Match 2 - Board 5

Board 5
Our side vulnerable

♠ A K 8 5 2 ♥ 8 ♦ A J ♣ K 9 8 7 5

Two passes to me. I know some people open one club with this pattern, and I used to be one of them. But I never had much success with that approach. (I can recall one deal where it did work spectacularly well. At rubber bridge, I opened one club with six-six in the black suits, LHO overcalled one spade, and partner made a negative double. Even with that result, however, I still think I've been a net loser opening one club.)

I open one spade, partner responds one trump, I bid two clubs, and partner corrects to two spades. I'm glad I'm not playing forcing notrumps, since I have only one more club than I've promised rather than two more. If partner weren't a passed hand, my advantage over the Eastern Science Fiction players would be even more pronounced, since my partner's upper limit in high cards would be lower. I would probably pass anyway, but I pass a bit more comfortably in my style.

LHO passes as well and leads the three of diamonds:

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

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

East plays the queen, and I take the ace.  Frequently, when one is concerned about a bad break in a side suit, it is right to start the side suit before touching trumps. If the side suit splits badly, you may be able to compress your trump losers and your side suit losers.  With only two trumps in dummy, however, this doesn't look like the right approach. If someone ruffs the second club and plays a trump, I may be sorry I started clubs early. I cash the ace and king of spades. West plays ten-jack; East plays four-six.

A priori, the odds are about four to three that trumps are four-two rather than three-three. Has West's carding changed that? West could have begun with (A) jack-ten doubleton, (B) queen-jack-ten, (C) jack-ten-nine, or (D) queen-jack-ten-nine. Let's assume that, initially, each of these four cases is equally likely. (Yes, (B) and (C) are slightly more likely, but not by enough to make much of a difference in our analysis.) The principle of restricted choice dictates that the true relative frequency of each case is the a priori frequency divided by the number of ways West might play his cards. In theory, West could play his cards in any order with any of these holdings. Certain orders, however, wouldn't make sense. For example, queen-ten, queen-nine or, to a lesser extent, jack-nine would be a poor choice, since declarer would be disinclined to play West for a doubleton after such a sequence. So let's assume that West would always choose touching cards if he played his cards in descending order. That means he has two ways to card from (A), five ways from (B) or (C), and nine ways from (D).

The number of cases where the suit can split three-three, then, is one fifth (for B) plus one fifth (for C): a total of .40. The number of cases where the suit can split four-two is one half (for A) plus one ninth (for D): a total of .61. Thus the odds of a four-two versus a three-three break are roughly three to two. Of course, I didn't go through this calculation at the table.  I already know that the odds of a four-two break go up when restricted choice comes into play.  And on this particular deal, I don't care by how much.  I included this calculation in the post only because I've never seen anyone discuss the touching-card assumption before or how it affects the calculation.

I cash the diamond jack--four--seven--eight, and play a club to dummy's ace. West plays the deuce; East, the four. I play the king of diamonds--ten--heart eight--five, then lead the ten of clubs. East plays the six. I doubt West has a stiff club, but it probably won't hurt to let this ride. Even if West wins and gives his partner a club ruff, it will probably be with a natural trump trick. I play low. West wins with the jack and plays the nine of diamonds, on which East pitches the queen of clubs.

I ruff, and I'm down to:

	NORTH ♠ -- ♥ Q 9 7 5 ♦ -- ♣ 3
	SOUTH ♠ 8 5 ♥ -- ♦ -- ♣ K 9 8

West was either 3-3-5-2 or 2-4-5-2. If I play a trump now, I'll make five in the former case or go down one in the latter. If I play clubs, I guarantee making four. Since this looks like a normal contract and since declarer can be held to three on a heart lead however trumps split, I suspect making four is above average. So I see no reason not to settle for that result. I play the king of clubs. Making four:

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

Because of the favorable position in the black suits, we can make five clubs. But I can't see getting there even if I bid three clubs over two spades. Plus 170 turns out to be worth nine out of twelve matchpoints. Three other pairs were plus 170, two were plus 140, and one reached four spades and went down.

Me: +170 (9 MP)
Total: 39 MP (65%)
Current rank: 1st

Match 2 - Board 4

Board 4
Both sides vulnerable

♠ A J 9 4 ♥ Q J 8 7 3 ♦ A 2 ♣ A 3

One diamond--pass--one spade to me. I think the best way to handle this hand is to bid one notrump, hoping to be able to introduce hearts later. (In other words, bid it like a two-suiter, showing your higher-ranking "suit" first.) If you can get the heart bid in, partner will have a fair picture of your hand. The primary advantage to bidding one notrump is that partner might be able to raise with a hand where he would pass a two-heart overcall for lack of a fit. One notrump overcalls are frequently the easiest way to reach game on power.

I know that many players treat a one notrump overcall in sandwich position as unusual, but that makes no sense to me. Yes, a natural notrump overcall can be dangerous. But that just means you don't use the bid indiscriminately. Frequently you will have a six-card minor to run to if you're doubled. This time, safety is provided by the five-card heart suit and your spade length (which increases the chance that you will find partner with heart support).

Over one notrump, LHO bids two diamonds, which is passed around to me. This couldn't have worked out better. I bid two hearts. LHO bids three diamonds, passed around to me again. If partner sees no reason to act, I can hardly argue. I pass, and partner leads the ten of spades.

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

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

This must be a singleton. Why would partner lead a doubleton in dummy's suit in preference to my suit? On the other hand, how could South bid this way with three spades? Even if he chose to rebid diamonds rather than raise spades the first time (not a choice I would make), surely he would bid two spades rather than three diamonds at his next turn.

Is it possible to construct a layout consistent with partner's lead, partner's bidding, and declarer's bidding? Perhaps declarer failed to support spades because he has seven diamonds. That gives him 3-1-7-2 or 3-2-7-1 (giving partner 1-4-2-6 or 1-3-2-7 respectively). Partner must have, at the very least, four high-card points, since declarer didn't bid three diamonds the first time (or double one notrump). Is it conceivable partner would fail to bid with 1-4-2-6 or with 1-3-2-7 and four high-card points? Maybe--if he has diamond wastage. Perhaps something like:

♠ 10 ♥ x x x x ♦ Q J ♣ J x x x x x

In any event, I'm sticking with the idea that partner's spade is a singleton. If I'm right, we have five easy tricks. If I'm wrong, perhaps persisting in spades to promote trump tricks for partner is the right idea anyway. I take the spade ace, and declarer unimaginatviely plays the deuce. (Declarer should infer the stiff spade also. So he might try the effect of dropping the king from king third as if he were unblocking from king doubleton for a dummy entry.)

I return the spade four (suit preference for clubs). Declarer plays the eight. Partner ruffs with the seven and shifts to the six of clubs. Surprise! I wasn't sure Jack would understand the spade four. I was half expecting him to return a heart, in which case I would have to hope declarer had bid this way with only six diamonds. I take the club ace, and declarer drops the five.

Partner shifted to his lowest club. It can't be from seven, since it's inconceivable he has king-queen-jack seventh and didn't bid. Can partner really have five clubs? That would give declarer 3-1-6-3. If that's his shape, I should return a club. Then, when I take my diamond ace, I can give partner a spade ruff and get a club ruff for down two.

If I return a club and it turns out that partner, for some reason, has led lowest from queen-jack sixth, I could be letting declarer make this. But if other pairs are making heart contracts our way, there could be a big difference between plus 100 and plus 200, so I decide to take the risk. I play the three of clubs.  Declarer plays the jack, a card I wasn't expecting to see. That means partner is about to win this trick.  And he does--with the king. Partner returns the nine of clubs. I ruff as declarer follows with the queen. I play the spade nine, and partner ruffs declarer's king with the eight of trumps.

We're beating this at least three. If partner has a stiff queen of diamonds left, we can take two more tricks for down four. Partner can lead a club for me to ruff with the ace, then score his queen on an uppercut. But partner shifts to the six of hearts, so the ace of diamonds is the only trick we have left. Down three. Plus 300.

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

Both declarer's three diamond bid and partner's pass are incomprehensible. I guess partner was right not to compete to three hearts, which is probably what I would have done. Plus 300 is better than plus 140 or 170. But it seems awfully pessimistic to expect three hearts to go down, so passing is not an option at matchpoints. If partner chooses to defend, he must double.

We earn two out of twelve matchpoints for this result. We are the only pair not to reach four hearts. Fortunately, one declarer managed to go down. I imagine everyone else overcalled two hearts with my cards. South bid something (two spades, three diamonds, or a support double), and West raised hearts. Since East held substantially more than he had promised, he was trapped into bidding on. So he reached an anti-percentage game that happened to make. That's why I prefer the one notrump overcall: I can get my strength into the auction and not have to guess how high to bid later on.

It may seem strange to gloat about staying out of game when we wound up with only two matchpoints. But look at the odds we were getting. We get two matchpoints when four hearts makes and twelve when it goes down. I'm not going to bother calculating the chance of game with these cards, but I'm pretty sure they're less than 57%. So, in the long run, we did the right thing not to bid game. Of course, had we doubled, we would be getting twelve matchpoints whether four hearts makes or not.

Score on Board 4: +300 (2 MP)
Total: 30 (62.5%)
Current rank: 2nd

Match 2 - Board 3

Board 3
Opponents vulnerable

♠ A 10 7 5 ♥ A 9 8 ♦ K 8 4 ♣ Q 3 2

My opponents at this table are playing "2/1 GF with forcing NT," the same card as the previous table with "almost" removed.

I open one notrump (12-14) in first seat. Partner bids two diamonds, a transfer to hearts. I bid two hearts, and LHO doubles. This double should show a singleton or void in hearts and support for the other three suits. It isn't clear is how good a hand it shows. Immediate actions over a weak notrump should show roughly an opening bid. An opponent's strong notrump opening creates a presumption that you don't have a game on sheer power, so you can afford to bid obstructively. But an opponent's weak notrump opening creates no such presumption, so your bidding needs to be constructive.

This second-round double, though, is ambiguous. It could be: (1) A good hand where you had no sensible call on the previous round, or (2) a "pre-balance," that is, a hand where the primary reason for acting is your heart shortness and the fear that, should LHO pass, partner's heart length will constrain him from balancing. Playing sensible methods (i.e., Astro), (1) is pretty much confined to 3-1-4-5 or 3-1-5-4 patterns, since you would have bid two diamonds on the previous round with any good hand containing four spades and heart shortness. Playing most other methods, there is a wide variety of hands that fall into category (1).

Partner passes, and RHO bids three spades. I pass, and three spades ends the auction. How bad can this be? The opponents are in three spades, and we didn't even have to push them there. If only my opponents always played three spades (or five spades or two notrump).

What should I lead? Declarer rates to have four hearts, so a heart lead is unattractive. I could try to find partner with some help in one of the minors so I could start a tap. But, since I can't continue the tap beyond the third round, it's not clear that will accomplish anything even if it works. A trump lead, giving up on scoring the spade ten, seems weird, but it might actually be the safest choice. Nothing really appeals. In the end, I settle on the four of diamonds without much confidence.

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

West	North	East	South
1 NT	Pass	2 ♦1	Pass
2 ♥	Double	Pass	3 ♠
(All pass)
1Jacoby-transfer

Even after looking at dummy, I have no idea what I should have led. Dummy plays the diamond queen, partner plays the six, and declarer plays the five.

Partner probably has the diamond jack. It's possible he is discouraging from ten-six, but declarer's play makes that unlikely. There are fifteen high-card points outstanding. Unless declarer has thirteen of them, partner might have had the diamond king from declarer's point of view. So declarer would be unlikely to play the queen holding the jack himself. Declarer probably needs both black kings for his three spade bid. So my inclination is to place him with a hand such as

♠ K x x x ♥ x x x x ♦ A x x ♣ K x

If so, he will probably lead a heart at trick two and come to nine tricks via a crossruff.

Declarer surprises me by leading the spade jack at trick two--deuce--three. I'm not sure what's going on, but I see no gain to winning this trick. I play the five. Now declarer plays the king of hearts--deuce--six. It seems declarer has changed his mind and is reverting to a crossruff after all. Maybe I'm being gullible, but it seems right to win and play ace and a spade, holding declarer to one club ruff.

I take the heart ace and cash the spade ace--eight--six--four. Declarer bid three spades on a three-card suit? How bizarre! There is no reason North had to have four spades for his double. I'm holding declarer to no club ruffs. I play a third round of trumps--nine--diamond jack--spade king. I suppose partner is holding on to his hearts for fear declarer has five of them.

Declarer plays the four of hearts, I play the nine, and declarer pitches the three of diamonds from dummy as partner plays the heart three. Declarer wouldn't be pitching a diamond from dummy unless he had four in his hand, so he must have

♠ K x x ♥ ? x x x ♦ A 10 x x ♣ K x

I'm going to score the diamond king, and it's hard to see how I can score any other trick unless partner has the queen of hearts, enabling me to tap the dummy. It's also hard to see how partner can have the queen of hearts, given declarer's line of play. But it doesn't appear to hurt to play a heart. Even if I'm leading into declarer's queen-ten, I'm still not losing my king of diamonds. I play the heart eight--club four--jack--queen. Eventually I score my diamond king. Making three.

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

The opponents could have made three notrump or four spades (by ruffing one club and guessing the spade ten), but it's hard to see how they can get to either contract after this start. What can South do after the double? He can't drive to game opposite a possible "pre-balance." Two notrump would be a fine call if that were natural, but I doubt most experienced partnerships play it that way. My notes define it as lebensohl, in which case South could bid a constructive three diamonds. But that doesn't help. North can hardly move over that.

Playing Astro, North would bid two diamonds over one notrump, showing four or five spades and a second suit (in this case, a third suit as well). South would bid two notrump, an artificial game invitation showing exactly three spades. With five spades, North is supposed to bid three or four spades. With only four spades, he is supposed to bid his five-card suit. With 4-1-4-4 and not enough values to bid three notrump, he has something of a problem. I imagine he would bid three spades. I'm not sure what South should do now. It's hard to be objective when you know all the hands. Certainly pass, three notrump, and four spades are all possibilities.

In any event, minus 140 is a top for us. Only one other North-South pair played a partscore: two notrump making four. The others either reached three notrump or collected 500 against three clubs doubled.

Me: -140 (12 MP)
Total: 28 (77.8%)
Current rank: 1st

Match 2 - Board 2

Board 2
Our side vulnerable

♠ A 10 ♥ A Q J 9 7 5 ♦ J ♣ 7 6 4 3

RHO opens one heart in first seat. I pass. The auction continues one spade--pass--one notrump back to me.

Two clubs seems like the obvious choice. This is pretty much the hand this bid should show (i.e., a hand where I would have opened one heart and rebid two clubs if RHO hadn't beaten me to it). I doubt Jack knows this, but my hand has too much potential just to sit back and let the opponents steal from us. Even if partner doesn't understand what my bid is supposed to mean, he should have a fair picture of my hand anyway from the opponents' auction. Once LHO fails to support hearts, partner will know the opponents have at most seven of them. Although partner might not appreciate the fact that two hearts by him should be natural, possibly a "preference" with a small doubleton.

Over two clubs, LHO bids three spades, partner bids four clubs, and RHO bids four spades.

We have a fair chance to beat this. Partner leads a heart. I win and shift to a diamond. When I take the spade ace, I play a club to partner's putative ace for a diamond ruff. Or I might be able to do some damage to declarer's trumps by persisting in hearts at trick two. Of course, partner needn't have the club ace, and declarer needn't follow to the first heart, so our prospects are hardly good enough to warrant a double. I pass, LHO passes, and partner bids five clubs. Oh, come on, partner. If you're going to do that, bid five clubs the first time. Why give opener a chance to show spade support at the four level?

RHO passes; I pass. LHO doubles, ending the auction, and leads the four of hearts.

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

West	North	East	South
		1 ♥	Pass
1 ♠	Pass	1 NT	2 ♣
3 ♠	4 ♣	4 ♠	Pass
Pass	5 ♣	Pass	Pass
Double	(All pass)

RHO plays the heart ten, and I win with the queen (a less revealing card than the jack).

East is probably 3-5-3-2. He could be 3-5-2-3, but that would mean West doubled with 6-1-5-1, which is unlikely. To give West sufficient values for his three spade bid (and to prevent East from having a strong notrump), I need to credit West with one of the three minor-suit honors. That gives East either

♠ ? x x ♥ K 10 x x x ♦ A x x ♣ A x,

♠ ? x x ♥ K 10 x x x ♦ K x x ♣ A x,

or

♠ ? x x ♥ K 10 x x x ♦ A K x ♣ x x.

There are ten ways for East to have ace third of diamonds, ten ways for him to have king third, and five ways for him to have ace-king third. So, a priori, East is four-to-one to have one honor in each minor. If we consider the auction, the odds are even higher. With two small clubs, East might (I would go so far as to say should) raise spades rather than rebid one notrump.

The question now is: can they make four spades? It all depends on the location of the ten of diamonds. If East has it, yes; if West has it, no.

I need to get started on diamonds, so I play the diamond jack. West plays the three. I play low and East wins with the king. He shifts to the deuce of spades. I win with the ace as West plays the nine. West is still four-to-one to have the remaining diamond honor. Because of restricted choice, the fact that East won with the king rather than the ace does not change the odds. It's going to be a struggle to hold this to down one, but perhaps I can manage if East has the diamond ten (as I must assume he does anyway to keep this from being a phantom sacrifice).

I lead the heart ace, West ruffs with the nine, and I overruff with the ten. I now lead the queen of diamonds. My plan is to pitch a spade, letting West take his ace. If East does have a singleton ten remaining, I will be able to establish diamonds with one ruff. Unfortunately, East covers the queen with the ace. Oops. I guess I should have led a low diamond. Now I'm in trouble. I ruff and play a trump. West takes his ace. It costs nothing to unblock dummy's eight, so I do. East follows with the deuce.

West shifts to the eight of diamonds. I cover with the nine, and East plays the ten. Whew! I was wrong about the minor-suit honors, but at least I was right about the ten of diamonds. I ruff and draw the last trump. There's no way to avoid the spade loser, so I'm down one.

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

Did I misplay this? Yes, I did. The queen of diamonds was the right way to handle the diamond suit, but I shouldn't have been playing diamonds at all. If clubs are two-two as I assumed, I can guarantee down one by playing a trump at trick two, unblocking the eight if West plays the ace. The opponents shift to a spade. I win, draw the remaining trumps, then lead a third round of clubs to my seven and drive the king of hearts, pitching dummy's spade. My hearts are now good.

Why didn't I see this? I didn't think I had the tempi to set up hearts, because I assumed I would re-enter my hand by ruffing diamonds. The key is to reach my hand with the gratuitous third round of trumps. This saves a tempo and enables me to pitch dummy's spade loser. Somehow I missed that. That's what happens when I take a month off.

Could East foil this plan by playing low on dummy's eight of hearts at trick one? No. That would be a better effort, but I have a counter. I play as above except that I ruff a heart in dummy (with a middle spot) after winning the spade ace.

Now for the critical question. Were we beating four spades? Not if I defend as I envisioned during the auction: a heart to me and a diamond shift. If we avoid breaking diamonds, however, declarer will probably play a diamond to the ten at some point and go down. So, while minus 200 is par on a double-dummy basis, it rates to be below par in practice.

And it is. We score four out of 12 matchpoints. Although, surprisingly, defending and defeating four spades would not have improved our score. Two pairs played four spades, one making four, the other making five. But the other four pairs reached three notrump, going down either two or three. I'm not sure why that was such a popular contract, since I can't even construct an auction to get there.

Score on Board 2: -200 (4 MP)
Total: 16 MP (66.7%)
Current rank: 3rd

Match 2 - Board 1

Board 1
Neither vulnerable

♠ Q 10 8 ♥ Q 7 ♦ K 10 ♣ K J 10 7 6 4

My opponents at table one are playing a card Jack describes as "2/1 almost GF with forcing NT." Not that it matter on this deal, since partner opens with three diamonds, buying the contract. West leads the ace of clubs.

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

West	North	East	South
			3 ♦
(All pass)

There are some, perhaps even many, who believe that East should signal suit-preference on this trick. There is no obvious shift, they argue, and continuing clubs is unlikely to be the right idea. As you probably know by now, I am not a member of this school. Let me pose this question: Just how sure are you that continuing clubs can't be the right idea? If the opening bid had been one diamond instead of three, it wouldn't be at all hard to construct a layout where continuing clubs is right. It's harder opposite a three diamond opening, but I'm still not sure it's impossible. And it actually doesn't matter whether it's possible or not. The fact that I can say "I'm not sure" is all that matters. If, in order to determine what a signal means, you need to pose a question that can't be answered accurately in under two seconds, you need to change your carding agreements. It's fine to have to work to decide what message to send. But if you have to work to determine how to send it (that is, to determine whether a signal is attitude, count, or suit-preference), then you're going to have accidents.

I would have no objection to playing a rule such as "If you lead an ace and dummy hits with five or more cards in that suit headed by the king, partner's card is suit preference." Or "If you lead an ace and dummy hits with a singleton and at least four trumps, partner's card is suit-preference." Maybe such rules make sense and maybe they don't. But at least they're unambiguous. If, however, you adopt rules such as "If you lead an ace and it is unlikely to be right to continue the suit led, partner's card is suit preference," you had better have a higher tolerance for misunderstandings than I have.

I play the four from dummy, and RHO plays the five. What card do you play?

I don't know what meaning my opponents attach to East's card, but I do know that, whatever the meaning, the five is intended as "high" (if East has a choice). Therefore I must play "low" to create maximum ambiguity. Let's take time out to see why this works. If I play the three, then, from West's point of view, there is only one way the five could be high (when East's spots are five-deuce) but three ways the five could be low (when East's spots are nine-five, eight-five, or nine-eight-five). So the five, even though I know it is "high," is apt to appear "low" to West. If, instead, I play the eight, then I help East convey his message. There will be three ways the five can be high (from five-three, five-deuce, or five-three-deuce) and only one way it can be low (from nine-five).

There is no need to work all this out at the table. You can simply follow this rule: If your opponent plays high, you play low, and vice versa. (I know. I know. This becomes much more complicated if you take into account that West might expect you to play this way. But, in practice, few people seem to know this rule. When they start catching on, then I'll worry about the game theory considerations.)

I play the club three, and West shifts to the deuce of spades. I play the ten from dummy, the card I would play if I held a small singleton. East plays the jack, and I win with the king.

What just happened? Perhaps West underled the spade ace, hoping to find two entries to his partner's hand for two club ruffs. Or perhaps East has the ace and thought his partner had shifted from the king.

I play a diamond to the king and a diamond back to my ace, on which East pitches the four of hearts. On the queen of diamonds, I pitch a club from dummy, since I have one more club than I could possibly need, and I don't want to give the opponents any clue about how useful or irrelevant dummy's major-suit holdings are. East pitches the four of spades.

Ace from ace-queen-third would be an unusual lead, so I suspect that either clubs are two-two or East has queen doubleton remaining. In the latter case, do I have any chance of endplaying him by running diamonds? Not really. He can't have the queen of clubs, ace-jack of spades, ace-king of hearts, and a singleton diamond and not have balanced. As long as he doesn't have all of those cards, he has a counter to anything I can throw at him in the end position. Perhaps my best chance for an extra trick is to duck a club and hope they can't solve the cash-out problem. If that's what I intend to do, I should do so now before the defense has a chance to signal any further. I play a club, West plays the queen, and I claim. Making six.

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

This, as you might, expect, nets 12 out of 12 matchpoints. Four pairs played three diamonds making three, one played three diamonds making four (a somewhat improbable result), and one defended four hearts, making four. I'm not a fan of offshape take-out doubles, but even I would have doubled three diamonds with West's hand. East might or might not drive to game. But even reaching three of a major would have been sufficient to win most of the matchpoints.

I'm still not sure what West was up to with his low spade shift. As I've mentioned before, it would be nice if Jack had a debug mode where it logged its analysis.

At first I chalked this result up to luck. But I've changed my mind. As an experiment, I replayed the deal several times, playing different clubs at trick one. Whenever I played the eight or nine, West shifted to the heart ace. Whenever I played the three, he shifted to a low spade. I can't tell you why. But, after all, the three is the right card. If playing the right card is responsible for my making six, I suppose I'm entitled to some of the credit even if I haven't the slightest idea why it worked.

Score on Board 1: +170 (12 MP)
Total: 12 MP (100%)
Current rank: 1st