Advanced Losing Trick Count

See Friday's post for a quick brush-up on the Losing Trick Count.

The LTC is certainly not infallible, especially in its simplest form that I’ve given you here. It tends to work quite a bit better when you introduce the concept of “cover cards”, which I’ll illustrate quickly with hand (C) from earlier:

(C) ♠AQ7632 ♥AT762 ♦5 ♣6

Let’s say responder has one of these two hands:

(C1) ♠K98 ♥KQ5 ♦98432 ♣A2

(C2) ♠984 ♥Q53 ♦KQJ42 ♣KJ

Opposite hand (C1), 6S looks great—on normal splits, we’ll lose only the ace of diamonds.

Opposite (C2), we’ll probably lose a spade, a heart, a diamond, and a club and go down in game!

What’s the difference here? Both hands have the same shape, the same HCP, and the same number of losers! What’s going on?

Well, hand (C1) has four cover cards, and (C2) has only one! Cover cards are defined as cards we know will cover (take care of) one of partner’s losers. Hand (C1)’s cover cards are the king of spades, the king of hearts, the queen of hearts, and the ace of clubs. Hand (C2)’s only cover card is the queen of hearts. So, opposite a major two-suiter, we’d much, much rather hold (C1) than (C2).

How do we know what’s a cover card? Listen to the auction! The auction on Hand (C) would start (opposite either hand) with

1S – 2D – 2H – ?

Hand (C1) is an amazing hand opposite the major two-suiter. Responder should jump to 3S, forcing to game and starting a cuebidding sequence:

1S – 2D – 2H – 3S – 4C – 4H – 4NT – 5D [Blackwood] or 5H [Keycard] – 6S

Hand (C2) is an awful hand opposite the major two-suiter. Responder should attempt to sign off as soon as possible!

Losing Trick Count

The Losing Trick Count (LTC) is an old, old method of evaluating your hand. It was first published in 1935 under the miserably long title of “The Losing Trick Count, as used by the leading contract bridge tournament players, with examples of expert bidding and expert play.” This book didn’t make much of a splash, but Ron Klinger’s fabulous 2001 book Modern Losing Trick Count took the bridge world by storm. Here’s the basic idea behind the LTC:

When you have a good fit (8+ cards in one suit between the two hands) with your partner, you can evaluate your “losers” to see how powerful the fit is.

Count one loser for every missing ace, king, or queen in your hand. Only count one loser for a singleton, and two for a doubleton. Never count the fourth (or higher) card in a suit as a loser. Here are a few example hands:

(A) ♠AQT94 ♥A853 ♦Q2 ♣75

This hand has seven losers: one in the spade suit (missing K), two in the heart suit (missing KQ), two in the diamond suit (missing AK), and two in the club suit (missing AK). 1+2+2+2 = 7. Your average minimum opening hand (and minimum game-forcing hand over partner’s opener) will have seven losers.

(B) ♠KQ652 ♥AK32 ♦52 ♣83

This hand has the same shape and same HCPs, but only six losers: one in spades (missing A), one in hearts (missing Q), and two in each minor suit (AK in each). 1+1+2+2 = 6. The LTC says that hand B is one trick stronger than hand A.

(C) ♠AQ7632 ♥AT762 ♦5 ♣6

This is a great hand with only five losers: one in spades (missing K), two in hearts (missing KQ) and one in each minor (A in each). This has fewer HCP than hands A and B, of course, but much more playing strength.

(D) ♠Q632 ♥KJ62 ♦76 ♣A52

How many losers does this hand contain?

REMEMBER: Only use the LTC when there’s a known trump fit!

A good rule of thumb: Take your number of losers, add the number of partner’s losers (let’s say I have 7 losers, and partner’s opened the bidding and shown a minimum: assume 7 losers, therefore 14 total) and subtract that number from 18. This figure tells you the contract you’ll make most of the time. In this example, you have 14 – subtract from 18. That leaves you with 4—you’ll be able to make four of your suit on most layouts of the cards. Bid game!

When you’ve opened the bidding with a 5-loser hand and partner’s given a single raise (9 losers), you have 14 total again. Bid game!

When you’ve opened the bidding with a 6-loser hand and partner’s forced to game (7 or fewer losers), you have at most 13 total losers, quite possibly less. Time to make a slam try!

Tune in Monday for a more advanced use of the LTC.

Ack!

At all white at teams, you hold

AKQT862 5 AQT8 5

and RHO opens 2S! What's your bid?

If you pass, everyone else does too. What's your lead?

Brilliant defense

England's Michelle Brunner, in the 2007 Venice Cup (Womens' World Team Championship) found a very clever defense to defeat a grand slam:

North-South had blasted their way to seven clubs on the uncontested auction

1C (1) - 1D (2)
2S (3) - 2NT
3C - 4C
5NT - 7C

(1) Strong, artificial, and forcing
(2) 0-7 HCP
(3) Huge hand with long spades

Michelle's partner led the jack of hearts, declarer covered with the queen, and Michelle ducked! She knew there were plenty of spade winners to cover the losing heart, so wouldn't be giving a trick away. Declarer's 5NT was asking for good trumps, so she knew that the only trick for their side could possibly be in the club suit. When she ducked smoothly, declarer found herself very conveniently in dummy to take the trump finesse...

Deja vu?

Last week I played the Fort Lauderdale Regional with Robert Todd. One afternoon, he showed me his latest article for the Sunshine Bridge News, ACBL District 9's bimonthly magazine.

Follow this link for that article. Read it before the rest of this one!

Two boards into the next session, we had this eerily similar defense:



N-S wound their way to 3H over our 3D. I started out with the queen of diamonds. Robert overtook with the king and switched to a low spade through declarer. South misguessed, playing low, and I won with the queen. I shot a spade to Robert's ace, and he returned the eight of diamonds (suit-preference) to my known jack. I then gave him a spade ruff for the first undertrick. My queen of clubs late made for a very satisfying down two.

Bridge on TV

...but not where I can see it, of course.

England's SkyTV has put together a celebrity bridge competition for their SkyArts channel. You can read all about it here.

Also, here's a short video of the introduction to the programme.

Does anyone know how we could see full episodes of this show?

Time off again...

The Southeastern Regional is over. We had a fabulous time in Fort Lauderdale, making new friends and playing some good bridge. I have a few hands to share... but right now, time to rest. What a week!

A couple of nice auctions from the club

Board 11 Dlr: S Vul: None	QJ8652 A8 AK3 AT
3 9762 65 K87543		K9 Q3 QJ987 QJ92
	AT74 KJT54 T42 6

We were N-S and bid this one uncontested:

P - 1C [16+ any];
1N [8-10, 5+H] - 2S [natural];
4C [splinter raise; usually 4531 or 4621] - 4N
5C [one keycard] - 6S (all pass)

Making 7 easily on the trump finesse and hearts coming home. Only three of 22 pairs bid this 26 HCP slam.

Board 18 Dlr: E Vul: N-S	6 K32 Q64 Q97642
KQ43 JT98 AJ92 8		AJ8 65 KT8753 A3
	T9752 AQ74 KJT5

This time we had opponents to deal with:

(1D) X (1H) 2C;
(2D) 3C (3D) 5C (all pass)

With trumps breaking 2-1 and spades setting up for a heart pitch, 5C was easy. [5D is a maker if they guess trumps correctly.]

A neat defense from Gatlinburg

In the Friday two-session Swiss teams in Gatlinburg last week, Robert Todd and I put together a nice defense. E-W subsided in 2NT after an invitational sequence in which West may or may not have had four spades. I got off to the lead of the two of diamonds. Declarer played low from dummy, and Robert made the very thoughtful play of the seven! Declarer won with the king, cashed the king of clubs (Robert playing the six, his lowest, as a Smith echo - showing that he liked my opening lead), and played a diamond up. Not yet believing that partner had made the good play in diamonds, I split my honors to guarantee me a trick in the suit if RHO had KQx(x). East let me hold the trick. Not really seeing anything else constructive to do, I played another low diamond. Dummy won and declarer pitched a heart. A club was led to the ace, and a spade to the queen. Two more rounds of clubs were played, ending on the table, and I pitched down to AJ of spades, KJ of hearts, and the good jack of diamonds. A heart was led to my jack; I cashed the good diamond and exited the now-stiff king of hearts to the now-stiff ace, and a spade through the queen was our sixth trick for down one. At the other table, our teammates were +400 in 3NT!

Well defended hand

My partner Pat Riding put together a nice defense on this board to get us a plus score and top board on the way to 1st overall on Tuesday:



We were defending 2H in the East. Pat started things off with a low diamond to the ace. Declarer led a club to Pat's ace. She laid down the king of diamonds and played a third round, ruffed by declarer. East now played a club to the board to play a heart to the jack. Pat won with the king and pushed her deuce of diamonds through dummy. I ruffed with my lone queen of hearts, declarer overruffed, and Pat now had four trump tricks to go with her ace of clubs and king of diamonds for +100! Well done.

On the road again

I'm in the airport at the moment waiting to head off to the Toronto Regional. If you're there, come over and say hi!

Building fences

West led a spade to his partner's king, which held the trick. East looked at the two tricks in his hand and the menacing club suit in dummy, and thought "the only way we're going to set this contract is if partner has the ace of diamonds. Then he can give me a ruff for our fourth trick." So East led his singleton diamond. West won the ace, thought for a while, and decided his partner wanted a spade led through the queen. So he tabled the spade jack, trying to smother declarer's supposed ten. Declarer ruffed, drew trumps, and claimed +420. East berated his partner for never giving him ruffs.










A few boards later, this was dealt:



West led a spade to his partner's king, which held the trick. East looked at the two tricks in his hand and the menacing club suit in dummy, and thought "the only way we're going to set this contract is if partner has the ace of diamonds. Then hopefully he'll figure out to duck the first one so when I'm in with my trump ace I can lead another diamond and he can give me a ruff for our fourth trick." So East led his doubleton diamond. West, having been yelled at just a few hands prior, jumped up with the ace and led another one back. Declarer scooped up the tricks, drew trumps, and claimed +420. East yelled at West for never knowing what the hell was going on at the table.








What went wrong here?

I think East was the culprit in both of these hands. First of all, his behavior was horrible. If you can't keep from yelling at or berating partner when he makes a mistake, you need to take up a new game. All players make mistakes. You do, I do, Jeff Meckstroth does. If you can't live with you or your partner making mistakes, bridge is not the game for you.

Incidentally, I heard a local player the other day analyzing a two-session event he'd played the day before. "I made three errors yesterday," he said. This person is fooling himself. Even the top experts make several errors per session. I asked my friend and top Canadian expert Cam Doner once, "What's the biggest number of hands in a row you've gone without making a mistake?" His answer: "One." Now there's a man who's honest with himself.

Every player makes mistakes, but it's the good players that work hard to keep their partners from making mistakes. On the first board, East should have won the first trick with the ace of spades. "Knowing" that declarer had the king, West would see no future in the spade suit and return the diamond for East to ruff. On the second board, when East wins with the king and puts a diamond back again, West should realize that now that he has a partner who's trying to get the right information to him, the defense isn't a blind guess any more. He needs to weigh the possibility that East has led a doubleton diamond [it can't be singleton since the king won the first trick] against the possibility that he led from three or more diamonds and needed a spade led through.

My reasoning would be this: It's far more likely on the auction that East is 5=2 in spades and diamonds than that he's 4=3 or 4=4, because I know he has at most two hearts. If he had a good hand with 4=2=3=4 or 4=2=4=3 or 4=1=4=4, he'd probably double 1H rather than overcall 1S. Since he did overcall 1S, I'll play him to have five spades and two diamonds. I'll duck this one, hope partner has a trump trick so he can lead a second diamond to get his ruff!

See how much easier the defense is to figure out when West knows that East's diamond isn't a singleton?

Amusing hand from bidding practice

Last night, I was practicing bidding with my partner Garth. Garth and I are playing several upcoming tournaments, and we have a very complicated bidding system, so we want our agreements to be in tip-top shape for our first big test-- Gatlinburg in just over a week. We've been practicing several hours a week, and getting better every time.

This hand came up as the last one of the session.


I was very amused to notice that game was most likely on in all five strains - these hands will probably make 3NT, 4H, 4S, 5C, and 5D! I've been experimenting with the E-W hands a bit, trying to see if I can make a full hand where N-S can make game in all five strains but can't make slam in any of them. I've come close, but it seems like 6C by South is always making. Can you come up with a better construction than I did?

Tools and toys over 2C openings, part one

The standard two clubs opening can be somewhat ungainly if you're not prepared. Here's a few tools that can help your strong auctions go more smoothly.

Two Diamonds Positive, Two Hearts Negative:

I like to play that an artificial, negative 2H response is the only way to stop short of game, thus leaving the 2D response positive and game-forcing. Auctions are much easier when both partners know that they won't be passed below game. I have the agreement with some partners that the "positive" bid should show an ace, a king, or at least six points in quacks, but with others, we allow "shape positives" - hands without the high cards, but with enough distribution to suggest lots of tricks, maybe

JT87532
842
9
74

or

Q8652
97
J9874
3

I'm actually undecided as to which way works out best. Shape positives work really well when a fit is found, but can be disastrous with a big misfit. I welcome any thoughts or suggestions in the Comments section.

Kokish

The Kokish 2H is a very necessary tool for 2C opener. When your partner bids 2D, you can bid an artificial 2H with two handtypes: hearts or balanced. Responder is forced to bid 2S, and opener will clarify his hand. In short, the auction will go like this:

2C -2D - 2H - 2S - ?

With a balanced hand, opener rebids 2NT, and all systems are on as if he'd opened 2NT. With the "hearts" hand, he makes the most natural rebid possible. So,

2C - 2D - 2H (Kokish) - 2S (forced) - 3D shows 5+ hearts and 4+ diamonds. Simple enough, right?

The real gain in Kokish comes from being able to better define the ranges of your balanced hands. Since 2C shows 22+, here's how Kokish tightens up the ranges:

2C - 2D - 2NT = 22-23

2C - 2D - 2H (Kokish) - 2S (forced) - 2NT = 24-25

2C - 2D - 3NT = 26-27

2C - 2D - 2H - 2S - 3NT = 28+

"Strip Squeeze" isn't as dirty as it sounds

Last night in the Swiss, I picked up Qxx 9x Ax AJTxxx at all red. Partner opened 1D (10-15 HCP, 2+ D), RHO overcalled 1S, I bid 2C, partner raised to 3C, and I put us in 3NT. The S9 was led, and I saw:



It looked like nine tricks if the club finesse was on, but a few other chances if not. I put up the ace of spades at trick one (trying to get LHO to continue the suit if she won a club trick) and led a top club from the board. This lost to LHO's king, and she duly continued spades. RHO won with the king and cleared spades, but five more rounds of clubs turned her hand to mush. In order to keep all of her spades, she had to either pitch her ace of hearts or come down to the stiff king of diamonds. She decided to stiff her king, but I was able to read it and play ace then queen of diamonds for my ninth trick. Had she pitched one of her spades, I would have thrown her in with the ace of hearts and forced her to lead away from the king of diamonds at the end. Here's the whole hand:

Portland Regional Update

Hi folks---

Things are going well so far at the Portland Regional. Meg and I won Bracket 2 of the Monday-Tuesday KO with friends from Vancouver, BC, and we placed 3rd in the Wednesday Open Pairs. We start a new KO this afternoon. If you're around, please come check out my lecture this evening starting at 6:15 in the main playing area. I'll write up some of the more fun hands of the week when I get some time.

Oregon Trail Regional

The fabulous Oregon Trail Regional starts today. This tournament, held at the Vancouver, WA Hilton, would be one of my favorites even if it wasn't my "home" regional. There's lots of friendly people, nice giveaways, and a great playing site in a cool downtown area. Also, District 20 has a surprising number of excellent players, and the standard of play here is quite a bit higher than you'll find at the average regional. This is gonna be great!

Quick bidding problem from the Sarasota Regional

Via Robert Todd:

♠ KQJT3
♥ none
♦ KJ7
♣ KJ753

All white at matchpoints, your partner opens 1C. RHO pops to 2H; you bid 2S. LHO jumps to 4H, which gets passed back to you.

(A) What's your call?

(B) LHO makes the cheapest heart bid (up to 6H) over your bid. Partner and RHO pass this too. Now what's your call?

Hands from the Charlottesville Regional

The Charlottesville Regional was a huge success! Almost 1600 tables, great people, great hospitality, and a great job done by both our directing staff and the hotel staff. Thanks again to Millard and his team of directors, as well as Mark and his team at the DoubleTree.

I’ve been so busy since the tournament that I haven’t had a chance to share all the tough hands that I ran across then! Here, almost a month later, are a few of the problems I faced.

In problems A and B you’re playing with an unfamiliar, but expert, partner. All problems are from knockout (IMP) play.

(A) Red vs. white

A652 3 AJ74 AQT9

You open 1D (promising 4+), LHO overcalls 1H, partner bids 1NT, and RHO raises to 2H. You’re up. [Double would be for takeout here.]

(B) All red

K763 QJ95 J8752 –

Partner opens a strongish (good 14 to 17) 1NT, and RHO passes. What’s your bid / plan?

(C) Red vs. white

A65 AJT65 – T9843

Partner opens 1S, and RHO sticks in a 2D call. Systemically, here are your choices:

2H, natural and forcing to 3H;
3C, natural and forcing to game;
3D, invitational or better spade raise;
3H, invitational with long hearts and a spade fit, at least nine cards between the two suits;
4C, game-forcing with long clubs and a spade fit, at least nine cards between the two suits;
4D, game-forcing spade raise with at most one diamond;
And, of course, Other.

What’s your call?

(D) White vs. red

A3 KQJ85 Q QJT62

You open 1H in first seat, and your LHO’s weak 3D bid gets passed around to you. What’s your call?

Play problem

You're playing IMPS, and the auction has gone:

West	North	East	South
			1NT
2♠	2NT	p	3♣
p	3NT	p	p
p

1NT was 15-17, and 2S was natural. 2NT was lebensohl - it could have been lots of different handtypes, but after your forced 3C call, partner's 3NT bid revealed a raise to 3NT with a spade stopper.

LHO leads the king of spades, and you see:

♠ A75 ♥ 742 ♦ AQ432 ♣ 98

♠ J2 ♥ AT3 ♦ K986 ♣ AK54

What's your plan here?

First thing's first: Count your tricks. Ace of spades, ace of hearts, ace-king of clubs, and five diamonds add up to the nine tricks you need for 3NT. Great!

Next: Are there any problems that might arise? There's a big one, if you're not careful! Take a closer look at the diamond suit:

♦ AQ432

♦ K986

You can't run all five tricks due to the blockage in the diamond spots (unless the opposing diamonds break 2-2, which only occurs 40% of the time). Sadly, the defense has just started an assault on the side entry to the long diamond. On a heart lead, you could have won the ace, played four rounds of diamonds ending in your hand, then led to the ace of spades to cash the last diamond. But no use despairing of what could have been... can you see the way around the problem?

Just duck the first two spades! On the ace of spades you can drop one of your big diamond spots and the suit will now look like

♦ AQ432

♦ K98

Now, king, ace, and queen of diamonds will leave you in the right hand to enjoy the fifth diamond.

What if the defense doesn't do your dirty work for you? An astute West might switch after the first spade. If he switches to a heart, he sets up another trick for you there, so he'd probably lead a club. Win that club, cash two rounds of diamonds ending on the board (you never know-- they might be 2-2 this time) and duck a spade. Win the (likely) club return, lead up to the last diamond honor on the table, discard that offensive high diamond from your hand on the ace of spades, and claim your nine tricks.