Free Weekly Instant Tournament - September 15 - Board 5

Board 5
Our side vulnerable

♠ K 10 3  ♥ A K J 4  ♦ A K  ♣ Q J 4 2

Two passes to me. I open with two notrump and partner raises to three. LHO leads the five of hearts.

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

West	North	East	South
Robot	Robot	Robot	Phillip
	Pass	Pass	2 NT
Pass	3 NT	(All pass)

I have eight cashing tricks. One possibility for a ninth is to find at least one club honor onside, a seventy-five percent chance.

Another possibility is to go after diamond tricks. I will need to find diamonds three-three or to drop the queen or ten in two rounds. My gut instinct says that's less than 75%. But the fact that this line yields two tricks instead of one makes it more attractive than playing clubs even if it is somewhat less likely to work.

Do I have time to develop a long diamond even if someone has queen-ten fourth? I cash the ace king, lead a heart to the queen, and play a diamond. No. I have only one dummy entry left, so I can't set up the last diamond and get back to cash it.

Maybe I can combine my chances, though. I can cash the ace and king of diamonds. If an honor drops, I set up diamonds. If it doesn't, I can consider switching to clubs. I'll still have two dummy entries to lead clubs twice.

I might as well start by inserting the heart nine. I don't see how that can hurt, and it will give me some clue about the lie of the heart suit. I play the nine, East plays the three, and I play low. West has apparently led from ten third or fourth unless East is playing a deep game.

I lead a diamond to the king. (The ace would suggest the king. The king is more ambiguous.) East plays the four; West, the three. The deuce is still out. On the ace of diamonds, West plays the deuce; East, the six. One opponent is giving honest count; the other isn't. Against humans, I would assume whoever doesn't have the queen is being honest in case his partner has the ace and needs to hold up. The player with the queen probably sees no reason to give honest count. 

In fact, I can state that more strongly. The hand with the queen must give false count. Any time one hand must give correct count in case his partner needs it, the other hand must give false count. Since declarer knows one hand can't afford to falsecard, he can trust the carding if the defenders' signals are consistent. But if one hand gives correct count and the other gives false count, declarer has no way to know which defender to trust.

These inferences aren't valid against robots, however. They don't think about such things. Their carding when declarer leads a suit appears to be random.

Since I didn't see the ten or the nine, should I switch plans and play on clubs? The two remaining diamonds are roughly 50% to split. (East can have queen-ten, West can have queen-ten, or they could be evenly split two ways. So they split in two cases out of four.) The club play works 75% of the time, so it is by far the better choice.

I play the jack of hearts to dummy's queen. West plays the seven; East, the six. Now five of clubs--seven--jack--ace. West continues with the heart ten. I win in my hand as East discards the club three. If East has the king, he probably has king fifth. He wouldn't pitch from king fourth, handing me a long club trick.

I cash the last heart and pitch a diamond from dummy. East pitches another club, the six. This isn't looking good. He wouldn't pitch two clubs from king fifth, so it looks as if the club king is offside. Maybe I can cash the ace and king of spades and toss West in to force a club lead. West would need to be 4-4-2-3 with the queen-jack of spades. Or maybe 3-4-3-3 with queen-jack of spades and the diamond queen. Neither seems likely. If East has nothing in spades, he might have pitched spades instead of clubs. Maybe West has ace-king tight of clubs and I can duck the king out.

I'll worry about that after I play a club from dummy. I play a low spade to the ace. West plays the deuce; East, the four. West might have split from queen-jack of spades, so I doubt he has both honors. Endplaying him is out. 

I play the eight of clubs from dummy, not entirely sure yet whether I'm going to duck it or not. East solves my problem by hopping with the king, and West pitches the ten of diamonds. I see. King sixth of clubs on my right. That's why he could afford to pitch two of them. Making three.

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

Plus 400 is worth an astounding 96%. Why?

It turns out the field is persisting in diamonds even after an honor fails to drop, taking their 50% line instead of their 75% line. But hold on. Maybe the field is right. In calculating the odds, I completely forgot to factor in that the diamond play yields two tricks if it works. I did say that fact made the diamond play "more attractive than playing clubs even if it is somewhat less likely to work." But I never quantified that "somewhat."

Half the time, the diamond play does a trick better than the club play. When does the club play do better? We need both the club play to work (75%) and the diamond play to fail (50%). So the club play is better only 37.5% of the time. 

Why did I have this blind spot? I think once I calculated the diamond play worked only half the time, I instinctively rejected it. One doesn't usually risk one's contract for an overtrick on a coin toss. But that's because the alternative is usually ensuring your contract. When the alternative is only a 75% play anyway, a coin toss is sufficient. I made the right play at IMPs but the wrong play at matchpoints. .