Free Weekly Instant Tournament - September 19 - Board 7

You can, if you prefer, watch Alex analyze this deal on Gargoyle Chronicle's YouTube channel:

Board 7
Both sides vulnerable

♠ A 7  ♥ K J 8 7 4  ♦ Q J 10 3  ♣ K Q

I could open with one notrump, but I don't like opening one notrump with a five-card major unless I have a rebid problem. With this hand, I have an easy two-diamond rebid, so I open with one heart. 

Partner bids one notrump, and I rebid two diamonds. Partner bids three hearts, showing an invitational raise with only three trumps. I bid four hearts. Everyone passes, and LHO leads the nine of diamonds.

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

West	North	East	South
Robot	Robot	Robot	Phillip
			1 ♥
Pass	1 NT	Pass	2 ♦
Pass	3 ♥	Pass	4 ♥
(All pass)

I have two aces to lose. I can lose a second heart trick or a spade trick, but not both. I'd like to set up clubs for a spade pitch, but the opponents are threatening a diamond ruff, so I can't do that right away. I have to get trumps going.

I win in dummy with the diamond ace. East plays the deuce. I must play an honor from my hand for two reasons: (1) It leaves open the possibility that I can reach dummy twice more in diamonds. And (2) if West's nine is a singleton, it leaves open the possibility that the lead was from a doubleton. (I could be 3-5-3-2 for my two-diamond rebid.)

What should East's deuce mean? I think it should be discouraging, suggesting either the ace or king of clubs. Since clubs is dummy's weaker suit, that's the obvious shift. With a club card, he discourages; without one, he encourages. If he encourages and West needs to find his entry (perhaps to get a diamond ruff), then West knows either it's in spades or East doesn't have one.

Some would play suit preference here, since West may be looking for your black-suit entry. But I think making ad hoc exceptions like that is a serious error. It gains nothing. Attitude works just fine, and always playing attitude rather than switching back and forth between attitude and suit preference based on some subjective criterion avoids misunderstandings. In this particular case, a low card suggests clubs whichever signal you intend, but you aren't always so lucky.

The robots, of course, understand none of this. The deuce means nothing at all.

I play the heart three from dummy. East plays the deuce. What's my best play?

West probably wouldn't have led a short suit with a singleton trump. And if he has four, it makes no difference what we do. So let's assume trumps are three-two. Let's also assume the diamond lead was a doubleton--not a singleton. We can revisit that assumption later.

Here, then, are the possible heart layouts:

Heart Layouts

West	East
♥ A Q	♥ 10 x x
♥ A 10	♥ Q x x
♥ Q 10	♥ A x x
♥ A x	♥ Q 10 x
♥ Q x	♥ A 10 x
♥ 10 x	♥ A Q x
♥ A Q x	♥ 10 x
♥ A 10 x	♥ Q x
♥ Q 10 x	♥ A x

That's a lot of possibilities to consider. Fortunately, we can simplify the analysis by canceling out holdings where the right play is simply a guess. For example, If West has ace-queen tight, my best play is the eight, which guarentees holding my losers to two. Similarly, if West has ace-ten tight, my best play is the jack. And if he has queen-ten tight, my best play is the king. In all those cases, the "wrong" play isn't necessarily fatal, but it does require me to guess right on the next round.

The upshot is, if West has two honors doubleton, my best play is toss up (if I have a three-faced coin). So the first three cases cancel out and I can ignore them.

Can we ignore any other layouts? If West has queen doubleton, it makes no difference what I do. I'm losing two tricks whether I play the king, jack, or eight. I also lose two tricks whatever I do if West has ace-queen third. So we can ignore those two cases as well. We have only four cases left:

Relevant Cases

West	East	King	Jack	Eight
♥ A x	♥ Q 10 x			Y
♥ 10 x	♥ A Q x		Y
♥ A 10 x	♥ Q x		Y	Y
♥ Q 10 x	♥ A x	Y
Total		1	2	2

The first two cases are the only layouts where I can hold my losers to one. If West holds ace doubleton, I must play the eight. If he holds ten doubleton, I must play the jack.

In the last two cases, I always have two natural losers. The trick to avoid losing a ruff as well. If West holds ace-ten third, I must play the jack or the eight. If I play the king, West can win, play his second diamond, then get a ruff when his partner wins the queen. If West holds queen-ten third, I must play the king. If I lose to West's ten or queen, he can play his second diamond and get a ruff when his partner wins the ace.

The bottom line: The jack or the eight is best in two cases each. The king is best in one. So my best play is a toss-up between the jack and the eight.

Is there any way to break the tie? Perhaps. Let's revisit our assumption that West has a doubleton diamond. If he has a singleton (or even if East thinks he has a singleton), then East might hop with ace-queen third to give him a ruff. That reduces the likelihood of one of the cases where the jack is right. So our best play is the eight.

I play the eight. West wins with the ten and cashes the ace of clubs on which East plays the three and I play the queen. So it was a stiff diamond and he's trying to find his partner's entry? No. He shifts to the four of diamonds now. Not sure why he cashed the club ace before doing that.

I win in dummy with the king. East plays the eight, and I continue to unblock by playing the jack. We've reached this position with the lead in dummy:

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

I play a heart--queen--king--ace. The opponents can't stop me from pitching my spade loser. Making four.

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

Plus 620 is worth 75%. We're sitting at 70% with one board left in the set.

What would have happened if I had opened with one notrump? Partner would raise to three, which makes on the normal club lead for 46%. But if West finds a spade lead, three notrump actually goes down--assuming that, when declarer plays a spade honor from dummy, East ducks his king to preserve communication.

Interesting that, even though partner is 4-3-3-3, the eight-card heart fit is better. Declarer's being 5-4-2-2 does make a difference, since it gives declarer two vulnerable suits. Switch one of South's diamonds for one of East's spades, and three notrump can't go down.