Driving The Getaway Car

PARENTAL ADVISORY: This post is a bit more difficult than usual, but trust me it's worth it. We build upon an earlier post where a defender unblocked an honor to create a "get out of jail free" card. That's a hint, in case you want to refresh your memory...

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

West	North	East	South
			2 ♦
Pass	2 N1	Pass	3 ♦2
Pass	4 N3	Pass	5 ♥4
Pass	6 ♦	All pass

asks for outside feature no outside A or K key-card Blackwood two keycards, no Q

Matchpoints. You are West and lead the ♥ J. Declarer plays the ace and partner follows low.

At trick two, declarer leads the ♣ A from dummy and partner plays the ♣ K (!) Declarer follows low. Your play?

Let's stop and look things over for a moment. Where is the ♠ K?
Declarer denied any outside A or K, so partner must have the ♠ K.

Is it possible that partner's ♣ K is a singleton?
Yes, possibly. But if so, then declarer has four clubs to the queen and only three cards in hearts and spades. In that case, declarer is making seven. Nothing you can do about that.

Could partner have the ♣ KQ doubleton?
Possibly, but that's bad news too. Declarer should play out the hearts and trumps first, and then you can only watch in horror while partner gets endplayed in clubs. She will have to give declarer a ruff-and-sluff in hearts, or lead into dummy's spade suit. Nothing you can do about that.

Could partner have the ♣ Kx doubleton, trying to avoid an endplay and hoping you have the ♣ Q?
Possibly. Nice try, partner, but alas you don't have the ♣ Q. Nothing you can do about that.

Could partner have ♣ KQx, trying to create an escape card with her small club?
ANSWER: Bingo!! There is something you can do about that. Play the ♣ 8, encouraging, to let partner know you have the ♣ J just in case partner has king-queen-small. If partner started with ♣ KQx, she won't know whether to play the ♣ Q next -- getting endplayed, but at least holding declarer to six -- or duck the second club hoping that you have the ♣ J and can lead spades through dummy for down one.

Partner might have started with the singleton or doubleton ♣ K. If so, your play here doesn't matter. But if partner is trying to get out of jail with a small club from ♣ KQx, you need to tell her that you will show up with the getaway car -- the ♣ J!

THE PRINCIPLE: When partner makes a play that seems unusual, think through the possible reasons for that play. There might be something that she needs to know about your hand.

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

At rubber bridge or IMP scoring, East should always duck the second round of clubs; if West doesn't have the ♣ J, the 6 ♦ contract cannot be defeated. But at matchpoints East has a more difficult choice, whether to try to defeat the contract or just prevent an overtrick. West's signal in clubs -- encouraging or discouraging with respect to the ♣ J -- will make East's decision much easier.

BONUS MINUTE: I think this hand is a great example of why bridge is such a fascinating game. Declarer sees that a potential endplay offers the best chance for success, at worst falling back on the spade finesse. East anticipates declarer's likely line of play, and plans to escape the trap. West recognizes what her partner is doing, and collaborates to ensure declarer's demise. How cool is that?!

-- Ray

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

Reading The News, Part 1

"You can observe a lot by just watching." -- Yogi Berra

In this exercise we will use the first step in Declarer's Arch to do some observing.

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

West	North	East	You
			2 ♦
Pass	2 NT1	Pass	3 ♦2
Pass	4 NT3	Pass	5 ♥4
Pass	6 ♦	All pass

1. asks outside feature
2. no outside A or K
3. key-card Blackwood
4. two keycards, no ♦ Q

West leads the ♥ J against your 6 ♦ contract. What can you tell about the opponents' hands? (These opponents play standard leads.)

Step 1: Analyze the lead:

It looks like the jack from jack-ten-whatever. But it could be the jack from jack-doubleton, or even the singleton jack. It could even be the jack from queen-jack doubleton. So which is it?

• Could it be a singleton jack? There are eight hearts in the opponent's hands. A 7-1 split occurs less than 3% of the time; any specific card being a singleton on your left is approximately a 0.2% chance. A singleton jack isn't worth worrying about here.
• Could it be a doubleton jack? A 6-2 split only happens 17% of the time; your left-hand opponent will hold the doubleton half of that. A doubleton jack on your left is something less than 2%; not very likely.
• So who has the ♥ Q? It's most likely that West's lead is a normal jack from jack-ten-whatever, so East most likely has the heart queen.

What about diamonds? You're only missing two small diamonds. West could have led a diamond as a passive lead, but chose not to; that's not much of a clue in this case.

Who has the spade honors? There aren't many clues about the spade suit. West knows better than to underlead a king against a slam. But if West doesn't have the ♠ K, she might have been willing to lead a spade. You denied any outside ace or king, so West doesn't have to worry about finessing her partner. Since West had a reasonable natural lead from the jack-ten of hearts, there's no reason to think she would have preferred leading from a broken spade holding. So you can't tell much about the spades.

Who has the club honors? There is a critical observation here: West did not lead the ♣ K. If West held the ♣ KQ-whatever, the king would have been a much more likely lead against a slam in a suit contract. So West probably does not have both high club honors. East almost certainly has either the ♣ K or the ♣ Q, and might have both. By the same reasoning, West probably does not have the  ♣ QJ either.

So here's what you know, not for sure but close enough:

• West has the ♥ 10
• East has the ♥ Q
• West does not have the ♣ KQ or the ♣ QJ
• East has either the ♣ K or the ♣ Q, and might have both

That is quite a lot of information from just one card, don't you think?

And now that you now that East has one of the high club honors, maybe you can endplay her with one of them.

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

Start With The End

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

West leads the ♥ J against your 6 ♦ contract. What is your plan?

Let's go through Declarer's ARCH: Analyze. Review. Count. How?

Analyze the lead: It looks like the jack from jack-ten-whatever. This implies that East has the queen.
Review the auction: The opponents passed throughout the auction after you opened  2♦.
Count your tricks: In a suit contract, it's usually more effective to count losing tricks
 - maybe a spade loser, depending on where the ♠ K is
 - no heart losers, you can ruff your third heart in dummy
 - no diamond loser
 - one loser in clubs
How to play the hand?The club loser looks to be unavoidable. If the spade finesse works (50%), you make the contract. Is there any better way?

What if you can get East to lead spades? Or give you a ruff-and-sluff to discard a spade from your hand? Can you put East on lead with a club trick late in the hand?

If East has the ♣ KQ doubleton, she will have to win a club trick. If she has ♣ KQx or ♣ Kx and isn't paying attention, she might not unblock the king under your ace; same result, she will win the second round of clubs. And if she has ♣ KJx or ♣ QJ or ♣ QJx and West doesn't come to her rescue: same result, East will be stuck on lead. And if none of that works out and West ends up on lead, you still have a 50% chance with the spade finesse!

The effect you are trying to accomplish is called a "throw-in" play. To make it work, you need to figure out how to put East on lead, but first eliminate all other safe exits. So, here we go...

• Win the A♥. and lead the A♣ right now (I'll talk about why later on...) 
• Then draw trumps using dummy's high diamonds; save your high diamonds for later entries.
• Then K♥, and a diamond to your hand
• Ruff your last heart. Now, both your hand and dummy are out of hearts and clubs. The opponents are out of diamonds.
• Make a wish before leading dummy's last club: hope that East wins the trick! 

If East wins the club trick, either

1. she leads a spade into dummy's ♠ AQ, making six, or
2. she leads a heart or a club, you can discard a spade from your hand, making six

And if West wins the club trick, you are no worse off than you were before. West will lead a spade and you will try the spade finesse. Alas, the finesse doesn't work this time; good thing you were able to endplay East!

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

BONUS MINUTE: Declarer should play the ♣ A at trick two, just in case East and West haven't thought through the entire hand and recognized the possible need for East to escape the endplay. If declarer draws trumps and clears hearts before leading clubs, the impending endplay will be much more obvious. One more reason to always think through the hand before playing to the first trick...

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

Randomness And Bridge Hands

NOTE: No lesson here, just an essay that I want to preserve for future use. Local players have already seen this via email.

Every experienced bridge player I know – every experienced player, myself included – has had the same reaction when first encountering computer-generated deals:  “What the **** is it with all these wild distributions and bizarre splits? This can’t be for real!”

The bad news: it is for real. They are actually truly random.  All those hand-shuffled deals all those years, alas, were not.

The good news: it is for real. They are actually truly random. There are plenty of good statistical analyses to back that up.

Bridge differs from some other card games because the entire deck is dealt out, and the play of the hand tends to re-concentrate suit holdings. In rubber bridge for example, three spade tricks in a row to declarer generates a chunk of ten to twelve spade cards in the shuffle stack. Those spades are more likely to be evenly – rather than randomly – distributed in the next hand. Playing duplicate bridge, the chunks are smaller but they still exist; those spade cards are now in chunks of three in each hand. Or consider, for example, the KQJ-fifth of your trump suit that you play in sequence at duplicate. These create structured chunks of cards in the shuffle stack that don’t occur in, say, poker or cribbage.

Manual shuffling does not completely break up those chunks and sequences; they then are distributed evenly (not randomly) by dealing one card at a time to each hand in order. The resulting manually-shuffled hands thus have flatter distributions than statistically random deals.

Here’s a simple test you can do: How many times do you normally shuffle the cards before dealing? Okay… Take a fully-sorted deck – AKQJ… AKQJ… and so on – and shuffle it that many times. Now turn the deck face up and examine it.

Every time two cards appear still in their original sequence – the 6-5 of diamonds, say, or the K-Q of spades – is a flaw in your shuffle. Given the six of diamonds, the five should have a 1-in-4 chance (okay, 12-in-51 to be exact) of being in the same hand. Due to the flaws in your shuffle, they have a zero chance of being in the same hand on the next deal. Likewise for those sequenced cards that are now separated by only one or two positions in the stack. And if your shuffles are typical, you’ll also see some sequences of three-out-of-four (or worse!) in the same suit; these get distributed evenly rather than randomly.

For comparison, I am a truly horrible card shuffler. After my usual three shuffles, my deck contains anywhere from 10 to 15 flaws! My wife has an excellent riffle shuffle, learned from a professional dealer; she averages 1-2 obvious flaws after five shuffles. Five good shuffles, and still not a random deck! There is sound mathematical analysis that suggests it takes at least seven good shuffles to get a fully random deck, and that’s for casino-professional-grade riffle shuffles; shlubs like me need far far more. (If you try the test, feel free to reply to me with your results; discretion and anonymity assured).

So are you lamenting that those 3-3 splits aren’t coming in 40% of the time like they used to? Yeah, it’s a drag. But 36% is the probability for statistically random deals; 40% was an artifact of incomplete manual shuffling.

And finesses that now only work 50% of the time, instead of 51 or 52%? Yep, I’ve been through that. And the queen does not lie ahead of the king 53% of the time like it used to? Argh!

So... if you are appalled by these computer hand distributions: me too. I’ve been there. I feel your pain. But I will take truly random deals, hands down, every day of the week. Manually-shuffled hands don’t meet that standard. They sure were fun, but they sure weren’t random.

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

A Perfect Minimum

A friend recently asked me, "What is the most noticeable difference between average bridge players and the real experts?"

I'll save that answer for the end. Right now, you hold this 20 HCP monster
♠ A Q 10 5   ♥ A K   ♦ Q J 10 5 4   ♣ A 10

Partner deals and opens 2 ♦, vulnerable. Your partnership agreement is that a weak two opening contains 5-10 HCP and a six-card suit. Your call?

ANSWER: Push hard for slam! Just bidding 6 ♦ would be a good choice. Going through 2 NT (feature-asking or Ogust, however you play it) is fine, but all roads lead to at least 6 ♦ here.

Perhaps you are concerned that a combined total of only 25-30 HCP isn't enough for a slam? Let's consider some possible hands partner might have...

• Is your partnership agreement that a weak-two opening must contain two of the top three honors? Then partner could have as little as
  ♠ x   ♥ x x x   ♦ A K x x x x   ♣ x x x
  making six, the only loser is a club
  
  or perhaps ♠ x x   ♥ x x x   ♦ A K x x x x   ♣ x x
  and need the spade finesse (or maybe a defensive error) to make six.
  
  Or she might have more than her minimum; the heart queen or either black king would be a huge bonus!

• Can partner open a weak two with any honor-sixth? Then she might have as little as 5 HCP
  ♠ x   ♥ Q x x   ♦ K x x x x x   ♣ x x x
  Dummy's club loser goes off on the ♥ Q, losing only the trump ace to make six.
  
  Or ♠ x   ♥ x x x   ♦ A x x x x x   ♣ J x x
  and we need the diamonds to split 1-1 (a 52% chance)
  
  Then again she might have an almost hopeless
  ♠ x x   ♥ x x x   ♦ K x x x x x   ♣ Q x x.
  
  But she might have more than her minimum; again, the heart queen or either black king would be a huge bonus!

THE PRINCIPLE: When considering a seemingly aggressive contract, bid it if it will make when partner has a perfect minimum. If you need partner to hold a perfect maximum, it might be a good idea to restrain your enthusiasm.

Were you considering the potential for 6 NT or even 7 ♦ on this hand? There are hands that partner could hold where those contracts are likely to make. But it will be hard to find out if partner has the exact cards you need, and those holdings tend to fall into the "perfect maximum" category.

FINALE: My answer is that "real experts" don't spend much time thinking about point-count. They imagine specific possible holdings for partner and the opponents based on the auction and play thus far, and then visualize how those hands might play out. (and they usually do it in a few seconds). Developing that visualization skill will make a huge difference in your bridge game!

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