Match 2 - Board 32

Board 32
Opponents vulnerable

♠ 7 5 4 ♥ A J ♦ J 9 8 ♣ Q J 4 3 2

Partner opens one notrump (12-14) in second seat and buys it. West leads the jack of spades.

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

West	North	East	South
		Pass	1 NT
(All pass)

I play low from dummy, East plays the king, and I play the deuce. East continues with the eight of spades. I play the queen. West takes the ace and cashes the ten of spades, on which East pitches the five of clubs. It's hard to imagine that the club king is onside. What club holding that includes the king would East be willing to pitch from?

I'm going to have to make two discards on West's spades. What should my plan be? One possibility is to pitch down to

(A) ♠ -- ♥ Q 8 ♦ A Q 10 5 3 ♣ A.

The defense needs to take two tricks to beat me. If East discards correctly, West should be able to tell that I've stiffed the club ace and should find a club shift. After winning the club ace, I must take at least six more tricks without losing the lead. I have two choices:

(A-1) Take a heart finesse. If this wins, I'll make an overtrick if the diamond king is onside and go down one if it's not. If the heart finesse loses, I'm down. In fact, if the diamond finesse loses as well, I'm down some ridiculous number of tricks, since the defense will be able to run the heart suit.

(A-2) Lead a heart to the ace and take a diamond finesse. This gives me my best chance to make the contract. I'll make it if the diamond finesse wins and go down many tricks if it doesn't.

Another possibility is to pitch down to

(B) ♠ -- ♥ Q 8 3 ♦ A Q 10 5 ♣ A.

This has the advantage that I will never go down a lot, since the opponents can't establish the heart suit. But, against best defense, it reduces my chance of making the contract to 25% (as in line A-1). Assuming West finds the club shift, I will will need both red kings onside to make it. If the heart finesses loses, I'm down one if the diamond king is onside (losing a trick to the heart king and club king) and down two if it's not (losing a trick to each king). As an interesting aside, note that if West somehow fails to find a club shift, I still make two when both red finesses are on. Assuming I'm right that West holds the club king, he is caught in a criss-cross squeeze on the run of the diamonds.

A third possibility is to hold a club, thus preventing West from establishing his club king. For this to gain, however, I need some place to pitch the club later. That means I must hold

(C) ♠ -- ♥ 8 ♦ A Q 10 5 3 ♣ A 7,

and the heart king must be onside. But then what have I accomplished?  West will play a heart. I finesse and cash the heart ace pitching my club.  If the diamond finesse is onside, I'm no better off than I would have been adopting A-1.  And if it's offside, I'm considerably worse off. C is never superior to A-1, so I can forget about it.

That means I have three strategies to choose from. What makes it especially hard to choose is I have no idea what will happen at the other tables, so it's hard to estimate how many matchpoints each one of my possible results is worth. I must do the best I can, however, so I am going to make some guesses (assuming a 5 top to keep the arithmetic simple):

+120	5 MP
+90	3 MP
-50	2 MP
-100	1 MP
-more	0 MP

Since the opponents are vulnerable, I've made the difference between plus 120 and plus 90 greater than the difference between the other scores on the assumption that there will be plus 100s floating about. If the opponents were not vulnerable, I would make the difference between plus 90 and minus 50 greater.

Now let's construct payoff tables for each of my three possible strategies:

A-1 (pitch club and heart, finesse heart)

	♦ K onside	♦ K offside
♥ K onside	5 MP	2 MP
♥ K offside	2 MP	0 MP

A-2 (pitch club and heart, don't finesse heart)

	♦ K onside	♦ K offside
♥ K onside	3 MP	0 MP
♥ K offside	3 MP	0 MP

B (pitch club and diamond)

	♦ K onside	♦ K offside
♥ K onside	3 MP	2 MP
♥ K offside	2 MP	1 MP

Because of my assumption that there will be a significant difference between making one and making two, A-1 turns out to be the winner. At least it's the winner if I think it's 50-50 who has each of the red kings. If East's discards offer some clue about the location of the kings, then the other strategies might prove more attractive.  (If, for example, I decide that the diamond king is probably offside, then I should adopt B.) So my initial plan is to go with A-1, but I am open to changing my mind if I get more information.

West cashes another spade. I can't afford a diamond pitch from dummy. I may need to take three finesses if East has king fourth. So I pitch a club. East discards the club six. This should be present count (assuming the first discard was attitude), so East should have begun with four small, and West should know this.

Why is East reluctant to pitch a red suit? A diamond pitch would be dangerous from almost any holding. A pitch from king-seven third, for example, will cost if I have ace-queen empty fifth. (It allows me to pitch a diamond from dummy, unblocking the suit.) Even a pitch from three small might cost, since it might induce me to drop an offside doubleton queen. Jack, however, always assumes declarer is double-dummy, so he won't worry about pitching from three small. Against Jack, I think the odds that the diamond king is onside are now better than 50%, making B an unattractive strategy.

Why is he not pitching a heart? He might have the king and be hoping hearts represents a source of tricks. Or he might have ten fourth of hearts and be afraid a pitch will give me a trick if I have king fourth.

What should I pitch? A club, retaining the option of adopting strategy B is the most flexible. But I think I've pretty much decided against B on East's failure to pitch a diamond. An immediate heart pitch offers a peculiar advantage: it makes it safe for East to pitch a heart from ten fourth. If I pitch a heart now and East still refuses to pitch one, I can be fairly confident that he has the king. So I make the "discovery play" of the three of hearts.

West cashes his last spade. I pitch another club from dummy. East pitches the deuce of hearts. East's heart pitch isn't especially meaningful. There are a variety of reasons a heart might be his most attractive pitch with or without the king. But if he hadn't pitched a heart once I told him that it was safe to pitch from ten fourth, that would be significant. I would assume he had the king, and I would switch to strategy A-2. Since that didn't happen, I'm sticking with my original plan of A-1.

I pitch the club seven. West, somewhat surprisingly, fails to find the club shift. He shifts to the four of hearts. I play the jack, and East plays the deuce. The diamond king is onside, so I make two.

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

We are the only pair to play the hand our way. Every other table played one spade by East-West. Why didn't I think of that? I was so wrapped up in constructing my payoff tables, I didn't even stop to ask what would happen after a one diamond opening. If I had, it wouldn't be hard to predict that one spade by West would be a popular contract. Actually, I suppose I should be happy I didn't think of that. It took long enough to play this hand as it was. If I started calculating how many tricks we were apt to take against one spade in each of the four scenarios and adjusting my payoff tables accordingly, I'd still be in the tank.

Not that it's easy to tell what would happen in one spade, even looking at all four hands.  Assume the defense starts with a diamond to the queen and a heart shift. It seems natural for declarer to rise with the heart king, since, if the ace if offside, he must lose three heart tricks anyway via a ruff. But if he does rise, he gets tapped out and goes down. If he ducks, he retains control and gets to score the club king for his seventh trick. In practice, three declarers went down in one spade, one made one, and two made an overtrick.

We can now check the accuracy of my matchpoint estimates. Here is what various scores would have yielded, adjusted to a five top.

+120	5.0 MP
+90	2.5 MP
-50	2.5 MP
-100	1.7 MP
-more	0.0 MP

I was right that the biggest difference was between plus 120 and plus 90. Although it didn't occur to me that there would be no difference at all between making one and going down one. Overall, my estimates were pretty good, except that minus 100 was a better score than I thought it would be. I hadn't anticipated the minus 110s.

Score on Board 32: +120 (12 MP)

Total: 262 MP (68.2%)

Current rank: 1st