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.