesse against the king of hearts. Unfortunately, I must make up my mind now. If I run diamonds to get more information, I can no longer lead toward the heart queen without cashing the ace first. If I do, West can hop and lead a spade, tangling my communication.

So who is more likely to have the heart king? I already decided that if West is 4-4-4-1, he probably has it, else he would have pitched a diamond. And if he's 2-6-4-1, he is six-to-two to have it a priori. So a heart toward the queen is clearly the percentage play. Too bad. Endplays are more fun than finesses. But that's the way it is.

I lead the four of hearts--deuce--queen--king. Making four.

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

Plus 430 is worth 79%. I would have scored 100% had I gone for the endplay, but it's a clear error to do so. The heart king is three to one to be on my left on the actual layout, and would be close to 100% if hearts were four-four.

Free Weekly Instant Tournament - May 10 - Board 5

Board 5
Our side vulnerable

♠ K Q J 9  ♥ 9 7 6 3  ♦ A K J 5  ♣ A

Two passes to me. I open with one diamond. Partner bids one spade, and RHO bids one notrump, showing at least five-five in the unbid suits.

With five losers, I have enough to drive to game. Some avoid splintering with a singleton ace, but that's less important when the splinter is in an opponent's suit. In that case, the ace is less likely to be useful to partner, and your shortness may be the key to getting to slam. So I bid four clubs.

LHO doubles, and partner bids four spades. I have nothing more to say. Everyone passes, and West leads the king of hearts.

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

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

If you didn't play in this tournament, stop now and plan the play. See if you can do better than nine of the other twelve declarers.

Partner has more club wastage than I expected, given the double of four clubs. Even so my only certain loser is the spade ace. I could make six if trumps split. But, since West should have a singleton in one pointed suit or the other, it's quite possible they won't.

Let's assume for the moment that East has ace-ten fourth of spades. Can I hold him to his two trump tricks and make five? Say I ruff the opening lead, lead a club to the ace, ruff another heart, then cash the king and queen of clubs, disposing of dummy's hearts. When I lead a trump to the king, East will duck, and I'll find myself in this position:

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

Now I'm in trouble. East will win the next trump and tap dummy with a heart, and I've lost control. I'll score dummy's trump and, assuming diamonds are two-two, two diamond tricks. But East will ruff the third diamond and cash a heart, holding me to four.

To maintain control, I must have a trump left in my hand when East takes his spade ace. So ruffing the second heart is a mistake. Let's try at a different line. 

Suppose I ruff the opening lead and lead a spade to the king. East ducks. Now I unblock the club ace. We've reached this position:

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

If I lead a second spade, what can East do? If he wins and leads a third trump to stop the ruff, I take the rest. I don't actually need the second ruff. I have enough pitches to take care of dummy's three hearts.

If East wins and leads, say a diamond, I win in dummy, ruff a heart, and pitch dummy's remaining hearts on the king and queen of clubs. Now I can just lead diamonds until East ruffs in with his natural trump trick. Making five.

What if East ducks the second round of spades? Now I can abandon trumps. I ruff a heart and cash winners. East can score his two trump tricks whenever he wants, but that's all he gets. Again, making five.

And what if trumps were three-two all along? If the defense wins the second spade, I have the rest whatever they return. And if they duck, I can run winners until they ruff in with the spade ace. Either way, I make six.

So, while ruffing a second heart may feel natural, it's a mistake. It gains nothing if trumps break and loses a trick if they don't break.

I ruff the opening lead in my hand and lead a spade--six--king--eight. Now the club ace--three--deuce--four. We've reached the position above. I lead the spade queen. East takes the ace, and West discards the five of hearts. East chooses to exit with the queen of hearts. I ruff in my hand, cash two clubs, and claim eleven tricks.

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

I like this deal because it involves no esoteric technique. There are no squeezes or throw-ins. All you have to do is think ahead a little bit and consider what might happen if you take your tricks in the wrong order. Still, that's apparently harder than it looks. Quite a few ruffed a second heart too early and held themselves to four. So plus 650 is worth 89%.

Free Weekly Instant Tournament - May 10 - Board 4

Board 4
Both sides vulnerable

♠ A K 9 5 4  ♥ A 8 7  ♦ A Q 10 9  ♣ 6

One club--pass--pass to me. I'm sure some will start with a double. But unless you have a very offensively oriented hand, you should try to end your sequences with double. If you start with one spade then double when the opponents bid more clubs, partner has the option of defending. If you double first, then bid spades, partner doesn't have that option.

I bid one spade. Partner raises to three spades, which the tooltip says shows four spades and seven to nine total points. So it's pre-emptive? That makes no sense. If responder couldn't bid at the one-level, why are we worried about his bidding at the three-level? Pre-emptive raises are unnecessary after a balancing overcall. You should simply raise to whatever level your hand is worth.

But I have no say in the robots' methods, so I have to deal with partner's determination to silence RHO once and for all. Fortunately, I have a good enough hand that partner's depriving me of a game try makes no difference. I have five losers and a clear four-spade bid.

I bid four spades, which ends the auction. LHO leads the king of clubs.

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

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

I'm losing at most a club, a heart, and a spade. If spades come home and the heart king is onside, I could make six.

What do I know about the layout? I know that East has at most 5 HCP. Even so, he might have raised to three clubs pre-emptively with five-card support. So there is some inference that West has at least six clubs.

East plays the club three, and West continues with the ace of clubs. East plays the jack, and I ruff. I'll assume the jack is an honest card and West has the club queen.

I cash the ace of spades--deuce--three--seven. In a vacuum, playing for the drop in spades is slightly better than taking a finesse. But it doesn't take much to sway the odds. Is my assumption that West has at least six clubs enough?

It's true this inference isn't 100%, since East won't always bid three clubs with five. But, just for drill, let's say it is 100%. Would that be enough to tip the odds?

A common method for making such decisions is to consider vacant spaces. In general, I'm not a fan of vacant spaces. It's a flawed approach and in some cases can give significantly incorrect answers.¹ But it does have the advantage of being easy to use. And in this particular case its shortcomings won't be an issue, so let's give it a try.

If I lead a diamond to dummy, lead the jack of spades, and East follows, then I will know eight of West's cards: six clubs, one diamond, and one spade. That leaves him with five vacant spaces. I'll assume we would have heard from West again if he had eight clubs, so East must have at least three. That means I know six of East's cards: three clubs, a diamond, and two spades, leaving him with seven vacant spaces. So East is seven to five to hold the spade queen.

But distribution isn't the only consideration here. We also know that East is limited to 5 HCP, and he has already shown up with the club jack. While this doesn't preclude East's holding the spade queen, it does make it less likely.

How do we take this factor into account? There is a variety of ways to do this. But so long as we are using vacant spaces for distribution, let's use it for honors as well. There are two significant honors outstanding: the heart king and the spade queen. East can hold at most one of them; West can hold both. So East has one "vacant honor space," and West has two. That makes it roughly two to one that West holds any specific honor. That's more than enough to offset the distribution inference, so playing for the drop is the percentage play.

I cash the spade king--eight--jack--queen. East has the club jack and the spade queen, so the heart king must be offside. Still, I have nothing to lose by leading the heart queen from dummy, even though I have no intention of finessing. I play the ten of diamonds to the king. East drops the jack.

What's going on? Why is East going out of his way to show me these minor-suit jacks? He didn't have to show me either one. It's almost as if he wants to make sure I cash the heart ace. Could his pass of one club be a psych? If Lowenthal were on my right, I would consider taking the heart finesse. But robots aren't that devious. I lead the queen of hearts--three--ace--king. Making six.

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

Plus 680 is worth 100%! Really? I'm the only one to drop the heart king?

East's club jack at trick two was a careless play. I never would have dropped the heart king if East had concealed both his jacks. But East made the same play at every table, so I'm not sure why everyone else finessed. Perhaps they didn't notice the club jack? Sometimes it can be hard to pay attention when the hand looks routine.

The "vacant honor spaces" analysis is an interesting approach, isn't it? It's not well known. And rightly so, because it doesn't work. There are some specific cases where it does give the right answer, and this is one of them. But, sadly, it doesn't generalize. Still, like regular vacant spaces, it's easy to use and it gives at least an approximation of the correct odds. Sometimes that's good enough.

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¹See The Vacant Spaces Trap for a discussion of the method's flaws.