Weekly Free Instant Tournament - Feb. 11, 2022 - Board 7

Board 7
Both vulnerable

♠ A J 10 9  ♥ A K 5  ♦ 9 8  ♣ Q 5 4 3

I have 14 HCP, but that metric undervalues my spade holding. I know I said the same thing back on board three, and it didn't work out well. But I consider that result unlucky. An old-fashioned criterion for a strong notrump is three and a half to four honor tricks. This hand has three and a half plus, so by that metric it is in the middle of the range. 

I open with one notrump. Everyone passes, and West leads the club deuce.

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

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

Before we begin, let me point out that, opposite this dummy, I'm happier holding this hand than I would be holding the same hand with AQ9x of spades. So my decision to evaluate this hand as at least as good as that one seems reasonable.

I might as well find out what's going in the club suit before I think too deeply about this deal. I play the nine from dummy, East plays the jack, and I win with the queen. 

Against some opponents I wouldn't be sure who had the club king. A former partner of mine might even have king-jack tight. But against these opponents, I’ll assume the club king is onside. That gives me three club tricks, two hearts, and a spade—six tricks. I need to develop one more; and if diamonds are five-three, I can afford to lose the lead only once. A double spade finesse gives me a 75% shot. Playing on hearts is probably better. Ace, king, and another heart loses only to queen-ten fourth or fifth of hearts offside. 

I don't know the odds of the heart break off the top of my head, so let’s make a rough calculation. Hearts are three-three about a third of the time. (I know. It's actually 36%, but I did say "rough.") That means each opponents has heart length about a third of the time.  

If East has long hearts, what are the chances he has both heart honors? He has both heart honors if West had two small hearts (six cases) or a singleton small heart (four cases), for a total of ten cases. He is missing a heart honor when West has queen doubleton or ten doubleton (eight cases), or queen-ten, stiff queen, or stiff ten: eleven cases in total. So if East has long hearts, he has both heart honors a little less than half the time. That means playing on hearts fails less than a sixth of the time. The spade play fails a quarter of the time. A priori, playing on hearts is better.

But there is another factor to consider. If the double finesse in spades works, I gain two tricks, not just one. So I have a better chance to make an overtrick by going after spades. The difference between plus 90 and plus 120 is often significant, because some pairs may be collecting 100 on defense. This looks as if it might be one of those deals, since if I open one club, the opponents may get into the auction and buy it in a diamond contract. Even though the double spade finesse works less often than playing on hearts, it's still a heavy favorite to work. And the matchpoint expectation may be higher. So that's the line I'm adopting.

I lead the club three—eight—ten—seven. It's encouraging to see West play the eight. Could he have led from king-eight-deuce? If so, I’ll end up taking four club tricks. I lead the spade three—deuce—ten—queen. West leads the king of clubs. I take the ace and East discards the diamond three. West has the club six left. He was just toying with me with those club plays.

I play a spade from dummy and East plays the king. I win with the ace and cash the jack. Everyone follows. That was a strange play hopping with the spade king. What if his partner held queen-jack tight?

Here is the current position:

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

I have eight tricks. East’s pitch of the diamond three was probably from a five-card suit, which means the opponents could have cashed out to hold me to seven. I've already gained one trick. Can I find another one? 

If East indeed had five diamonds, then he was 3-3-5-2. That means he has three hearts and four diamonds left, and West has three hearts, three diamonds, and a club. So nobody has a doubleton heart queen. My only chance for another overtrick is an endplay. 

I cash my last spade, pitching a diamond from dummy. West pitches the diamond deuce; East, the diamond six. I cash the ace of hearts—four—deuce—three. Unless East has ace-king-queen of diamonds and queen doubleton of hearts left, there is no endplay. Even if he had that, he could have escaped by unblocking the diamond queen, which shouldn’t be hard for him to see. Better to hope my construction is wrong and the queen of hearts is dropping after all. I cash the heart king. The queen doesn’t drop. Making two

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

96%! Almost everyone opened one club and played it there, taking anywhere from six to eight tricks. While I should like to take credit for this result by virtue of superior hand evaluation, hand evaluation had nothing to do with it. We didn't, after all, reach a game that other pairs missed. Partner happened to have a hand that would pass either one notrump or one club, and one notrump happened to be a better contract. So the result was due to superior luck, not to superior evaluation. Still, my anti-field evaluation led to an unlucky result on board three, so I suppose I'm entitled to a lucky result this time.

What about my declarer play? Was I right to play on spades rather than hearts? Apparently not—at least not in this field. It turns out no one is defending with the North-South cards. After one club—pass—pass, I would expect East to balance with one diamond, which could easily lead to some plus 100s for North-South. But he sold out to one club. Since there were no plus 100s but quite a few plus 70s, the biggest matchpoint difference was not between plus 120 and plus 90 as I anticipated but between plus 90 and minus 100. Plus 90 would have been worth 75% while minus 100 would have been worth 7%. I was risking a lot to gain comparatively little. I don't think there was any way for me to know that, and I doubt it would be true in a better field. So I stand by my decision.

My score is 74% going into the last board. I'm still in first place. Let's see if I can hang on.

Weekly Free Instant Tournament - Feb. 11, 2022 - Board 6

Board 6
 Opponents vulnerable

♠ K Q  ♥ 7 6 5  ♦ A K Q 9 8  ♣ A 10 9

RHO passes. I open with one diamond, intending to rebid two notrump. LHO spoils my plan by overcalling with one spade, which is passed around to me. I could balance with one notrump, showing 18-19 HCP, or I could double for take-out. With shortness in your opponent's suit, a take-out double is usually preferable to bidding notrump, so I double.

LHO bids two hearts. Partner passes, and RHO raises to three hearts. I have nothing further to say. I pass, and the opponents buy it for three hearts. Partner leads the heart jack.

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

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

Since South didn't use Michaels, he is probably five-four in his suits. Even if he's of the school that avoids Michaels with intermediate-range two-suiters, he would probably have accepted the game invitation with any five-five that he thought was too good for Michaels.

Declarer plays the heart three from dummy, I play the five, and declarer wins with the queen. 

As I've mentioned before, it's a good idea to try to predict how the play will go, so it will raise a red flag if declarer does something unexpected. My expectation here is that declarer will duck a spade to begin establishing his suit. But he doesn't. He plays the jack of clubs. Partner plays the king, declarer plays the five from dummy, and I follow with the nine. 

It appears declarer has a stiff club and is preparing for a crossruff. But if partner plays another trump and I play a third when declarer ducks a spade, he's not going to get a lot of crossruffing done. So maybe a crossruff isn't his objective. Could he be trying to establish clubs? If so—if clubs offer a better prospect for tricks than spades, his spades can't be very good. Partner would need jack-ten fourth or jack-nine fourth of spades to induce declarer to go after clubs instead of spades for tricks.

Partner shifts to the deuce of hearts. Declarer wins in his hand with the eight and leads the club four—three—queen—ace. So declarer is indeed trying to establish clubs. I cash the diamond king—three—seven—four, then the diamond ace—ten—five—jack. Here is the current position. Declarer presumably has ace fifth of spades and ace doubleton of trumps left.

	NORTH Robot ♠ 8 2 ♥ K 10 ♦ — ♣ 7 6 2
		EAST Phillip ♠ K Q ♥ 7 ♦ Q 9 8 ♣ 10

If I play a trump, declarer will win in dummy and ruff a club to his hand. Then dummy is good except for a spade. So he's down one.

Is there any way I can do better?  What happens if I play a third round of diamonds? Let's switch to declarer's point of view:

	NORTH Robot ♠ 8 2 ♥ K 10 ♦ — ♣ 7 6 2
	SOUTH Robot ♠ A x x x x ♥ A 9 ♦ — ♣ —

If the defense continues diamonds, it's tempting to ruff in your hand and pitch the spade loser from dummy. In fact, allowing you to pitch your spade loser looks like a defensive error. But if you do that, you're down two. You can cash the spade ace and crossruff, but that yields only five tricks. You lose the last two.

You do better by refusing the "gift." Take the ruff in dummy, ruff a club with trump ace, establishing the suit, then play a trump to dummy and cash your two club tricks. You lose a spade at the end for down one.

But is it clear to do that? You don't know clubs are three-three after all. If you ruff the diamond in dummy, ruff a club, and they don't split, you are in trouble. If you concede a spade, the defense plays another trump and you wind up with the spade ace and three trump tricks for down three. Taking the sure line for down two might be the right decision.

Can it hurt to give declarer this option? Say I play a diamond. Declarer ruffs in his hand, pitching a spade from dummy, plays ace and ruffs a spade, then leads a trump to his hand and claims. Now I've just let him make a contract we were supposed to beat. But that means he has ace-jack-ten fifth of spades, and I decided at trick two that his spades can't be that good. So offering him the option to play safe for down two can't cost.

I play the diamond queen. He doesn't fall for it. He pitches a spade from his hand, ruffs in dummy, then ruffs a club with the ace. Down one.

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

Plus 100 is worth only 29%. At over half the tables, the final contract was three spades by South. How do they get there? To begin with, East balances with two diamonds rather than double. That should show six diamonds, and there is no reason to distort your hand when you have two better options available. This time, however, the call works for a strange reason. It seems to convince North that his hearts are spades and vice versa. 

First, after South bids two hearts, North takes a false preference to two spades. Then, when West competes to three diamonds, he bids three spades. Why the two-diamond bid causes North to lose his mind is a mystery. This is the second board in a row where one's choice of actions had an effect on the result that was apparently related more to the vagaries of the robots' programming than to the merits of the choice itself. The first time I benefited; this time I lost.

While balancing with two diamonds is a mistake, I'm inclined to think my double was a mistake as well. I should have bid one notrump. I avoided one notrump because of my doubleton spade. But when RHO doesn't raise spades, there is a fair chance partner has some spade length, so my shortness is less of a liability than it would be in a different auction. And doubling could give me headache on the next round. What do I do, for example, if partner bids two clubs? We could still have a game, but it's dangerous to bid again when partner could have nothing. Balancing with one notrump gets my values across and allows me to leave further bidding to partner. Fortunately, this time my choice probably made no difference--unless, like two diamonds, one notrump would have had some voodoo-like effect on the opponents' auction.

Despite this result, I am still in first place, with 71%.

Weekly Free Instant Tournament - Feb. 11, 2022 - Board 5

Board 5
Our side vulnerable

♠ A Q J 5 4  ♥ 4 3  ♦ A  ♣ K Q 10 5 2

Two passes to me. I open with one spade, LHO bids two diamonds, partner bids two spades, and RHO passes. 

Culbertson's rule for slam bidding states: If partner's perfect minimum gives you a laydown slam on normal breaks, you should invite. That's a useful rule for game-bidding as well. Here, all I need for game is the spade king and club jack, which is less than a perfect minimum. So I don't invite game; I just bid it. Everyone passes, and West leads the club ace.

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

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

There is a fair chance the lead is from a singleton. Even if it isn't, I doubt West has the club jack, so I will probably hook East for the jack at some point. I play the four from dummy; East plays the club three. There is no reason to let West know East played his lowest club, so I play the five.

West shifts to the five of diamonds—three—eight—ace. I could lead a heart to dummy, pitch a heart on the diamond king, and lead the spade ten for a finesse. But even if it wins, it’s not clear I’ve gained anything, since I won’t be able to re-enter dummy for the marked club finesse. If I have two finesses to take and I'm only going to be able to take one of them, I might as well take the one that's almost certain to work. So I'm inclined to play spades from my hand.

Will I regret that decision if East has king doubleton of spades and gives his partner a club ruff? If that happens, I have a trump left in dummy with which to ruff my last club, so I have the rest of the tricks. I lose the club ace, the spade king, and a ruff. Making four. If I take the spade finesse (assuming I lead the ten to do so), I take five spades, a heart, two diamonds, and two clubs. Also ten tricks. So even in that case, I break even playing spades from my hand.

I cash the spade ace—deuce—three—nine. Should I lead a low spade to the ten or an honor? If East wins the spade king and shifts to hearts, I'd like to be able to draw the last trump and stay in dummy. So leading an honor looks better.

I lead the spade jack. West takes the king, and East pitches the heart deuce. Now that I  know West has at least nine cards in spades and diamonds, the likelihood that the club ace was a singleton has gone up. If  he has six diamonds, it was surely a singleton. He would not have lead from ace doubleton of clubs with a stiff heart. Could he be 4-2-5-2? That's possible, but the club ace would be a strange lead with that hand. A diamond, hoping to start a tap, would be a more attractive choice. 

There is further evidence that I wouldn't have playing against humans: East's discard of the heart deuce. As I've noted previously, the robots tend to give count on their first discard, so the heart deuce is a strong indication West is 4-3-5-1.

Here is the current position. West holds two more spades and, presumably, all red cards.

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

If West shifts to a heart, I can win with the ace and pitch a heart on the diamond king. But I'm stuck with two club losers. I can't get back to dummy after drawing trump to take the club finesse. Maybe I can survive if West has both heart honors. Say he shifts to the heart king. I win, cash the spade ten, then, instead of taking my pitch, I ruff a low diamond, draw the last trump, and play a heart. West wins, and I have the rest whatever suit he returns.

What if West shifts to a low heart in the above position? If I'm right about the stiff club, I go down if I rise with the heart ace, so I might as well insert the jack. If West is being sneaky with both heart honors, I make an overtrick. If East wins, I just have to hope I'm wrong about the club break.

But West doesn't play a heart. He shifts to the diamond six. I win with dummy’s king, East plays the deuce, and I pitch the heart three. I cash the spade ten, ruff a diamond, draw the last trump, then play a heart to the ace for a club finesse. East began with five clubs as I had assumed, so I have to lose the last trick. Making four.

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

100%! No one else made this game? Why was this deal so hard?

Some declarers got a diamond shift at trick two, then went down because they used their heart entry to take a spade finesse. But not all declarers got a diamond shift. Some Wests shifted to the heart king. Why would West shift to a diamond sometimes and a heart at other times? Apparently West shifted to a diamond if declarer played the club five at trick one but a heart if he played the club deuce. While the club five is in principle the correct play, it's hard to see how it mattered. Most likely it was simply a butterfly effect. Or perhaps the bridge gods chose to bestow an award for careful play.

How should South proceed after a heart shift at trick two? You could try an immediate spade finesse, but winning and leading a club to the ten gives you two chances instead of just one. If West doesn't ruff, you're in good shape. You can cash the diamond ace and lead another club. If West ruffs in with the spade king and cashes a heart, you have the rest. If he doesn't, you can pitch your heart on the diamond king and take the spade finesse. You might wind up making six.

As it happens, West ruffs when you lead a club to the ten. He will then cash the heart queen and play a diamond, sticking you in your hand. You can now take your second chance: ruff a club to dummy and try the spade finesse. You won't be able to pick up king third, since West will ruff in when you play a club, forcing you to overruff with the ten. But once East shows up with five clubs, he is unlikely to have three spades anyway.

Since the club ace is singleton and the spade king is offside, this line doesn't work. There are other lines that do, but I don't see any reason to choose one of them. I 'm sure I would have gone down after a heart shift, so most of the credit for this result belongs to that butterfly.

I'm still in first place, with 78%.

Weekly Free Instant Tournament - Feb. 11, 2022 - Board 4

Board 4
Both vulnerable

♠ A 10  ♥ A K Q 8 7 3  ♦ 8  ♣ K 10 9 4

Three passes to me. I bid one heart and LHO passes. Partner responds one spade, and RHO doubles.

Had RHO passed, I would bid two clubs, intending to bid three hearts next. I could bid three hearts immediately, but there are a number of ways two clubs can work out better. For one, if I get a chance to follow through with my plan, I will have painted a better picture of my hand, enabling partner to evaluate the fit more accurately. For another, it's possible clubs is the right strain. We might even make a slam in clubs that isn't available in hearts. The downside of bidding two clubs is I may be dropped there. But even that isn't necessarily a bad thing. Sometimes, I will be happy we didn't get any higher.

Once the auction gets competitive, however, our priorities change. I want to get as much information across as possible quickly. I no longer have the luxury of taking the auction slowly.

After the double, an immediate three-heart bid has two advantages: (1) It may make things harder for the opponents. If I bid two clubs, allowing the opponents a round of bidding to exchange information, then bid three hearts, they are better placed to make the right decision. (2) It may make things easier for us. Say, for example, I bid two clubs, LHO bids two diamonds, partner passes, and RHO bids four diamonds. Now what? Four hearts is an overbid. But I'm practically forced into it. Partner has no idea my hand is this good or that I have a self-sufficient heart suit. But if I bid three hearts now, I'm done. Partner knows I have six good hearts and seven and a half to eight playing tricks. I can comfortably sit back and leave further decisions to him.

I bid three hearts, LHO passes, and partner bids three notrump. I see no reason to disturb this contract, nor do my opponents. West leads the club five.

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

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

That's an aggressive three notrump call, given the heart void. Perhaps partner thought I wasn't making three hearts anyway. If we rate to go down in whatever contract we play, we might as well play a contract that has some upside.

The lead appears to be from QJ75 or QJ753, so I have three club tricks. Three hearts tricks and the spade ace brings me up to seven. I need two more.

Last week, someone questioned my tendency to start my analysis by asking how I'm going to make my contract. Since this is matchpoints, he pointed out, my concern even from the start should be maximizing my expected number of tricks--unless I have reason to believe I'm not in the field contract. That may be true, but my mind just doesn't work that way. I can't even think about how to maximize tricks until I have a starting point, and the best line to make my contract is a useful starting point. Once I've determined that line, I might then decide to give up on a slim chance in order to hold undertricks or to risk my contact for overtricks. So when I say "I need two more," understand I am simply setting my reference point. That goal is subject to revision.

If hearts are four-three, I can set up two heart tricks, but that's unlikely after West's double. My best shot is to find West with honor doubleton of spades. Actually king-queen third should work as well. If I win the club lead in my hand and play a spade, he can't split, or I will set up my spades. So he ducks and I win with dummy's ten. That's eight tricks. Now I cash my winners and toss him in with a club. He can cash two clubs, one spade, and the diamond ace, but must give me the diamond king.

I need to win this in my hand to start spades, so I play low from dummy. East discards the heart deuce. Whoa! East would not discard a heart from four or five. And on the auction it's unlikely he has three. Could he have six hearts? It's not clear he can afford a heart pitch from six. More likely, he has all seven. That means West is not apt to have a doubleton spade. My prospects of making this just went way down. But at least I'm not in hearts. Any North playing in hearts won't be happy. 

I win with the club six in my hand and play the spade three--six--ten--king. East shifts to the diamond queen. He might do this without the jack in an attempt to run the suit, so I can't be sure where the jack is. I cover with the king and West takes his ace. Dummy follows with the eight. The seven is the only high spot remaining, so if West returns a low diamond into my ten-nine-six, I will have two diamond tricks. There is a good chance he will do that. There is no future in clubs, and spades is the suit I'm going after.

No such luck. He shifts to the spade deuce. The fact that he didn't continue diamonds strongly suggests he holds the spade queen. If he didn't have that card, then I could conceivably be taking the rest of the tricks after a passive return. So he would likely try to cash whatever diamonds he could. 

East plays the spade five. If I'm right that hearts are seven-zero, then West is either 4-0-4-5 or 3-0-5-5. This is the current position:

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

I haven't made much progress in finding those two extra tricks. Do I have any chances left? The opponents have taken two tricks, and they have the spade queen and diamond jack ready to cash. So if I give up a heart trick, I'm down. Or maybe not. If East has the diamond jack and is out of spades, West's spade queen is stranded. So I will assume that's the case. If so, is there anything I can do? 

Perhaps I'm wrong about the seven-zero split. Suppose West is 4-1-3-5 with a stiff jack, ten, or nine of hearts. If I cash the heart ace, then exit with the seven, East can't return a heart without giving me two heart tricks. So he must play a diamond. If he has the seven, I can finesse the six, and I have two diamond tricks.

I doubt West would have doubled one spade with 4-1-3-5. But I don't see how it hurts to cash the heart ace to make sure. I cash it, and East follows with the six. I pitch the spade eight, and West pitches the diamond deuce. Too bad. Hearts are seven-zero, as I suspected.

Can I execute the same endplay for down one? If I exit with the heart seven, East will win with the nine and lead the jack. I duck, presenting the defense with their fourth trick. But now East can't lead hearts. If he is out of spades, the best he can do is cash the diamond jack for down one. If he has another spade or if West has the diamond jack, they can cash two tricks for down two. But I was always going down two, so it doesn't hurt to try this.

I lead the seven of hearts, East wins with the nine, and I pitch the club deuce. West pitches the club seven. East now cashes the diamond jack. He must have another spade and is cashing out for down one. He could have beat me two by leading the heart jack first. So I'm happy to accept down one.

West follows with the diamond three, and I pitch the heart three from dummy. Surprisingly, East continues with the diamond seven, and I claim. Making three.

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

All he had to do to beat me was to lead the heart jack before cashing the diamond. Why didn't he? Can it ever cost? It can cost if his partner has the diamond ten and I have enough tricks ready to cash to make my contract. But that's impossible. If that were the case, I wouldn't be ducking a heart. The robots' inability to draw inferences from their opponent's line of play is their biggest weakness, and here it proved fatal.

Plus 600 is a top. Making this was almost overkill. Even down one would have been worth 79%. The board was won when I bid three hearts over West's double. Most of the field bid slowly to three hearts and were doubled, going down anywhere from one to five tricks. East might have doubled three hearts even on my auction, but it's dangerous to double when the auction is still live, especially when you haven't had a chance to show your fit. Whether he should have doubled or not, it is clear he had a tougher decision than his counterparts at the other tables. So the three-heart bid did its job.

My score is now 72%, and I am back in first place.