Jaz Hands -- Board 10

Board 10
Both sides vulnerable

This week, we continue our discussion of the Ong-Tan vs Noervita-Sugandi match from the SEABF Mixed Teams.

You can watch Hope's discussion of Board 10 on our YouTube channel:

♠ A K 8 4  ♥ A 7 5 3  ♦ Q 8  ♣ A 6 2

Desy opens one notrump, showing 11-14, balanced. Jazlene doubles, which she tells me they play as showing 13+ HCP. I know that's a popular agreement: double their notrump when you have the maximum of their range. But I've never understood it. I don't see what their range has to do with anything. You need just as many tricks to beat a weak notrump as you do to beat a strong notrump. If they open one notrump with six to eight HCP, I'm not doubling with eight.

Personally, I think double should show 15+ HCP regardless of their range. To be fair, I do loosen up a bit when they play weak notrumps, because you do have to worry that it's your hand on power, something you generally assume isn't true when their one notrump is strong. But I don't loosen up on the high-card points. To double a strong notrump with a mere 15 or 16 HCP, I need to have a good opening lead. I don't worry about that against a weak notrump.

In any event, Jazlene's methods are a given, so, in the ensuing auction, we must take into account the fact that she could have an ace less.

Paulus redoubles, which shows a single-suited runout and asks partner to bid two clubs. Gideon passes, and Desy dutifully bids two clubs.

My choice here would be to pass. You may have seen our video explaining my methods when I open one notrump and they interfere. If you haven't, it's worth checking out:

While I didn't say so in the video, I play the exact same methods when they open one notrump and we double.

So double here would show a doubleton club. With three clubs I pass. If LHO passes also, partner will reopen with a double if he has a doubleton club and 7 HCP or so. If he has three clubs (and not enough in high cards to be concerned about missing a game), he will pass. If LHO corrects two clubs to two diamonds and that gets passed around to me, now I will double, showing a doubleton diamond. The idea is that we want to defend if they have a seven-card fit, since this may be our last plus. If they have an eight-card fit, we want to bid, since now it is more likely that both sides can make something.

Jazlene chooses to double, which she plays as take-out. She doesn't have the right shape for a take-out double, but with four cards in each major and an ace more than she has shown, she apparently judged an offshape double was called for.

Paulus corrects to two diamonds. Gideon chimes in with two spades, and RHO raises to three diamonds.

Now what?

Can we have a game? Jazlene still has an ace more than she might. With a classic shape for a take-out double, she would have doubled even with a minimum. What do we need for game? Perhaps something like

♠ Q x x x x  ♥ K Q x  ♦ x x x  ♣ x x ?

Maybe. But Desy's diamond raise makes that hand unlikely. Her partner could be broke, so she wouldn't be raising diamonds without four of them. If Gideon has a doubleton diamond, we probably don't have a game. He would then need five spades and four cover cards. With that much, he would have bid three spades over two diamonds. So I would judge we don't have a game.

Jazlene judges differently. She bids four spades. I suspect she would have simply invited with three spades had RHO passed. But after the raise, three spades isn't a game try any more. It's simply competitive. The only way to "invite" game here is to bid it.

I'm switching directions to make declarer South. 

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

West	North	East	South
Desy	Jazlene	Paulus	Gideon
1 NT	Double	Redouble	Pass
2 ♣	Double	2 ♦	2 ♠
3 ♦	4 ♠	(All pass)

Desy leads the king of diamonds; Paulus plays the deuce. Desy cashes the diamond ace, on which Paulus plays the six, then switches to the seven of spades. We have four more losers, which will put us down three. It appears they're making three diamonds. Minus 300 will be a five-imp loss. We can hold that to three imps if we find another trick.

If hearts are three-three, we can set up a heart trick if they don't get clubs going in time. If hearts are four-two, can we endplay someone? If Desy has king queen of clubs and a doubleton heart king and forgets to unblock, perhaps we can endplay her. That gives her ace-king of diamond, king-queen of clubs, king of hearts. No. That's fifteen. It seems we're stuck with Plan A.

Gideon cashes the ace and king of spades. Both follow.

What's the best way to attack hearts. If possible, it looks better to lose the first heart to Desy . A club shift rates to be harder from the West side than from the East side. So I would play a heart from dummy now. Gideon, however, judges to go the other way. He plays a trump to his hand. Paulus discards the diamond seven; Desy, the diamond three. He leads the six of heart and passes it when Desy plays the four.

Paulus wins with the heart jack and shifts to the five of clubs. The only hope now is for Desy to have the club king and to believe Gideon started with queen third instead of jack third. If so, when he wins this trick, he will be reluctant to continue clubs. Gideon plays low, Desy wins the the nine, and Gideon ducks in dummy. It works. Desy shifts to the ten of hearts. Gideon wins and plays a third heart. They split. Down two.

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

Gideon's play of a low club on Paulus' shift was critical. Had he played the jack, Paulus  would win with king and would have no reason not to continue clubs. Nice play, Gideon.

This should be minus three imps. Let's see what happens at the other table. West opens one diamond, North doubles, and East raises to two diamonds. That's passed back around to North, who doubles again. South bids two spades and East-West break the Law by selling out. West certainly should have competed. Responder usually has five diamonds for his raise. And, even if he doesn't, West knows the opponents have an eight-card spade fit. So it can't be right to let them play the two-level. That's a recipe for going minus at both tables. East has no reason to complete in balancing seat. He's said his piece. For all he knows, his partner is 4-4-3-2 and neither side has a good fit.

Here's the full auction:

West	North	East	South
Peter	Della	Huijun	Emmy
1 ♦	Double	2 ♦	Pass
Pass	Double	Pass	2 ♠
(All pass)

Having under-competed, the pressure is now on to beat this. East-West can make three diamonds, so they must go plus.

The defense begins just as it did at the other table: two high diamonds and a trump shift. Except that East plays ten-deuce on the top diamonds. I'm not sure what their signaling methods are. Personally, I would discourage on the opening diamond lead to show tolerance for a club shift. (Clubs not hearts, because hearts is a possible source of tricks. And only tolerance. It's not a request.) On the second diamond, I would give count. That would make the defense easy. With king-ten nine of clubs, West can shift to a low club. East will win and return one. The defense gets their club tricks in before anything bad happens.

Declarer wins the spade shift in dummy and immediately plays a heart. That's a nice play. If you don't draw trump, sometimes the opponents think it's a good idea for them to do so. The opponents don't know you have five spades, so playing a heart immediatly may make it appear you want to ruff hearts in your hand. East doesn't fall for it. He hops with the heart king and shifts to the deuce of clubs.

Unlike Gideon, he's not going to talk the opponents out of a club continuation no matter what he does. Since they need two club tricks to beat the contract, West will always continue clubs after winning this trick. Delcarer does have one chance left, however. He can hope hearts are four-two and the hand with the doubleton heart must win the club trick. If so, he can win the second club, draw trump, cash the heart ace, and exit with a club. That hand will now have to give him a ruff sluff.

If anyone has four hearts, it must be West, so declarer wants East to win the third round of clubs. Therefore he must play the jack, driving West's honor, then hope East forgets to unblock on the club return. It was correct for Gideon to duck the club shift, but Emmy must rise with the jack. He does.

West covers with the king, declarer ducks. West continues clubs, and declarer wins in dummy with the ace. No queen from East, so things are looking up for him.

Declarer cashes the last spade, plays a heart to the ace, and exits with a club to East's queen. Unfortunately for him, East has another heart. Down one.

That's minus 3 imps for the good guys.

Jaz Hands -- Board 9

Board 9
Opponents vulnerable

This week, we're starting a new series. We will be analyzing a match played by Jazlene Ong and Gideon Tan, from Singapore, in the Southeast Asian Bridge Federation Mixed Team Championships. They came in third in the event. This is a match they played against the eventual winners.

In return, Jazlene will be reviewing one of my sessions in her Jaz Plays Bridge channel.

In Gargoyle Chronicles style, we'll discuss one board per week in depth. The boards will be presented from Jazlene's perspective. Their opponents are Desy Noervita and Paulus Sugandi, from Indonesia.

You can also watch this analysis on our YouTube channel.

♠ A 10 5  ♥ K 8 6  ♦ Q 7  ♣ A Q 10 8 2

North and East pass. Jazlene opens one notrump; Gideon bids two clubs, Stayman; and Jazlene bids two diamonds. Paulus chimes in with a double.

This is a strange time to double. Presumably you are going to be on lead, so why double? It might help partner a bit in the defense, but I suspect it will be a bigger help to declarer.

Gideon raises to 3NT, and Paulus leads the spade three.

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

West	North	East	South
Paulus	Gideon	Desy	Jazlene
	Pass	Pass	1 NT
Pass	2 ♣	Pass	2 ♦
Double	3 NT	(All pass)

Gideon apparently decided to treat his weak five-card heart suit as a four-card suit. Coincidentally, I recently discussed with Jazlene the possibility of bidding Smolen without four cards in the other major, and this looks like a good candidate.

Missing a five-three heart fit when partner has four spades may be OK. So if partner responds two spades to Stayman, you can bid three notrump.  But missing a five-three heart fit might not be a good idea if partner is short in spades. So, if partner responds two diamonds, you can bid three spades, Smolen, to show five hearts. Ostensibly this shows four spades as well. But who cares? If partner doesn't have heart support, she's bidding three notrump. Ideally, you do this without ever discussing it with partner, so it might keep the opponents off a spade lead. Of course, having discussed it (or even having done it once), partner would now have to disclose that possibility, so that advantage disappears.

Even if this is what Gideon was planning (and I doubt it was), the double of two diamonds throws a monkey wrench into the plan. If you bid three spades and partner doesn't have a diamond stopper, she might choose to bid four hearts with a doubleton honor, which is unlikely to be right. Even worse, she might chose the four-three spade fit, which is even less likely to be right. So you pretty much have to bid three notrump now.

Anyway, here we are in three notrump. Jazlene wins in dummy with the king and Desy plays the deuce.

The opponents play standard attitude, so presumably Desy discouraged because she has nothing in spades, giving Paulus queen-jack fourth of spades and five or six diamonds to the king-jack-ten. The double of two diamonds and the play at trick one have given you a pretty clear picture.

Incidentally, I don't agree with Desy's spade deuce. Normally, attitude in notrump is about the suit led. But I think you should make an exception when you know partner didn't lead his best suit. Here, I think discouraging should promise a diamond card. If partner gets in, you don't want him switching to a diamond, which is probably what he will do if you discourage in spades. So I would encourage even with the five small spades Desy presumably holds.

Back to the play. You are looking at eight tricks. If the heart ace is on onside, you have nine. So let's assume it's offside. Is there any way to make this if that's the case?

Running five clubs might put some pressure on West. But if you do that, you can't lead up to your heart king anymore. So running five clubs is out. Will it accomplish anything to cash four clubs before playing a heart?

Probably not if West defends accurately. But if he has, say, ace-jack third of hearts, he may be afraid to pitch one. And he may be afraid to come down the king doubleton of diamonds as well. If he comes down to 

♠ Q J  ♥ A J 9  ♦ K J 10  ♣ --

and you read it, you have a shot. 

You now lead a heart off dummy. If East plays low, you duck. West wins and exits a spade. You toss him back in with a spade and he must give your ninth trick.

You would need to be quite confident the heart ace is offside to do that. If it's onside, you are going down in a cold contract. But I don't see what it hurts to run four rounds of clubs to test the waters, even if you just wind up leading a heart to the king anyway.

Actually, I take that back. Maybe there is a reason not to cash four clubs. West doesn't know you have a running club suit. For all he knows, hearts is your source of tricks. So, if you lead a heart to the king and the ace is offside, he may duck. If you run four rounds of clubs first, he won't. He now knows the heart king is your ninth trick.

For whatever reason, Jazlene plays a heart from dummy at trick two. Desy plays the nine. Jazlene plays the king and it holds. Making three.

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

I'm surprised Desy ducked the heart ace. Surely it's right to hop and play a diamond.

If declarer has to lose the lead only once, it makes no difference whether you hop or not. (You know from the Stayman auction that partner has at least two hearts, so you aren't crashing his stiff honor.) But if declarer has to lose the lead twice, you want to be the one to gain the lead first, so you can put a diamond through.

Imagine, for example, that Jazlene held

♠ Q J x  ♥ K x x  ♦ Q x  ♣ A Q J x x

Now ducking the heart gives her the contract.

At the other table, South also opened one notrump. North didn't ignore the five-card heart suit, but he chose a middle ground. He transferred to hearts, then bid three notrump, treating his hand as balanced to give partner the option of spurning the five-three fit. South corrected to four hearts and made five, picking up 2 imps.

Free Weekly Instant Tournament - November 14 - Board 8

Board 8
Neither side vulnerable

Watch Hope discuss this deal on our YouTube channel:

♠ J 7 6  ♥ A K J 10 6 3  ♦ A 3  ♣ 7 3

Three passes to me. In fourth seat, a weak two-bid typically shows a full opening. Even so, this hand may be a bit too good. If I had the spade suit, I would just open one. But with the heart suit, I want to make it hard for the opponents to come in. And, with seven losers, I'm not too worried about missing a game. So I open two hearts.

Everyone passes, and LHO leads the jack of clubs.

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

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

I cover, and East takes the ace. It makes no difference which card I play. From East's perspective, the lead could be a singleton or a doubleton whichever card I choose. I choose the three for purely psychological reasons. Declarers typically "falsecard" by playing high in this situation. For no particular reason--that's just what they do. If the lead is indeed a singleton and I play the three, East might wonder where why I didn't falsecard. Of course, such mind games against computers are pointless. But I always pretend I'm playing against humans if it doesn't matter--just to keep in practice.

East returns the five of clubs. West follows with the nine, and I win in dummy. We've reached this position, with the lead in dummy:

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

How should I play hearts. A finesse gains only if East has specifically queen third. If he has queen doubleton, it's dropping anyway. If he has queen fourth, I have an unavoidable trump loser.

When does finessing lose? I might go down two. If West wins the queen, leads a spade to partner, and gets a club back, I'm OK. I can simply pitch a loser. But suppose they cash three spades, then East plays a fourth one. I can pitch a diamond on that trick, but now the last club hurts. I may lose to a trump promotion.

That's quite a parlay, though. West must have the heart queen. East must have long spades. West must find the spade switch rather than a diamond. And even if all that comes to pass, I'm still OK if trumps are three-three.

Queen third of hearts onside is half of the three-three breaks (18%). The parlay requires the heart queen on my left and spade length on my right. That's 25%. If we then eliminate the three-three heart breaks, we're already at less than 18%. And I haven't even taken into account the fact that West might not find the spade switch. So the finesse is considerably better than cashing ace-king.

There is another possible line, however. I can cash the ten of clubs and pitch a spade. If West has queen third of hearts, he's ruffing with a natural trump trick, so I compress my losers. Taking the finesse gains when East has queen third. Taking the pitch gains when West has queen third. Is it simply a toss-up?

Not quite. If West has queen third of hearts and a doubleton spade, he can ruff the club, then play spades to promote his queen of hearts. That tips the odds in favor of the finesse.

I play a heart to the jack. It holds. I cash the ace and king of hearts. They split three-three. That's eight tricks. I've made my contract. Is there any scenario where I can take an overtrick?

I don't see how. But let's cash some hearts and see what happens. West pitches the four of diamonds. That's probably low from five, making West 3-3-5-2. East pitches his last club. Yes, I guess he doesn't need that card.

On the next heart, West pitches the three of spades; East, the five. West has pitched down to a doubleton spade. That's promising.

On the last heart, West pitches the five of diamonds. I've been pitching clubs from dummy, so I'm down to three-three in the pointed suits. Jack-nine third of diamonds may prove useful, so I pitch a spade. East pitches the seven of diamonds. We're down to this position:

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

Is there any way to manufacture a trick here? Maybe. If I've read the the cards correctly, West is down to two spades and three diamonds. If he holds two spade honors and honor-ten third of diamonds, then the layout looks something like this:

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

I can exit a spade. If West cashes two spades and exits with a small diamond, I can insert dummy's nine. East will play his honor and I can take my ace and lead toward dummy's jack. Of course, West can avoid this by cashing two spades and exiting with his diamond honor. But it's worth a shot.

I exit with a spade. West wins with the queen and cashes the ace. He now leads... the six of diamonds. I play the nine from dummy. East plays the queen. I win and play another diamond. West has king-ten left, so I make an overtrick.

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

I'm surprised. Leading the diamond king instead of a low one in the end position should not have been a hard play for the robots to find. 

Plus 140 is worth 100%. It turns out the overtrick was immaterial. Any plus score was worth 100%. If you open one heart, as everyone else did, the auction continues one notrump--two hearts, and your opponent doesn't let you play it. And by opponent, I don't mean LHO or RHO. It's your center-hand opponent who doesn't let you play it. CHO bids three clubs, and you go can no longer go plus.

Opening two hearts works not because it shuts up East-West but because it shuts up partner.

In Gargoyle Chronicles, the rule is that, during the play, we discuss only what I thought about during the play. If I overlooked something, that waits until the post mortem. And I did overlook something.

At the critical juncture above, I said taking the heart finesse works when East has queen third and pitching on the club works when West has queen third. But there's another case where taking the pitch works: when West has queen doubleton of hearts. If I finesse, I go down. If I take the pitch, I later drop the heart queen and take eight tricks. Playing for the drop works, too. But I already rejected that line. 

So the finesse is right when East has queen third of hearts. Taking the pitch is right if West has queen third or queen doubleton (minus some fringe cases where he gets a trump promotion). So I should have taken the pitch and gone down. I fell just terrible saddling the opponents with a bad board by misplaying the hand. But that's life.

Next week, we're doing something a bit different. Jazlene Ong analized one of my sets over on her JazPlaysBridge YouTube channel. So, over the next eight weeks, I'll be returning the favor by analyzing one of her matches from the Asian Mind Games.

Free Weekly Instant Tournament - November 14 - Board 7

Board 7
Both sides vulnerable

Alex walks you through board 7 on YouTube:

♠ A J 3  ♥ A 5  ♦ Q J 9 6 3  ♣ A K 10

I have 19 HCP and a balanced hand. I'm sure some will add a point for the five-card suit and open two notrump. That makes no sense to me. Am I really going to miss a game if I open one diamond and it gets passed out? I don't think so. I would be more worried about going minus if two notrump is passed out.

And it's not as though opening two notrump will make my auction easier if partner has a good hand. Minor-suit slams are difficult to bid after a two notrump opening. If we belong in six diamonds, I am almost surely better off opening one diamond. In short, I just don't see the upside in opening two notrump. Two notrump is a weak spot in standard methods. It's a bid you should try to avoid, not a bid you should go out of your way to make.

I open one diamond. LHO bids two hearts--pass--pass back to me. I double, and partner bids three diamonds. I like to play lebensohl after opener's two-level reopening double. If we were playing that, I would bid three notrump, since I know partner isn't broke. As it is, passing is probably the percentage action. I pass, and West leads the king of hearts.

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

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

Maybe there is some upside to opening two notrump after all. One diamond gives the opponents a chance to pre-empt. If I open two notrump, partner would raise to three. Since East rates to have the diamond ace, three notrump is probably making.

Or is it? If the auction goes two notrump--three notrump, declarer won't know West has six hearts. If hearts are four-four, you're cold if you win the first heart. If you duck, West may find a spade switch and beat you in a cold contract. Ducking is not only playing for a six-two split, it's playing for the diamond ace on your right as well. So perhaps those in three notrump will win the first trick and go down.

I'm not convinced winning the first trick is the right play. But I'll think about that later. In three diamonds, there is no reason to duck. I take the heart ace and lead a low diamond.

West pops the ace. West has the ace? Really? That's quite a pre-empt! But it's good news. It means three notrump is going down.

West cashes the queen of hearts, on which East follows. Then he taps me with the jack of hearts. There is no way for me to avoid a spade loser. Making four.

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

Plus 130 is worth 89%.

How should you play three notrump if you reach it with no opposing bidding? Should you win the first heart or duck? As I said, ducking runs the risk that West will find a spade switch to beat you when hearts were four-four all along. 

But is that a serious concern? West isn't looking at your hand after all. Will he really switch away from a spade honor into the two-notrump bidder? It seems wildly unlikely. And even if he does, you're not necessarily down. The defense needs to take three spade tricks after winning the diamond ace.

In general, you shouldn't assume the opponents will defend double-dummy. Even though six-two hearts with the diamond ace is on your right is unlikely, it's more likely than that West will find a killing spade switch. So, if were in three notrump, I would duck at trick one.

And, for what it's worth, six-two hearts isn't as unlikely as you might think. In fact, if he we assume West would lead low from king-queen empty fourth, then six-two hearts is actually more likely that four-four hearts. 

Why is that? There are five small hearts outstanding. If we give West king-queen-jack fourth of hearts, then he has one small heart, and there are only five ways for that to happen. If we give West king-queen-jack sixth of hearts, then he has three small hearts. There are ten ways for that to happen. So there are twice as many ways for West to hold six hearts as to hold four.

Of course, that's not the whole story. If West holds six hearts, then he is shorter in the remaining suits. But even after taking that into account, a six-two break is still more likely than four-four.

I'm not going to step through the calculations. But here are the final results if, as Alex might say, you want to check the receipts:

West's Holdings

Heart holding	Remainder	Frequency
♥ K Q J x	9	5C1 x 18C9 = 243,100
♥ K Q J x x x	7	5C3 x 18C7 = 318,240

Obviously you can't do this calculation at the table. But you don't need to. Here's how to think about it: Treat the small hearts as a separate suit. Playing for four-four hearts is playing for a one-four split in the small-hearts suit. Playing for six-two hearts is playing for a three-two split, which is more likely. That's a trick worth remembering.