Fifteen Seconds for Sleuthing

From a Wydaho online game earlier this year...

East Deals None Vul	♠ K J 8 6 ♥ K 9 5 3 2 ♦ 7 4 ♣ 9 8
♠ Q 5 3 2 ♥ A Q J 8 7 ♦ K 3 ♣ Q J	N W E S

WEST	North	East	South
		Pass	Pass
1 ♥	Pass	2 ♦	3 ♣
All pass

You opened 1 ♥ in third seat. Partner's 2 ♦ bid was natural and nonforcing (as a passed hand). 

You led the ♦ K, partner played the encouraging ♦ 9 and declarer played the ♦ 5. You decided to play the ♥ A at trick two, building a fence for partner so she will return a diamond for you to ruff after you lead your remaining diamond at trick three. We're sure that partner does not have three hearts; declarer won't ruff the ace.

What else can we figure out on this hand? 

• Who has the ♦ A? Partner's 2 ♦ bid promised at least a decent five-card suit, and a decent hand considering that she passed as dealer. Your king held the first trick, and partner played the ♦ 9, an encouraging card. Partner must have the ace. 
• How many diamonds does partner have? She needs at least five for her two-level bid. With a six card suit, she might well have opened a weak two diamonds. So assume that partner has five diamonds.
• How strong is partner's hand? Her hand wasn't good enough to open; neither was declarer's. She could have passed, or bid 1 NT instead of introducing a suit at the two-level. You can see 22 high card points between your hand and dummy. It seems as if the remaining 18 HCP must be about even between partner and dummy. So, give partner -- and declarer -- roughly nine high card points.
• How many clubs does declarer have? Declarer wandered into the auction at the three-level with about nine points. If declarer had seven clubs, he might well have opened 3 ♣. Is declarer crazy enough to enter a live auction at the three-level with only a five-card suit and a nine-count? Probably not. So, declarer likely has exactly six clubs. And therefore partner has three clubs.
• Which club honors does declarer have? You have the queen and jack. Would declarer enter the auction at the three level with only nine points and a six-card club suit headed by ace-ten or king-ten? Seems unlikely, so give declarer ace-king-sixth of clubs.
• Who has the ♠ A? If declarer has it, he would have AK-sixth of clubs and the ♠ A. Surely that's an opening bid nowadays. So, give partner the ♠ A.
• How many spades does partner have?  If she had five, surely she would have bid them. With ace-fourth of spades... hard to say, she might have chosen to bid diamonds instead, showing a five-card suit and suggesting more-than-minimum values.  She has five diamonds, three clubs, and at most two hearts, so partner has at least three spades, and possibly four.  That means partner has at least one heart, possibly two. And the same for declarer.
• Who has the queen and jack of diamonds? If partner has both, would she have opened 1 ♦ with AQJxx and the ace of spades? Maybe, maybe not. But that would give declarer AK-sixth of clubs and nothing else for his passed-hand 3 ♣ overcall. If declarer has both diamond honors, would partner have bid 2 ♦ (instead of 1 NT) with ace-empty-fifth of diamonds and the ace of spades? Probably not. So it seems most likely the diamond queen and jack are split.
• Who has the ten of diamonds? Partner signaled with the nine. If she had the ten and the nine, she would have played the ten, signaling from the top of a sequence. Thus her play of the nine denied holding the ten. Declarer has the ten of diamonds.
• How many hearts does declarer have? We know he has at least one, because partner denied having three hearts. Partner has at least one heart, because otherwise she would have five spades and didn't bid them. And would declarer bid 3 ♣ holding two small hearts? That seems a bit unlikely; declarer is somewhat more likely to have the singleton heart.

THE PRINCIPLE: At trick one, all players are entitled to about fifteen seconds -- all players at the same time -- to think through the entire hand. Use that time effectively! And then play the rest of the hand in tempo.

That was a lot to sort out in fifteen seconds, but with practice you can do this. Not every hand will be as clear as this one. And there is definitely some guesswork and assumptions involved. But look how much easier this game is when you can work out all four hands!

	♠ K J 8 6 ♥ K 9 5 3 2 ♦ 7 4 ♣ 9 8
♠ Q 5 3 2 ♥ A Q J 8 7 ♦ K 3 ♣ Q J	N W E S	♠ A x x ? ♥ x ? ♦ A H 9 x x ♣ x x x
	♠ x ?  ♥ x ? ♦ H 10 5 x ♣ A K x x x x

x = a known spot card

H = a known honor card

? = a card that may or may not be present

On the actual hand, declarer did indeed have a singleton heart, and declarer's diamond honor was the queen.
Extra Credit: You can make a reasonable argument that declarer was a favorite to have the ♦ Q. Why?

-- Ray

Better Bridge in 5 Minutes. Guaranteed! (or the next one is free)