Restricted Choice

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

You are declarer in 3 NT, the opening lead is the ♠ 10. You play the ace, of course, hiding the spade queen from both opponents.. The spade suit presents no danger. The opponents can easily see that their best chance for tricks is in diamonds. If you lose the lead, you will likely go down. If you can win all six club tricks, you make the contract easily.

Can you play the club suit for no losers?

If clubs split 2-2, you win by simply cashing the two top honors, easy! If either player has queen-jack-third or queen-jack-fourth, you can't pick up the suit unless they make a glaring mistake. And if the suit splits honor-third and a singleton honor...?

You lead the ♣ K. East follows suit with the eight, and West (an expert player) plays the queen in tempo without hesitating. You lead the ♣ 5 from dummy, East plays the nine.What now? Play for the drop (ace) or finesse the ten?

• If the club suit split is Q and J98, then you must finesse the ten.
• If the club suit split is QJ and 98, you win by playing the ace.

ANSWER: Finesse the ♣ 10. This is a textbook-classic example of a restricted choice situation. Although the 2-2 split is slightly more likely than a specific 3-1 split here, there is an important hint in the play so far. If West has both the queen and jack, she might choose the queen or she might choose the jack (the expert randomly chooses either card 50% of the time, see below). But if she only has one card, she must perforce play it; that is, her choice is "restricted" by the fact that she has no choice at all. The odds are almost 2:1 in favor of the finesse at this point; the finesse might not work, but it is the clearly preferred line of play.

If West had hesitated before playing the queen, that would be a strong indication that she held both the queen and the jack; play the ace! It would also be a strong indication that she is not an expert; an expert player holding queen-jack doubleton would have planned her play as soon as dummy came down. Keep in mind that it is highly unethical to deliberately hesitate before playing a singleton (see Law 73E in the Laws of Duplicate Bridge).

If West is an inexperienced player who "always plays the jack from queen-jack doubleton", then you practically know for certain that the queen is a singleton here. If she had played the jack, you would play for the drop with odds just slightly better than 50-50. Adjust accordingly if she "always plays the queen".

These "restricted choice" situations arise fairly often, almost any time you are trying to suss out two touching honors in the opponents' hands and you have to choose between a finesse and a drop play. The queen-jack, the jack-ten, sometimes the king-queen, and even the ace-king in some situations.

THE PRINCIPLE: If the opponent could have freely played either of two touching honors, there is an inference available that she is less likely to have the other one because her choice might be restricted. This does not apply to opening leads, or third hand play when trying to win the trick, because the choice of honors in those situations is determined by partnership agreements. And of course if you have other information about the opponents' hands, like known high-card points or known distribution, use that information instead.

BONUS MINUTE: The optimal play for a defender holding doubleton honors is to randomly play either card with equal probability, as this gives up the least amount of information to declarer. Note that this does not apply to opening leads or to following suit when trying to win the trick. You'll need to make your choice well in advance -- like, before playing to the first trick -- because hesitating at your turn to play will give away the store. One simple way to make a 50-50 choice is to use the number of high-card points in your hand: with an odd number of HCP, play the "odd" card (the jack is the "eleven"), with an even number play the "even" card (the queen).

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

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

HSP: Don't Send A Boy

"When I'm your partner, the secret to this game is to Help Stupid Partner." -- Steve B.

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

West	North	You	South
1  ♠	Dbl	2 ♠	4 ♥
All pass

You considered bidding 3 ♠ (weak, preemptive) over North's takeout double, but decided to go low at unfavorable vulnerability.

Partner led the ♣ A. Your partnership agreement is to lead king from ace-king. Partner's ♣ A thus denied the king. Of course you knew that already, the king is in dummy!

At trick two partner plays the ♠ K, almost certainly from the ace-king of spades.
Which spade do you play at trick two?

ANSWER: Play the queen of spades, promising the jack. Don't send a boy to do a woman's work! If partner has a six-card spade suit, you won't get any more spade tricks, but at least let partner know that you have the ♠ J just in case it matters.

Next, partner played the ♠ 2; you won with the ♠ J as declarer followed low.
What do you lead at trick four?

ANSWER: Lead a club. Partner is screaming for a club ruff. How do you know that the ♣ A was a singleton? There are several clues here:

• Aces are made for capturing kings and queens. We usually don't lead an unsupported ace at trick one unless we are looking for a ruff. It's possible that partner started with ace-doubleton of clubs and was hoping you might have the king of clubs. But it's also possible that partner had a singleton ace; yes, that means that declarer has a six-card club suit, but it is possible.
• Partner could have started with the safe play of the two top spade honors. She didn't need to lead the ♣ A "to get a look at dummy." A top spade honor would be the normal lead and accomplish the same thing, but partner chose to do something abnormal. That makes another clue pointing toward a singleton ace of clubs.
• Partner led the ♠ 2 -- the lowest possible spade -- indicating preference for the lowest-ranking suit (clubs).

THE PRINCIPLE: When signaling encouragement in a suit, play the highest card you can afford. Don't send a boy to do a [wo]man's work.  From touching honors, always signal with the highest honor, promising the next highest honor.  

If you do not make it clear to partner that you have a spade entry, she will give up on her club ruff objective. She will instead cash the ♠ A, then the ♦ A. Unfortunately for you, declarer will ruff the diamond, draw trump, and run her good clubs to make the contract. The same thing will happen if you lead a diamond from your side.

E-W Vul	♠ 7 6 ♥ A K 5 4 ♦ K Q 7 6 ♣ K 10 9
♠ A K 9 8 3 ♥ 3 2 ♦ A 10 8 4 2 ♣ A	N W E S	♠ Q J 4 2 ♥ 9 8 ♦ J 9 5 3 ♣ J 5 2
	♠ 10 5 ♥ Q J 10 7 6 ♦ — ♣ Q 8 7 6 4 3

-- Ray 

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

Splinters and Voids and The Rabbi, Oh My! Part 2

The hands are rotated from Part 1 so that South is Declarer.

Matchpoints, both sides vulnerable.

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

West	North	East	You
	1 ♦	1 ♠	Dbl
Pass	3 ♠	Pass	4 NT
Pass	5 NT	Pass	6 ♥
All pass

 You had a lovely auction to reach 6 ♥. West led the ♠ 2. Let's start with Declarer's ARCH:

• ANALYZE the lead: East bid spades, it looks like West is leading low from a three-card holding. If it was a singleton, that would mean that east bid only 1 ♠ with a seven-card suit? Seems unlikely. If West had a doubleton spade, she would have led the higher of the two cards. So East has five spades.
• REVIEW the auction: East overcalled spades at the one-level. There aren't many high cards left out there, it seems that East is a favorite to have all the missing kings.
• COUNT your tricks: Two spades, given the opening lead (yay!) and a spade ruff in the North hand. Three top clubs. Two diamonds and a diamond ruff in the South hand, playing East for the ♦ K. Three top heart tricks, expecting to lose one heart to the ♥ K on your right. That adds up to twelve tricks, losing only one trick to the ♥ K, making your contract.
• HOW to play: Always make a plan before playing.
  .. Win the opening spade lead as cheaply as possible (East will probably play the ♠ K)
  .. Unblock the ♦ A, so that you can take a ruffing finesse against East.
  .. Ruff a spade in dummy before drawing trump, just in case the hearts split 4-0.
  .. Take the ruffing finesse in diamonds: lead the ♦ Q, playing East for the ♦ K.
  .. Draw trump, expecting to lose a heart to East's king.
  And play the hand out, making six hearts.

Wonderful, a small slam nicely bid and made. BUT this is matchpoints; can you make seven?

ANSWER: It seems most likely that East has the ♥ K, so the heart finesse is destined to lose. What if the ♥ K is singleton? If you play the ♥ A immediately and East has the guarded king, well, East is always going to score the king. You have all the other high hearts. But on a good day, East's ♥ K will be a singleton. It costs you nothing to start with the ♥ A, and you win big if you drop the singleton king. And dropping a singleton king always feels great! 

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

West	North	East	You
	1 ♦	1 ♠	Dbl
Pass	3 ♠	Pass	4 NT
Pass	5 NT	Pass	6 ♥
All pass

In a really strong field -- say, the Blue Ribbon Pairs -- 6 ♥ making seven will be an average or maybe average-plus result. But in our typical club game or a typical BBO online game, 6 ♥ making seven will be a cold top board. And it doesn't require anything flashy or complicated, just a series of solid intermediate-level skills that you've already learned. Nothing to be afraid of here!

• Negative double
• Splinter raise
• Void-showing responses to 4 NT
• Declarer's ARCH
• Room Measurements
• The Rabbi's Rule: When the king is singleton, play the ace!

-- Ray

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

Splinters and Voids and The Rabbi, Oh My! -- Part 1

Here is a hand from a recent online game that I thought was a lot of fun. It brings together a half-dozen themes that we've discussed in the past. Both vulnerable at matchpoints, you are the dealer. You hold:

♠ -- ♥ A Q 7 6 ♦ Q J 8 6 3 ♣ A K Q 4

Of course you make a plan before making your first call. What is your plan for this auction?

You'll open 1 ♦, and if partner peeps you'll almost certainly want to be in game. If partner bids hearts, diamonds, or clubs, you will definitely get excited and force to game. But if partner bids spades, you might want to allow for the possibility of partner having a bare minimum hand with only a couple of spade honors. Over a 1 ♠ call from partner, you can reverse to 2 ♥, forcing one round and almost-but-not-quite forcing to game, to allow partner to sign off with a weak spade hand.

West	Partner	East	You
			1 ♦
1 ♠	Dbl	Pass	?

Good news! Partner's negative double shows at least four hearts, and at least 6-7 points. You definitely want to be in game. Partner could even have a good hand -- negative does not mean nothing -- slam is not out of the question. Your call?

ANSWER: Get the tweezers, you have a splinter! Bid 3 ♠, a splinter bid showing four-card heart support, game-forcing values, and a singleton or void in spades. It's true that partner didn't actually bid hearts, but her bid showed hearts and she'll know that you are supporting hearts. And in the event that she thinks you might be asking for a spade stopper and bids 3 NT, you'll correct to 4 ♥ and she'll get the message.

You hold: ♠ -- ♥ A Q 7 6 ♦ Q J 8 6 3 ♣ A K Q 4

West	Partner	East	You
			1 ♦
1 ♠	Dbl	Pass	3 ♠
Pass	4 NT	Pass	?

Well! Partner definitely likes the slam idea; 4 NT is a keycard-ask with hearts as trump. Don't worry, one of us will get around to bidding hearts eventually... You play 1430 responses to keycard-asking bids. Your call?

ANSWER: You could bid 5 ♠, showing two keycards and the trump queen. That will commit us to at least a small slam. But there is a much better call available. Bid 5 NT, showing an even number of keycards and a useful void. A void in the opponent's suit is always useful. If partner is only worried about a spade loser, knowing that you are void will make it easy for her to bid a grand slam.

West	Partner	East	You
			1 ♦
1 ♠	Dbl	Pass	3 ♠
Pass	4 NT	Pass	5 NT
Pass	6 ♥	All pass

Partner signed off in 6 ♥. As you can see below, she knew we were missing a key card outside of spades. Fun auction, eh? A small slam and no one actually bid the trump suit until the very end!

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

It looks like a good contract. This is a robot event, so you'll have to play the hand. Stay tuned for Part 2.

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

Which Is More, 53 or 44?

Even the second-graders in the audience are saying "well, duh!" But bridge is a complex game...

♠	A Q 2
♥	A Q 5 4
♦	A J 5
♣	8 3 2

Partner deals and opens 1 ♠. Your right-hand opponent passes.. You are playing 2/1, of course. Your call?

ANSWER: 2 ♣. Not 2 ♥.  Bidding 2 ♥ right now would show a five-card suit. You don't have that, so you must bid a minor suit. Not 2 ♦. Bidding 2 ♦ would show longer diamonds than clubs. Yes, your club suit is loathsome. But your bid here is not about clubs: it is about creating a game-forcing auction. With three cards in each minor, give partner as much bidding space as possible. No matter how much enthusiasm partner might show for clubs, you will always insist on spades later. And don't worry about missing a heart fit. If partner has a four-card heart suit, she will bid it at her next opportunity.

You bid 2 ♣. Fortunately for our discussion here, partner bids 2 ♥.

West	North	East	South
	1 ♠	Pass	2 ♣
Pass	2 ♥	Pass	?

Partner shows at least four hearts here. You have an eight-card fit (or better) in both majors! Which do you choose: spades or hearts?

ANSWER: Bid 3 ♥, setting hearts as trump. Yes it is possible that partner has six spades and four hearts, in which case spades would be a better trump suit. But partner could also be five-five in the majors, making hearts a nine-card trump suit versus only eight in spades. With the information you have right now, there are two eight-card trump suits. Choose the 4-4 fit rather than the 5-3 fit.

You will easily find your way to 6 ♥ on this hand. But look what can happen if you play in spades instead of hearts:

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

If spades are trump, you must lose a spade trick due to the 4-1 split, and there is an unavoidable diamond loser. 6 ♠ is a hopeless contract here, as is 6NT. But if hearts are trump, you can ruff the fourth round of spades, and use the remaining spade to discard one of  South's minor suit losers, making 6 ♥ easily. (If both major suits were to break evenly, you would make 7 ♥ by discarding South's two diamond losers on the long spades. But 7 ♠ will never ever make, no matter how the suits split, no matter how inept the defense.)

THE PRINCIPLE: When you have a 4-4 fit and a 5-3 fit, choose the 4-4 fit. On average, making the 4-4 suit trump will yield about one trick better than the 5-3 suit. Whatever losers exist in the 4-4 suit, they always exist regardless of whether that suit is trump. If the 5-3 side suit splits evenly, there will be a place to discard two losers from the other hand. If the 5-3 side suit splits poorly, you can usually ruff at least one of the losers.

Note that after an auction 1 ♠ - 2minor - 2 ♥ - 3 ♥, hearts are trump. Period, full stop. There is no reliable way to get back to a spade contract. Any subsequent spade bids are cue bids showing either an ace or a control, per your partnership agreement. Ditto for the auction 1 ♠ - 2 ♥ - 3 ♥; opener will raise hearts with three-card support, knowing that responder has five hearts and we've found an eight-card trump suit. 

This is why responder needs five hearts to bid 2 ♥ over 1 ♠; we can always ensure that we are locating an eight-card fit. 

When we have a choice of eight-card fits, we want to be in the 4-4 fit. At the bridge table, 44 is more!

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

Who Called This Meeting?

Suggested soundtrack: Grateful Dead, "New Speedway Boogie"

	♠ A K 10 9 2 ♥ Q 10 ♦ J 2 ♣ K J 9 4

You	LHO	Partner	RHO
1 ♠	Pass	2 ♥	3 ♦
??

You were the dealer, vulnerable against not. Partner's 2 ♥ bid was game-forcing with at least five hearts. We are committed to keep the auction alive until we bid game (at least) or double the opponents.

The overcall does create a problem for you. If you bid, your options are:

• 3 ♠ now would show six or more spades. You don't have that.
• 3 ♥ now would show three or more hearts. You don't have that.
• 3 NT now would show a diamond stopper. You don't have that.
• 4 ♣ would show at least four clubs, and absolutely no tolerance for 3 NT. You don't have that. Partner might have a diamond stopper and want to play 3 NT. Your diamond jack might be a partial stopper across from queen-third or king-third in partner's hand.
• Double would be penalty, planning to give the opponents a Souvenir Minus Eight Hundred (or more!) for interfering against our presumptive vulnerable game when you have the rest of their diamonds. Nope, you don't have that either.

Anyway, it's still your call. What to do?

ANSWER: Pass. Partner called this meeting, let her run it. There's no need to be That Person in the meeting, blathering on with no useful information to contribute. We are in a game-forcing auction. RHO's 3 ♦ call ensures that partner has another call coming and the auction will continue. If you've got nothing new to say, there's no need to say anything right now. As a bonus, your Pass will tell partner that you don't have any of the hands described above.

You will be well-positioned to act after partner explains her agenda:

• She might bid 3 ♠ showing three-card support and suggesting some extra values; spades will be trump and you can proceed from there.
• She might bid 3 ♥ showing 6+ hearts; you will raise to 4 ♥ with your doubleton.
• She might bid 3 NT or 4 ♠  to play; you will Pass of course.
• She might bid 4 ♣; you'll show your honor-doubleton heart support and hope you aren't missing a club slam.
• She might bid 4 ♥ to play, showing a stand-alone suit and disavowing any slam interest. You will Pass, of course.
• She might Double, suggesting no clear direction and asking you to Do Something Intelligent. Note that it's unlikely that partner has a useful diamond stack sitting in front of the overcaller. 
• She might bid 4 ♦, suggesting a very strong hand and asking you to Do Something Intelligent but without the option of defending against 3 ♦ doubled.

THE PRINCIPLE: When you don't have anything useful to contribute to the discussion, don't say anything until you must. Partner set the agenda as a game-forcing auction, give her the floor to run the meeting.

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

Smell The Coffee

Suggested soundtrack: Mississippi John Hurt, "Coffee Blues"

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

Partner	North	You	South
2 ♦	Dbl	3 ♦	4 ♣
All pass

Partner led the ♦2. Declarer played the queen from dummy. You played the ace, of course. Now what?

Look again. Do you notice anything unusual?

Partner opened a weak-two in diamonds, usually based on a six-card suit. You play standard leads -- fourth best from length -- yet she led the deuce from a six-card suit. The  ♦2 can't possibly be her fourth-best diamond. Partner made a very strange lead. Wake up and smell the coffee! Partner knows that you know she has six diamonds. She led a card that is definitely not her fourth-best diamond.

ANSWER: Lead a spade. Give partner the spade ruff she is asking for.

THE PRINCIPLE: A very unusual carding play on defense should be regarded as an "alarm clock signal." Partner is trying to wake you up to something non-routine about the hand. Looking for a ruff in a side suit is the most common situation. But the key message is "Wake Up, Partner! Don't make the routine play here." It's up to you to figure out what unusual play partner wants.

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

BONUS QUESTION: Which spade do you lead for partner to ruff? 

ANSWER: Lead the two, your lowest spade showing suit-preference for the lower suit (diamonds). Partner almost certainly has the king; your jack is an entry to give partner a second spade ruff. Unless you tell partner, she might not know whether to return a diamond or a heart.

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