Free Weekly Instant Tournament - October 13 - Board 2

Board 2
Our side vulnerable

♠ K Q 6 3  ♥ A 8 7  ♦ K 10 4  ♣ A K 8

RHO passes. I bid one club and partner responds with one heart. I rebid two notrump, showing 18 to 19 HCP balanced, and partner raises to three. LHO leads the deuce of spades.

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

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

West appears to have three or four spades. What should I play from dummy at trick one? 

A lead from ace-jack third would be unusual, so I'll assume West doesn't have that. I'll also assume East will play the ace if he has it, rendering my choice at trick one immaterial. (If I decide to play the seven and East finds the eight from ace-eight third, I'll start holding my cards back.)

Under those assumptions, these are the only layouts I can think of where my play matters:

(A) ♠ AJxx	♠ 8x
(B) ♠ A8xx	♠ Jx
(C) ♠ Axxx	♠ J8
(D) ♠ Axx	♠ J8x

In (A), playing the ten gives me two spade tricks. I can take two spade tricks by playing the seven also, but I would have to lose a trick to the spade jack, and I would prefer not to do that.

In the remaining cases, I can take three spade tricks if I do the right thing. In (B), playing the ten works provided I finesse the seven on the next round, whereas playing the seven always works. In (C) and (D), playing the ten works provided I don't finesse the seven on the next round. Playing the seven again always works.

In summary: (1) playing the ten, intending to finesse the seven, works for (A) and (B) (six cases); (2) playing the ten and not finessing the seven works for (A) and (C) (four cases); and (3) playing the seven immediately works for (B), (C), and (D) (seven cases). A priori, then, the seven is the percentage play.

This assumes, however, that all these cases are equally likely, that West is just as likely to lead a spade from ace-jack fourth as from ace third. For a human, that's hardly true. He is more likely to lead from ace-jack fourth. So against a human, the ten might be a better choice.

Against that, the gain in playing the ten is uncertain. Against (A), I can always take two and only spade tricks. Playing the ten gains a tempo, not a trick. It's not clear at this point whether that tempo is meaningful.

Against a human, I'm not sure what I would do. But against a robot, who likes short-suit leads, I think the seven is probably better.

I play the seven, and East wins with the ace. So all this analysis was moot. I now have five diamond tricks, a heart, two clubs, and two spades. Ten tricks ready to cash. If I have three spade tricks, I have eleven.

At trick two, West shifts to the club queen. If the shift is from queen-jack-nine, I might be able to catch East in a club-heart squeeze for an eleventh trick. To set up the squeeze, I will have to duck a trick to correct the count, and I will have to isolate the heart guard in East's hand. If the heart honors are split, I can do both of these things by crossing to dummy and leading the heart jack. East can't afford to cover, so I will duck the trick to West. If West defends passively, I can run my winners, coming down to this position:

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

The last diamond squeezes East in hearts and clubs. West can break up the squeeze by continuing hearts. But if he has the heart nine, he can't do that.

I win the club shift with the ace; (The king clarifies the position for East.) West follows with the three. I might as well cash a spade to see if the jack drops. If it doesn't, testing for three-three spades will have to wait until after I duck the heart.

Actually, there is another reason to cash a spade. If West has jack-eight fourth, cashing a spade allows him to return the spade jack after winning his heart trick. The prospect of setting up his spade eight may make a spade continuation appealing and may prevent him from finding the heart continuation to break up the squeeze.

I cash the spade king. East follows with the eight. Too bad. Now West doesn't have a safe spade exit.

To lead the heart jack from dummy, I'll need to take the slight risk that diamonds are five-zero. I lead a low diamond to dummy's jack. Fortunately, both opponents follow. Now the heart jack--four--seven--queen.

West doesn't find a heart continuation. In fact, he leads away from his spade jack, giving my my eleventh trick in the spade suit. I claim the balance. Making five.

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

Plus 660 is worth 96%. The spade shift at the end made it easy, but there was nothing the opponents could do. East was going to be squeezed anyway.

Most declarers ran diamonds right away, destroying the possibility of a squeeze. Sometimes it's a good idea to run your winners early, forcing  the opponents to discard before they know what's going on. Sometimes that's true even it means giving up on a legitimate chance, provided that chance is small. 

I don't think that's the case here, however. The squeeze isn't all that unlikely. And it's hard to see what mistake the opponents will make if you run diamonds early. 

Free Weekly Instant Tournament - October 6 - Board 1

Board 1
Neither vulnerable

♠ 9 4 3  ♥ A K Q 6 4 2  ♦ A 6 2  ♣ A

Two passes to me. I open with one heart, LHO passes, and partner raises to two hearts. I'm worth driving to game, but it's not clear which game to drive to. I have eight tricks off the top, so one trick in partner's hand, assuming it's fast enough, is all I need for three notrump. Finding ten tricks in hearts may be harder. 

At IMPs, I would certainly bid three notrump, since it rates to be the safer game. But at matchpoints, the prospect of a spade or diamond ruff in dummy tempts me to try four hearts.

Players often get this backwards, spurning a major to play three notrump at matchpoints but not at IMPs. At matchpoints, it's better to play the major if it takes only one trick more than notrump. At IMPs, the major must take two tricks more (ten versus eight) before the major is better. So, in general, you should choose the major more often at matchpoints than at IMPs.

I bid four hearts, everyone passes, and LHO leads the seven of hearts.

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

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

Three notrump is clearly the right spot at IMPs. Unless the opponents can take five spade tricks off the top, three notrump is cold, and four hearts is tenuous. It's not clear what the right spot at matchpoints is.

It's unlikely West led a trump holding the ace-king of spades, so I will need to find my tenth trick in the club suit. I can take two ruffing finesses, but I need three dummy entries to do so. This means I need to reach dummy twice in hearts. Does that work? I can unblock the club ace, lead a heart to dummy, and lead the jack of clubs, ruffing if East covers and pitching a spade if he doesn't. Then another heart to dummy for the second club finesse. Finally, I return to dummy with the diamond king to take my pitch.

Yes, it works, assuming East has at least one club honor. The question is, do I have two trump entries? If I play low on this trick and RHO covers with the ten, then yes, I do. If the ten does not appear, I will need to decide whether to play for two-two hearts or to finesse West for the ten.

I play the heart eight. East covers with the ten. Problem solved.

I win in my hand with the king, cash the club ace--four--eight--deuce and play the deuce of hearts to dummy. West pitches the diamond four. So East made an error in covering. I would go down had he withheld the ten.

I lead the club nine. East covers with the queen, and I ruff. West follows with the six.

I lead another heart to dummy, lead the club ten, pitching a spade, and lose the trick to West's king. Eventually I pitch my diamond loser on the good club. Making four.

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

Plus 420 is worth 93%. No one was in three notrump. Most of the field was in four hearts going down. As I've observed before, the field in these Instant Tournaments is terrified of not drawing trump. Any time you must delay drawing trump, you get a ridiculously good result.

East could defeat this contract by playing a low heart at trick one. This is the kind of play a human is more likely to find than a robot. Robots decide what to do by generating random deals. If a robot doesn't happen to come across a deal where a particular play matters, it has no reason to find that play. 

Humans, on the other hand, can sometimes follow general principles without needing to construct a full deal. That's not always a good idea. Sometimes general principles fail. But here this approach works just fine. You can see that if you play low, you deprive declarer of a late dummy entry. That's often a good idea even if you can't see how it might help. So playing low should be routine for an expert human.

Robots would play better if they started with their deal-generating approach, then followed general principles if they thought their play didn't matter. But where should these general principles come from? A few years ago, the state of the art required deriving rules by interviewing human experts. This was always an unreliable process, since experts have often internalized their expertise and aren't consciously aware of why they do things. Now, with the advancements in generative AI, the technology exists to allow robots to generate their own rules. Using this approach, I suspect they will find rules we aren't even aware of. If anyone succeeds in doing this, we will see an astonishing improvement in how robots play.

Postscript:

In the above write-up, I stated "I'm worth driving to game" without comment, since I didn't think that would be open to question. But when I posted the hand to the Bridge People group on Facebook, the majority of respondents simply made a game try. So I suppose I should justify my statement.

The lazy way to decide what the hand is worth is simply to count points. You have 19 total points: 17 HCP plus one for the fifth heart and one for the sixth. Marshall Miles, in How to Win at Duplicate Bridge, suggested that, when partner raises your suit, you should add two points for holding six cards in your suit, two more for holding seven, one for a side singleton, and two for a side void. I've found this method of valuation to be quite accurate. Under this method, the hand is worth three additional points, bringing the total to 22. One normally makes a game try with 17 or 18 and drives to game with 19. So 22 is more than enough to bid game.

A more accurate way to decide what the hand is worth is to give partner a perfect minimum, say, two kings, three trumps, and a useful doubleton. If that gives you a virtually laydown game, then you should invite. If partner accepts with a maximum, perhaps the perfect minimum with be included in that maximum. If not, then perhaps game won't be cold but will still have decent chances. With this hand, all you need for game is  king doubleton of diamonds. That's a full king less than a game try by this method, so the hand is worth driving to game.

Free Weekly Instant Tournament - September 29 - Board 8

Board 8
Neither side vulnerable

♠ A K Q  ♥ K 9 6 2  ♦ Q J 8  ♣ K 9 7

Three passes to me. I have a balanced hand with 18 HCP, so I open with one club, planning on rebidding two notrump to show 18 or 19. LHO and partner pass, and RHO balances with a double.

I can now show my 18 to 19 HCP by bidding one notrump. The problem with that call is that LHO might well have a good hand with a club stack. If so, he is well placed to double me. Redoubling might be safer than bidding one notrump. It gets my values across, allowing partner to compete with a long suit. And if partner is broke, we can perhaps find a playable spot at the one-level.

Unfortunately, I haven't had much success engaging robots in complicated auctions. Even with my regular partners, I'm not sure what redouble should mean here. In particular, I'm not sure how prepared I should be to play in one club redoubled if LHO passes. So I'm not about to throw this auction at a robot. If I bid one notrump, at least there is no doubt in partner's mind what I have. (If anyone has a firm agreement about what this redouble shows, please comment.)

I bid one notrump. Everyone passes, and LHO leads the three of hearts.

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

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

Given the small heart lead and East's take-out double, hearts should be three-three. If West has led from jack third or ten third (or even ace third if I guess it), I have three heart tricks. Three spade tricks brings me up to six. LHO probably would have led a diamond with ace-king, so I should have a diamond trick. If the opponents give me the tempi, I may manage one or two club tricks as well.

I start by playing a low heart from dummy. East plays the jack, and I win with the king. The robots sometimes falsecard from equals in the middle of the hand, but I've never seen them do that at trick one. So I'm fairly confident the heart ten is onside.

I might as well set up my heart tricks. I'll have one heart entry to dummy. If I catch RHO with a doubleton club queen, I can set up two club tricks. Or I could play him for the ace and settle for one.

I play the deuce of hearts--ten--queen--ace. The ten? I suppose he was unblocking in case his partner had ace-nine fourth and I had made a curious play.

East shifts to the diamond deuce. Is the jack or queen most likely to induce West to shift after winning this trick? Perhaps if I play the jack, West will place me with AJ10 or KJ!0 and not wish to finesse his partner's queen. I play the jack, West wins with the king, and I unblock dummy's nine, trying to represent a good diamond holding in my hand.

I can't say whether my diamond plays worked or whether West was going to shift anyway. But, for whatever reason, West shifts to the heart four. I win in dummy as East follows with the seven.

East has the ace-jack of hearts and presumably the diamond ace. As a passed hand, he can't have the club ace, but he might have the queen. I lead the club five from dummy--four--nine--queen. West shifts to the nine of spades--three--deuce--queen. If I lead the club king, I assume West will duck it, preventing me from taking two club tricks. But at least I'll have my seventh trick.

I might as well cash my heart first and force discards. On the heart nine, West pitches the club three. I pitch dummy's diamond, and East pitches the club deuce. It appears East was either 4-3-4-2 or 3-3-5-2.

I lead the club king. West, of course, ducks, and East pitches the diamond six. I've made my contract. If I can guess the layout, I can take an overtrick. Here are the two possibilities.

(A)

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

(B)

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

In (A), I must cash one spade, depriving West of his exit, then lead a club. West must then lead a diamond up to my ace. If I make a mistake and cash two spades, East will have a spade to cash when he wins the diamond ace.

In (B), I must cash both spades before tossing West in. If I cash only one spade, he will have a spade to exit with, forcing me to lead diamonds out of my hand.

In any event, I must cash at least one spade. I cash the ace--eight--four--five. Now what? Which layout is more likely, (A) or (B)?

Perhaps with four diamonds West would have been more inclined to continue the suit after winning the king. In fact, maybe he would have bid two diamonds over one notrump with four of them. I don't know if he would or wouldn't. But at least he would have the option. With 3-3-3-4, he has no suit to bid. 

Neither inference is especially compelling, but at least they both suggest (B). I can't think of any other clues.

I cash the spade king. Everyone follows. I exit with a club and score my diamond queen in the end. Making two

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

Plus 120 is worth 100%. The overtrick made little difference. Even making one would have been worth 96%.

It's not my declarer play that made the difference, however. Weirdly, almost everyone is opening one notrump with this hand. I have no idea why. But against one notrump--all pass, West chooses to lead a diamond, which beats the contract.

That's also weird. I would do exactly the opposite. After one notrump-- all pass, one leans toward leading a major, since dummy won't have five cards in the major but partner might. But on the auction we had, partner is unlikely to have a five-card major, since he chose to double rather than overcall. If he has a five-card suit, it's probably diamonds. So I would choose a diamond on our auction but not after one notrump-all pass.

Free Weekly Instant Tournament - September 22 - Board 7

Board 7
Both sides vulnerable

♠ A K 10 9 8 4  ♥ K 9 7 4  ♦ A Q  ♣ K

I bid one spade; partner responds with one notrump.

Despite my 19 HCP, this hand hardly merits forcing to game. I have five spade tricks, one heart trick (half a trick for the king and half for the fourth heart), and one and a half tricks in diamonds. Seven and a half tricks in total plus a little for the club king. One generally needs eight and a half or nine to drive to game after a one-level response.

If I'm not going to drive to game, should I bid three spades or two hearts? Three spades has the advantage of getting my values across. Two hearts has the advantage of possibly finding a heart fit. If my heart suit were a minor, we might debate whether bidding three spades or showing minor will work out better. But we could easily belong in four hearts, so I don't want to risk missing a heart fit.

I bid two hearts, and partner corrects to two spades. My rule of thumb when partner shows a preference to my six-card suit is to bid one less than I would have bid had partner raised. If I would have invited game after a raise, I pass. If I would have bid game, I raise to three. With this hand, I would have bid four spades over a raise. So, by my rule, I should bid three spades now.

I'm inclined to override my rule however. After all, I would bid three spades even if my club king were the deuce. While I can't count the club king at full value, it's hardly worthless. To make the same bid with or without it feels wrong. Besides, stopping short of game with 19 HCP opposite a response is a scary prospect. Yes, I risked that when I bid only two hearts. But that was before I knew we had a fit. I'm not entirely confident with choosing four spades. But even if I'm wrong, I'm sure I'll have plenty of company.

I bid four spades. Everyone passes, and LHO leads the seven of clubs.

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

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

My choice between three spades and four probably didn't matter. With three spades and an ace, partner should raise to four anyway. Personally, I don't care for his one notrump response. I see nothing wrong with raising one spade to two.

I have a shortage of dummy entries. I'd like to lead up to the heart king and take the diamond finesse, but it's hard to see how I can do both. My only convenient entry to dummy is with a heart ruff, so I have no easy way to lead up to the heart king. I suppose I could win this trick in dummy, wasting my club king. But that's giving up a sure club trick for a potential heart trick. That doesn't seem like a fair trade.

Suppose I cash a high trump and drop the spade queen. Now I can reach dummy with the spade jack and lead a heart. But the opponents can then play a third spade and stop my ruff. Again, I'm giving up a sure trick for a potential one. I might as well simply lead hearts out of my hand.

Since I intend to lose two heart tricks, I have to avoid either the spade loser or the diamond loser. Let's step through the play to see how that works.

I'll win the club in my hand and duck a heart. East will win and play a trump. I win and play another heart. If East is out of trumps, the opponents can't play a second trump, so I can score two heart ruffs. I can then pitch the diamond queen on the club ace, losing only two hearts and a trump.

If East wins the second heart and plays another trump, I'll hop. If the queen drops, I have ten tricks: six spades, a heart ruff, two clubs, and a diamond. If West shows out, I can ruff a heart. If the ace falls, the heart king is my tenth trick. If it doesn't, I can pitch my heart king on the club ace and try a diamond finesse.

Is there anything to gain by cashing a trump before I embark on this plan? Not that I see. I've already noted that I can't exploit dropping a stiff queen. So all cashing a trump does is increase the possibility the opponents can play two more rounds, depriving me of my heart ruff.

I play a low club from dummy, East plays the deuce, and I win with the king. I play the heart four--five--deuce--eight. East surprises me by switching to the diamond king. 

The diamond king? What's that all about? I suppose he is catering to my having a stiff queen. He doesn't want to set up a ruffing finesse against his king. If he thinks his partner might have the diamond ace, that suggests the heart ace is on my left. If East held it, he probably would not expect his partner to hold the diamond ace. There's not much I can do with that information. But it's good practice to draw whatever inferences you gain when something weird happens. Unusually plays can be revealing.

I win with the diamond ace; West follows with the three. I play a second heart. Seven--jack--six--three. West continues with the diamond deuce. East follows with the four. I win and cash the ace and king of spades.

East pitches the diamond eight on the second spade. I ruff a heart, pitch my last heart on the club ace, and concede a trump. Making four.

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

Plus 620 is worth 86%. Lots of declarers cashed the ace and king of spades before attacking hearts. Drawing trump prematurely is a common mistake in these daylong tournaments. The declarers draw trump first, then look around for what to do next. They seem to be the victims of indoctrination.

I see I was wrong about the heart ace. Oh, well. It was only a inference, not a sure thing. But it's just as well it didn't matter. If I had needed to place the heart ace, I would have gotten it wrong.

Incidentally, look at that opening lead! With two unbid suits, West chose to lead from Q107 rather than from J1032. This is why I'm hesitant to draw inferences from the robots' opening leads. That choice makes no sense to me.

Free Weekly Instant Tournament - September 15 - Board 5

Board 5
Our side vulnerable

♠ K 10 3  ♥ A K J 4  ♦ A K  ♣ Q J 4 2

Two passes to me. I open with two notrump and partner raises to three. LHO leads the five of hearts.

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

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

I have eight cashing tricks. One possibility for a ninth is to find at least one club honor onside, a seventy-five percent chance.

Another possibility is to go after diamond tricks. I will need to find diamonds three-three or to drop the queen or ten in two rounds. My gut instinct says that's less than 75%. But the fact that this line yields two tricks instead of one makes it more attractive than playing clubs even if it is somewhat less likely to work.

Do I have time to develop a long diamond even if someone has queen-ten fourth? I cash the ace king, lead a heart to the queen, and play a diamond. No. I have only one dummy entry left, so I can't set up the last diamond and get back to cash it.

Maybe I can combine my chances, though. I can cash the ace and king of diamonds. If an honor drops, I set up diamonds. If it doesn't, I can consider switching to clubs. I'll still have two dummy entries to lead clubs twice.

I might as well start by inserting the heart nine. I don't see how that can hurt, and it will give me some clue about the lie of the heart suit. I play the nine, East plays the three, and I play low. West has apparently led from ten third or fourth unless East is playing a deep game.

I lead a diamond to the king. (The ace would suggest the king. The king is more ambiguous.) East plays the four; West, the three. The deuce is still out. On the ace of diamonds, West plays the deuce; East, the six. One opponent is giving honest count; the other isn't. Against humans, I would assume whoever doesn't have the queen is being honest in case his partner has the ace and needs to hold up. The player with the queen probably sees no reason to give honest count. 

In fact, I can state that more strongly. The hand with the queen must give false count. Any time one hand must give correct count in case his partner needs it, the other hand must give false count. Since declarer knows one hand can't afford to falsecard, he can trust the carding if the defenders' signals are consistent. But if one hand gives correct count and the other gives false count, declarer has no way to know which defender to trust.

These inferences aren't valid against robots, however. They don't think about such things. Their carding when declarer leads a suit appears to be random.

Since I didn't see the ten or the nine, should I switch plans and play on clubs? The two remaining diamonds are roughly 50% to split. (East can have queen-ten, West can have queen-ten, or they could be evenly split two ways. So they split in two cases out of four.) The club play works 75% of the time, so it is by far the better choice.

I play the jack of hearts to dummy's queen. West plays the seven; East, the six. Now five of clubs--seven--jack--ace. West continues with the heart ten. I win in my hand as East discards the club three. If East has the king, he probably has king fifth. He wouldn't pitch from king fourth, handing me a long club trick.

I cash the last heart and pitch a diamond from dummy. East pitches another club, the six. This isn't looking good. He wouldn't pitch two clubs from king fifth, so it looks as if the club king is offside. Maybe I can cash the ace and king of spades and toss West in to force a club lead. West would need to be 4-4-2-3 with the queen-jack of spades. Or maybe 3-4-3-3 with queen-jack of spades and the diamond queen. Neither seems likely. If East has nothing in spades, he might have pitched spades instead of clubs. Maybe West has ace-king tight of clubs and I can duck the king out.

I'll worry about that after I play a club from dummy. I play a low spade to the ace. West plays the deuce; East, the four. West might have split from queen-jack of spades, so I doubt he has both honors. Endplaying him is out. 

I play the eight of clubs from dummy, not entirely sure yet whether I'm going to duck it or not. East solves my problem by hopping with the king, and West pitches the ten of diamonds. I see. King sixth of clubs on my right. That's why he could afford to pitch two of them. Making three.

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

Plus 400 is worth an astounding 96%. Why?

It turns out the field is persisting in diamonds even after an honor fails to drop, taking their 50% line instead of their 75% line. But hold on. Maybe the field is right. In calculating the odds, I completely forgot to factor in that the diamond play yields two tricks if it works. I did say that fact made the diamond play "more attractive than playing clubs even if it is somewhat less likely to work." But I never quantified that "somewhat."

Half the time, the diamond play does a trick better than the club play. When does the club play do better? We need both the club play to work (75%) and the diamond play to fail (50%). So the club play is better only 37.5% of the time. 

Why did I have this blind spot? I think once I calculated the diamond play worked only half the time, I instinctively rejected it. One doesn't usually risk one's contract for an overtrick on a coin toss. But that's because the alternative is usually ensuring your contract. When the alternative is only a 75% play anyway, a coin toss is sufficient. I made the right play at IMPs but the wrong play at matchpoints. .

Free Weekly Instant Tournament - September 8 - Board 6

Board 6
Opponents vulnerable

♠ A Q J 9 8 7 5  ♥ J 10 6  ♦ A J  ♣ A

I have eight and a half playing tricks in spades. One spade followed by three spades typically shows seven and a half or eight, so this hand is too good for that sequence. My plan is to open one spade and bid four spades over partner's putative one-notrump response.

I don't get to open, however. RHO opens with one heart in front of me. I bid one spade, LHO and partner pass, and RHO reopens with a double.

Since partner couldn't bid, I'm not worth four spades any more. So I ratchet it in a notch and bid three spades. This alerts partner to the fact that I'm not simply competing. I still think we might have a game. A simple two spades would not accomplish that.

LHO passes, and partner bids three notrump.

In general, when partner suggests three notrump and you have three cards in the opponent's suit, you should respect his decision. That is certainly true here. We are apt to run into heart ruffs in spades, so it looks safer to try for nine tricks in notrump. I pass, and RHO leads the three of clubs.

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

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

I appear to have made the right decision. In four spades, the opponents will start with two hearts and a ruff. I will then be unable to reach dummy for a spade finesse or to score the club king, so I will probably finish down two. In this contract, I should manage six spade tricks and two aces. I have good chances for a ninth trick. But even if I can't find one, I may get a decent result for going down only one.

Where might I find a ninth trick? The spade king could be singleton. Or the opponents might persist in clubs when they gain the lead. Or I might be able to establish a heart trick. If the opponents can take two diamonds before I establish a heart, I'll go down. But if West has both diamond honors or one honor doubleton, they can't do that. 

I win with dummy's club ace. East plays the deuce. It's unfortunate he has that card. If his lowest card were higher than my five, I would conceal the five. But there is no way I can make the deuce look high, so I don't bother to falsecard.

I cash the spade ace--deuce--three--four. Now queen of spades--king--six--club four. So East has king third of spades. Four spades has no chance. Unfortunately, I allowed West to pitch a club. One of my chances was that East would continue clubs. Now he isn't going to do that. I wonder if I should have led the queen of spades at trick two and not cashed the ace.

East shifts to the nine of hearts. I play low and West wins with the king. I brace myself for the diamond shift, but he cashes the heart king and plays another heart. I have the rest. Making four.

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

I don't know why East didn't find the diamond shift. How can ace and a third heart ever be right? Plus 430 is worth 100%. 

It's strange to get 100% for doing nothing but taking the obvious action at every turn. What did everyone else do?

Several players doubled one heart. From the fact that I didn't discuss an alternative to one spade, you can probably tell that call didn't even cross my mind. The idea of doubling because your hand is too good to overcall is an old-fashioned one. I'm surprised it's even still around.

If it were just old-fashioned, that wouldn't necessarily be bad. But the idea is also misguided. Doubles should suggest flexible hands. Hands with an independent suit don't qualify. If double followed by a new suit shows an independent suit, it restricts your ability to make sensible rebids after a double. Sometimes, after partner's advance, you want to make an exploratory bid in a new suit without suggesting that a singleton, or even two small, is sufficient support. 

Some bid an immediate four spades over four hearts. I've never understood the appeal of pre-empting with good hands. If four spades rated to be a good save if it went down, it might make sense to bid it. But that's not the case here. You have too much defense. You are probably entitled to a plus score, so you don't want to bid four spades unless it's making.

One player bid one spade, then passed over the double (hoping East would defend?). When East bid two clubs, he competed to two spades. Then, when West balanced with three clubs, he took the push to three spades. This sounds like an eBay auction. Not only does this sequence let the opponents exchange information, increasing the chance they will make the correct final decision, it also makes it sound to partner as if you are reluctantly being pushed. If you're happy to complete to three spades, why not just bid it over the double so partner knows you're serious? 

A few players had the same auction I did but corrected three notrump to four spades. I'm sure one can construct hands where four spades is a better spot than three notrump, but it isn't easy. Holding three hearts is a red flag in this auction.

Free Weekly Instant Tournament - September 1 - Board 4

Board 4
Both sides vulnerable

♠ 5 2  ♥ A K 10 9  ♦ K 10  ♣ Q 10 9 7 5

Three passes to me. I have only 14 Casino points (HCP plus spade length). Conventional wisdom is you need 15 Casino points to open in fourth seat, but I think that's wrong. Average is 13 1/3. I think anything above average is worth opening, so I open with one club.

LHO passes, partner responds one spade, and RHO passes. I bid one notrump, and partner bids three spades, invitational. I have a minimum in high cards and no spade fit. And partner's spades probably aren't very good, since he didn't open with a weak two bid. So I'm not worth an acceptance. It is close, however. As minimums go, this a good hand. Four controls, three tens, two nines. But I think I need a bit more than that to accept with a small doubleton spade.

I pass. RHO leads the diamond ace.

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

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

I'm not sure why partner didn't open two spades with that hand. Because of the four-card heart suit perhaps? If he felt that way, he should have opened one spade. You have to bid either two or one. Passing with that suit isn't an option. Besides, if you're just going to ignore the heart suit and treat the hand a spade one-suiter anyway, what does passing accomplish?

East plays the diamond six, presumably encouraging with the queen. Should I play the jack or deuce? The jack suggests I have shortness, since it would be an unlikely play from jack third. I want West to worry that I have three diamonds so that he might shift to a trump, so I play the deuce.

West continues with the nine of diamonds. East plays the three. Does West's failure to shift to a trump mark him with the trump queen? No. He might have a stiff trump, which would also be an unattractive shift. Or he might have six diamonds and be unconcerned about a diamond ruff, since his partner will be overruffing. Or he might decide that stopping the ruff is the wrong approach altogether. Forcing declarer to ruff a loser is sometimes a better strategy than leading trump.

Imagine, for example, I had two small diamonds left and king-queen sixth of spades. Two rounds of spades stops the ruff. But who says I need the ruff? I may be able to pitch the third diamond somewhere. As long as I have the diamond king to stop the suit, there is no hurry to dispose of my third diamond. Knocking out the diamond king, however, may give me a problem. I win, play a spade to the queen, and it holds. Now what? What if I can't take my pitch without drawing trump first? If I play another trump, the defense can cash a diamond. If I ruff the diamond, I can't lead up to the spade king.

This is only one scenario where exposing the third-round diamond loser is a better strategy than leading trump. I'm sure you can think of others. In short, there is a variety of reasons West might have for not shifting to a trump. So I see no reason to spurn the spade finesse.

Should I take a first-round finesse or cash the ace to guard against a stiff queen? If I play a spade to the ace, I must then return to dummy with a heart to take the spade finesse. If the finesse loses and West plays another heart, I have a problem. If I take the heart finesse, East might win and give his partner a heart ruff. 

That's not even the only problem with this line. I may be able to set up two club tricks, so I can avoid a heart finesse altogether. But I can't do that if I waste heart entries. Suppose West has honor-jack tight of clubs, for example. After I draw trump, I play a club. If he hops and plays a heart, I win and lead the queen of clubs. I know from the opening lead West doesn't have both high club honors, so if East doesn't cover, I can let it ride safely, pinning the jack

To keep my heart entries intact, I'm going to pay off to a stiff queen of spades offside. I play a low spade to the jack. West wins with the queen and continues with the spade ten to East's seven and my ace.

If I draw the last trump, I have to pitch dummy's fifth club. Is there any scenario where I need that fifth club? Perhaps. If the opponents make a mistake and play a second round of clubs for me, I get two ruffs. Say, for example, West hops with honor third of clubs and plays another one. I ruff out East's jack and still have two heart entries to ruff out his other honor and cash my tricks. Or suppose West ducks with honor-jack third and East wins and plays another club. Again, I can score two ruffs, setting up two club tricks, and still have a heart to get back to cash them.

Neither of those mistakes is likely. But they are possible, and I can't exploit them without five clubs in dummy. I don't see any pressing need to draw the last trump. So why not lead a club now to give the opponents a chance to make a mistake?

I play a club, West plays the deuce, and East takes dummy's nine with the jack. East returns the diamond queen. I ruff. West follows with the diamond five.

The club suit didn't pan out. I draw the last trump, pitching a club from dummy. West pitches the heart six; East follows with the spade nine. 

West pitched a heart? What heart holding might he be pitching from? Not queen third. His partner might have jack doubleton. Queen fourth? Maybe. Although with that holding he might have shifted to a heart at trick two, trying to give his partner a heart ruff.

I play the heart deuce--seven--ace--four. Now that I've seen the four, I know West's six was his lowest. The robots almost always pitch count cards if the suit hasn't been played yet. So it appears West made a careless discard from three small hearts.

I lead the club ten. East covers with the ace. I ruff, and West follows with the four. Now jack of hearts--eight--king--queen. Making four.

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

Plus 170 is worth only 54%. I thought dropping the offside heart queen might have been worth more. But most declarers dropped it. Some dropped the spade queen also and made five. Perhaps because of West's failure to shift to a trump at trick two? As I said at the time, West has other reasons for not shifting to a trump. I don't think the inference he has the queen is strong enough to make an anti-percentage play in the suit.

I did, however, make a mistake in not drawing the last trump. There was a slight advantage in not drawing it, and at the time I didn't think it could cost. But I was wrong.

To see why, suppose West did have honor-jack doubleton of clubs as I hoped. I play a club. He hops and leads a heart. I win and lead the club queen. If East covers, great! But what if he ducks?  If I pitch a heart, the club jack drops, but now I'm stuck in dummy in this position::

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

The spade nine is still out. If West has it, I'm in trouble.

In fact, suppose East is clever enough to duck the club queen even with honor-jack fourth remaining. Now if I pitch a heart, I could actually go down. The clubs don't set up, so I might lose a trump and the heart queen. That might teach me to draw trump.