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.