BBO Daylong Tournament 1 - Apr 7, 2021 - Board 3

Board 3
Opponents vulnerable

♠ 9 8 6 ♥ 9 ♦ A K Q 9 7 4 ♣ K 7 6

I open one diamond and partner responds one heart. I rebid two diamonds, and partner bids two notrump. I have six and a half playing tricks. A typical three diamond bid is seven and a half or eight. This hand is one trick short of that, so it is a maximum two diamond bid and a clear acceptance. I bid three notrump.

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

West	North	East	South
Robot	Phillip	Robot	Robot
	1 ♦	Pass	1 ♥
Pass	2 ♦	Pass	2 NT
Pass	3 NT	(All pass)

If you want to follow the play using BBO's handviewer, you can click on "Board 3" above. But be advised that the East-West hands will be visible. Also, BBO does not thoughtfully rotate the deal to make South declarer as I do. 

West leads the spade three. I play the nine from dummy, and East plays the king. If diamonds break, I have nine tricks--ten if I guess the club queen. If I duck this trick, the opponents can cash two hearts, holding me to ten tricks. But since I can never do better than ten tricks, there is no reason not to duck. For all I know, East may shift to a club. Or the opponents may cash their heart winners, rendering the club finesse unnecessary. Furthermore, ducking tightens things up, which can be beneficial in a number of ways. It makes it more difficult for the opponents to find discards and, therefore, easier to count the hand. And it may lead to a squeeze position in the endgame that you can't anticipate yet. As a general rule, if you don't see how it can gain to win a trick, it's probably a good idea to duck.

Accordingly, I play the deuce. That was an error, by the way. I should have played the four. The deuce informs East that his partner did not start with five spades. There is no reason I should let him know that. 

East shifts to the four of hearts. I could duck this to the nine, but it's more deceptive to play the jack. The fourth round of hearts is never going to come into play, so squandering an honor can't hurt, and it might induce West to continue hearts.

West takes my jack with his ace (leaving the deuce and three outstanding) and continues with the queen of spades--six--ten--ace. It appears West began with QJ52 of spades; East, with K10. I lead the diamond ten--eight--ace--deuce. Then king of diamonds--six--three--five. I cash the diamond queen. East follows with the jack. I pitch the heart five; West, the heart six. East began with two spades and three diamonds, so he originally had eight cards in the round suits, and West had seven. The deuce and three of hearts are still missing. 

On the next diamond, East pitches the club nine. I pitch the heart queen; West, the heart seven. As I said on board one, the bots give count when making their first discard in a suit and are surprisingly honest about it. So it appears East has four clubs and was originally 2-4-3-4. On the penultimate diamond, the deuce and three of hearts finally appear (from East and West respectively). I pitch the spade four.This is the position:

	NORTH Phillip ♠ 6 ♥ -- ♦ 4 ♣ K 7 6
	SOUTH Robot ♠ 7 ♥ 10 ♦ -- ♣ A J 10

If my reading is correct, East has king-eight of hearts and three clubs left, and West has jack-five of spades and three clubs left. Who has the club queen? I don't have much to go on except that East began with more clubs than his partner. Perhaps when I cash the last diamond, East will pitch a heart. Then I can pitch my spade, come to my hand with the club ace, and toss him in. 

I cash the diamond. No such luck, East pitches the club five, coming down to a doubleton. He has to to do that whether he has the queen or not, so I can draw no inference from the pitch. I pretty much have to play East for the club queen. Not only is he more likely to have it, but if I finesse his partner for it and I'm wrong, I'll lose the last three tricks and go down. Since East is down to a doubleton club, I don't need to finesse. I can just cash the ace and king. And I might as well lead to the club ace and lead the jack along the way, just in case West decides to cover. I pitch the spade seven, and West pitches the club deuce. 

Did both opponent's really just pitch down to a doubleton club? It appears so. East must have the queen, and West saw no reason not to pitch a club from three small. There is no longer any reason to fish for a cover of the club jack, so I cash the king of clubs--three--ten--four. Then I play the club six from dummy, expecting to see the queen from East. Instead, he follows with the eight. 

What did I miss? Is there any reason West would pitch down to queen doubleton of clubs? At first blush, it doesn't seem likely. The bots don't worry about taking your guesses away. But for all West knows his partner has jack doubleton of clubs left, and the pitch loses a trick by force. Perhaps my construction was wrong and West started with two clubs. I'm pretty sure about the spade split. So if West did start with two clubs, he was 4522 and East was 2335. It would mean both players gave false count on their first club discard. That's unlikely, but it is not impossible.

If I take the finesse and I'm wrong, I'm going down. Everyone should be in game, but not everyone will be. So I stand to lose more by finessing than I stand to gain. Even so, finessing has positive expectation if I'm sufficiently confident it's working. How confident am I? Bots don't fall asleep, so West isn't being careless. If he can see that a club pitch from queen third might give me a trick, he won't pitch one. Is it possible he doesn't see the danger?

Remember that bots analyze double dummy. If West knows I have the club jack, then, once his partner has come down to a doubleton club, a club pitch from Q42 can't cost double dummy. Do I have to have the club jack? No. I have a two notrump rebid without it. But remember also that bots don't construct layouts by asking themselves when their plays matter. They construct a number of layouts consistent with the auction, then determine which play works most often. I'm not sure how many deals West constructed. But if I happened to have the club jack in all of his constructions, then he would have encountered no scenarios where a club pitch from queen third would cost, and he would choose at random between a club pitch and a spade pitch. 

Since that might easily be the case, I'm not going to risk my contract by finessing. I go up with the ace. West drops the queen. Making four.

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

It's important to know how the opponents card. And the only way to know is by observation. Even the most forthright opponents tend to be evasive if you quiz them about their carding in the middle of a deal. And who can blame them? Much of carding is a matter of judgment, not agreement. While your opponents are required to reveal any specific agreements they have, they aren't required to offer lessons in judgment. So in a face-to-face knockout match, I spend much of my time as dummy following the opponents' carding, trying to figure out what their tendencies are for future reference. I have also paid close attention to how the bots card. 

Note their carding on this deal. Both opponents gave honest count on their first club discard, as I expected them to do. But their other carding is harder to understand. East did not give present count on his second club. He played the five from 853. And all their plays in the heart suit appear to be random. East shifted to the heart four from K842. (Since their opening leads are fourth best, I doubt that choice is systemic.) West, with A763, won the ace, then later discarded the six, then the seven. If there is any method to this carding, I haven't figured it out yet. It's almost as if West thought they were playing hearts instead of bridge. Keep those low cards so you have something to exit with in the endgame. East, however, did not follow this hearts-like strategy. He pitched the heart deuce from K82. But, come to think of it, he couldn't afford the eight at that point. Maybe he would have pitched it if he could.

+430 was worth 68%. Most declarers found the club queen, but seven were not in game. Some passed two notrump; others corrected two notrump to three diamonds. That is simply a mis-evaluation. A six-and-a-half trick hand is an acceptance opposite responder's invitational two notrump. 

Added on 9/30/21: As Barry Goren points out below, the line I intended to take should West pitch a spade on the last diamond (playing East for queen doubleton of clubs) was wrong. If West pitches a spade, I can just toss him in with a spade and claim. So the end position was actually quite interesting. Neither opponent can afford to hold three clubs, else he is endplayed. It was a double strip squeeze, and I didn't even notice.