Free Weekly Instant Tournament - March 15 - Board 3

Board 3
Opponents vulnerable

♠ K Q 5  ♥ Q 8 6  ♦ A K 9 7  ♣ J 8 7

I open one notrump in first seat and buy it. LHO leads the three of hearts.

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

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

I play low from dummy and West wins with the king. What should I do if East continues with a low heart at trick two? A priori, East is twice as likely to have the jack as to have the ace by restricted choice. Yet one could argue that I should go up with the queen anyway, since East would lead the jack if he had it to smother dummy's ten.

But would he? He certainly would if he had the nine. But if he doesn't, then I might have it and leading the jack takes my guess away. True, leading low from jack-empty risks letting me take a trick I'm not entitled to. But if I'm going to hop whenever he leads low, leading low from jack-empty doesn't cost. 

But if I decide East will reach this conclusion and will therefore lead low from jack-empty, it becomes wrong for me to hop. I should go with the a priori odds and duck. But if I'm going to duck, East can no longer afford to lead low from jack-empty. But that means it is right for me to hop. And so on ad infinitum.

How do you escape this vicious circle? What's the right answer? It so happens I wrote a Bridge World article about this suit combination years ago. If you're interested, you can find my solution there. In this case it's moot, since East continues with the ace at trick two, and West follows with the nine.

At trick three, East leads the jack of hearts. I win with the queen, and West follows with the seven. I still haven't seen the deuce. Hearts could be four-four or either opponent could have started with five hearts.

I have six tricks. I need one more. If East has the spade ace, my contract is safe. I can lead a spade toward my hand. If East ducks, I'm home. If he hops, there is no scenario where the defense can take seven tricks. If East has five hearts, they can take four hearts and two aces. If West has five hearts, they can't cash them unless East leads a club to West's ace, solving my club problem. And if hearts are four-four, the best they can do is to take three hearts, a spade, and two clubs.

If West has the spade ace, however, I could have a problem. Say I play a spade to my hand, and West wins, cashes two hearts, and leads a low club. I'll need to hope West has a club honor and will have to guess which one in order to make my contract.

I could run all my diamonds before playing a spade to maximize my chance of guessing clubs. But then I won't be able to lead up to my spades twice. I'd like to do that, since if East has both aces and no more hearts, I can make an overtrick by taking two spade tricks.

It's not clear how much I will learn by running all my diamonds anyway. So I'll compromise by cashing three diamonds before playing a spade toward my hand. If the spade wins, I'll finish the diamonds and play another spade. If it loses, at least I'll have some extra information from having cashed three diamonds.

I pitch a club from dummy on this trick and cash the ace and king of diamonds. On the second diamond, West pitches the five of clubs. There are two lower clubs out. I can't tell whether that's a high club or a low one.

I play a diamond to dummy, and West pitches the ten of spades. That one's high. The robots like pitching count cards. So it appears West is 4-5-1-3 or 4-4-1-4. If he turns out to be 4-5-1-3, I'm going to play him for the club ace. I doubt his first discard would be a club from queen third.

We've reached this position with the lead in dummy:

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

I lead a spade from dummy. East plays the jack, and I play the queen. West takes the ace and cashes the five of hearts. I pitch a spade from dummy. East pitches the six of clubs. I'm happy to see that card. If East had both club honors, he wouldn't be pitching clubs. He would be hoping to run the club suit. So I'm sticking with my assumption that West has the club ace. Presumably this is the current layout.

	NORTH Robot ♠ 7 ♥ -- ♦ J 6 ♣ K 9
WEST Robot ♠ x x ♥ 2 ♦ -- ♣ ? ?		EAST Robot ♠ x x ♥ -- ♦ -- ♣ ? ? ?
	SOUTH Phillip ♠ K ♥ -- ♦ 9 ♣ J 8 7

West cashes the last heart. I pitch a spade from dummy, and East pitches the club three. East's coming down to a doubleton club was an error. I can now pitch a club from my hand safely. Even if I misguess clubs, I'm down only one. East would have done better to hold all four clubs. Then, if I think East has both club honors, I might decide to pitch a diamond from my hand and concede down one. Pitching a club retains the possibility of making but risks going down three.

I pitch a club, intending to play West for the club ace if he leads a low one. But he doesn't put me to the test. He shifts to a spade, and I claim three tricks. Making one.

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

Plus 90 is worth 61%. Most declarers ran all their diamonds before playing a spade. I think that's a mistake, though it didn't matter this time.

West's spade exit at the end was strange. That was simply giving up. But I see what he was "thinking." Since robots assume you are double-dummy, they will never put you to a guess if they have another option. West was hoping his partner had the last diamond and I had no way to get to dummy except to lead a club to the king, in which case he could win and cash a spade. In the robot's opinion, I'm more likely to have completely butchered the play earlier than I am to misguess a queen now.