Losing Trick Count – Less counting is more fun!

Early in our Bridge career we learned how to count traditional 4-3-2-1 High Card Point hand evaluation.  Back in the 1920’s when Milton Work published his point count book, hand evaluation improved immensely over general adoration of face cards.  While the HCP approach is easy to grasp and often works well, the approach can suffer unless the astute Bridge player makes some subtle adjustments. Sure, counting distribution points enhances hand evaluation.  Some methods use length points, some use short points, while others use a combination depending on factors such as who is the apparent declarer or dummy.  For your edification, check out the myriad of approaches to counting distribution points.

Aside from HCP and distribution points, as declarer in a suit contract we appreciate the values of quick tricks to make our contract.  Holding Aces and Kings we can quickly go about our business before the pesky opponents develop tricks of their own.  Losing Trick Count also distances itself from HCP hand evaluation when a player has a somewhat unbalanced hand.  Using a distribution point counting method is helpful but not nearly as robust as LTC.  It was F. Dudley Courtenay in his 1934 book "The System the Experts Play," who first described the Losing Trick Count hand evaluation technique.  In time, his approach gained such popularity that Ron Klinger wrote a revolutionary follow-up, "Modern Losing Trick Count.”

Ron’s LTC book is essentially based on counting effective losers in a trump contract.  Simply stated, once partnership has identified a suit fit of 8+ cards, each suit may be evaluated as containing between 0 to 3 losers.  Exceptionally, if a player holds a very strong-long major, e.g., a "self-sustaining suit" that’s sure to be trump, the player can immediately used LTC regardless of partner’s suit support. Once you’ve found an 8+ card trump fit, the basic tenants of LTC are:

1. Aces and Kings are not losers (except a singleton King)

2. Queens may or may not be losers depending on the supporting honors.

Here is a listing of honor card combinations and associated LTC losers:

Void = 0

A = 0

A K = 0

A K Q = 0

A K x [x x. . .] = 1

A Q x [x. . .] = 1 (tripleton or more)

A x = 1

A x x [x. . .] = 2

K = 1

K x = 1

K x x [x. . .] = 2

K Q = 1

Q J [x. . .] = 2

Side suit adjustments to LTC include:

- A J 10 [x...] = 1.5 losers
- Q x x = 2.5 losers
- Q 10 x = 2 losers (Queen honor support)
- A Q = .5 losers
- A Q x = 1 loser
- J 10 x = 3 losers
- Q x = 2 losers (but are considered a "plus")

Once a trump suit has been identified, a LTC calculation may be performed.  LTC theory is based on the concept that the game-going declarer is in the position to either promote a 4 card side suit or perhaps ruff a loser when dummy has less than 3 cards in the side suit.

While we are not particularly fond of performing extensive mental math calculations at the table, it’s worth spending a moment to review LTC math theory.  Accordingly, a player's LTC is subtracted from 12, with a maximum of 3 losers per suit. So with no Aces, Kings or associated Kings, the partnership’s maximum LTC would be 24 (12 for each player).  The combined LTC is subtracted from 24 to determine the achievable playing tricks.   Here are some examples:

Opener LTC = 7
Responder LTC = 9
Combined LTC = 7 + 9 = 16
Tricks = 24 – 16 = 8
Appropriate bidding level = 2 (part score)

Opener LTC = 6
Responder LTC = 8
Combined LTC = 6 + 8 = 14
Tricks = 24 – 14 = 10
Appropriate bidding level = 4 (major suit game)

Opener LTC = 5
Responder LTC = 9
Combined LTC = 5 + 9 = 14
Tricks = 24 – 14 = 10
Appropriate bidding level = 4 (major suit game)

Opener LTC = 4
Responder LTC = 9
Combined LTC = 4 + 9 = 13
Tricks = 24 – 13 = 11
Appropriate bidding level = 5 (major or minor suit game)

Opener LTC = 4
Responder LTC = 8
Combined LTC = 4 + 8 = 12
Tricks = 24 – 12 = 12
Appropriate bidding level = 6 (slam)

Now let’s review some suit combinations and evaluate our LTC:

3 Losers:

J 10 8
J 9 8 7
J 10 9 8 7 6

2.5 Losers:

Q 3 2 (Queen not supported with an honor)

2 Losers:

J 2
Q J
Q J 5 4 3
Q 10 3 2 (Queen is supported by an honor)
A 9 8
K 10 9
A J 6 5 4 3
K J 5
Q J 10 9 8 7

1.5 Losers:

A J 10

1 Loser:

K
K Q
A J
A K 10 9 8
K Q J
K Q 7 6
A Q 3 (tripleton or longer)

.5 Losers:
A Q (doubleton)

0 Losers:

Void
A
A K
A K Q
A K Q 2

Okay, let’s put our practice to work and evaluate total LTC for the opening bidder.  For this exercise we will assume partner supported our major suit opener.  Remember, LTC hand evaluation assumes a trump fit with partner.  Or as the cliché goes, don’t count your chickens before the eggs have hatched. Of course, if the opener holds a self-sustaining trump suit, one that should not lose more than one trick, the opener can immediately perform a LTC calculation.

A Q 3 2     = 1 loser
A K 10 9    = 1 loser
Q 2           = 2 losers
J 9 8         = 3 losers
Total         = 7 losers, 16 HCP

A Q 5 4 3 = 1 loser
K Q 2       = 1 loser
J 10         = 2 losers
Q 3 2       = 2.5 losers
Total        = 6.5 losers, 14 HCP

Q J 9 4 3  = 2 losers
A Q 9 2    = 1 loser
A 8 7       = 2 losers
6             = 1 loser
Total        = 6 losers, 13 HCP

8              = 1 loser
K 9 8 7 6 4= 2 losers
10 5         = 2 losers
A K Q 2     = 0 losers
Total         = 5 losers, 12 HCP

A J 10 4 3 2= 1.5 losers
3               = 1 loser
A Q 5 4 3   = 1 loser
2               = 1 loser
Total          = 4.5 losers, 11 HCP

A K 5 4 3 2 = 1 loser
K 8 7 6 5 4 = 2 losers
7               = 1 loser
--              = 0 losers
Total          = 4 losers, 10 HCP

Did you notice that on these carefully constructed hands, while the High Card Points drop, the losers are mysteriously decreasing! What’s going on here - more honors mean more tricks, right?  No, not necessarily.  Taking a closer look, notive that the trick-taking capability is actually improved on hands with longer suits – especially with primary honors.  Indeed, that’s why they call Aces and Kings suit “controls.”  Here are two extreme hands to illustrate the point:

A K Q 8 7 6 5 4 3 2
A
2
2

Q 10 9 8 7 6 5 4 3 2
A
A
K

Both hands have 13 HCP but clearly the first hand will take more tricks than the second hand.  On the first hand, we can bid slam when partner holds an Ace.  After all, we have 11 tricks in hand.  On the second hand we might lose 2 Spades and a Club unless partner holds an Ace.

Recall that Losing Trick Count hand evaluation is predicated on the partnership holding an eight card fit or one player holds a self-sustaining suit – typically one loser.   Here are a few examples where the opening bidder can immediately use LTC with self-sustaining suits:

A K Q J 2
K Q 3 2
A 3 2
2
LTC = 4 with an excellent self-sustaining Spade suit

Q J 3 2
K Q J 9 8 7
A Q
2
LTC = 4.5 with a nice self-sustaining Heart suit

A Q J 9 8 3 2
A J 10 2
--
K 2
LTC = optimistically, a 3.5 with a fair Spade suit

Okay, Losing Trick Count methodology is cute but how do we use it after opening the bidding?  While we will examine responder’s bids and opener rebids in a follow-up lesson, here are a few tips to pique your interest.   When opener holds 6 LTC, after our responder has made a constructive raise, we will learn techniques to explore bidding game using techniques such as game try bidding.  Or perhaps partner has made an invitational game bid and we have a nice 4 LTC hand – now it’s worth exploring slam.  After all, if we have 4 losers and partner can cover 3 losers with Aces and Kings, we should be able to take home that slam!  Ditto on making a major suit game when we have 6 LTC and partner can cover 3 of them – that’s 10 tricks.  Bingo!

In Part II of our Losing Trick Count series, we will explore responder’s hand evaluation techniques, including cover cards.  And if you simply can’t wait, you can always take a peek at our Losing Trick Count write-up in our online Bridge Encyclopedia.  And for those eMag newsletter subscribers going back to December 1995, we briefly covered LTC in our first Intermediate-Advanced newsletter.  Once again, you can Quiz yourself here on LTC here.

The Claim, the Law, the Appeal and the Verdict

The beat: Boston North American Bridge Championship

Date: November 22, 2008

It’s board 17 playing in the second session of the Daylight Pairs matchpoint game.  No one is vulnerable, North is dealer and the auction proceeds:

  N     E      S      W
(P)  - 3S – (P) –  P;
(4H) – P - (P) – 4S;
(P)  -  P  - (X) – AP;

           8
           K Q 9 3 2
           Q 8
           K J 9 8 7
J 9 4                K Q 10 7 6 3 2
A 8 5               10 7 6
A 3                  K
Q 6 5 4 3         10 2
           A 5
           J 4
           J 10 9 7 6 5 4 2
           A

So East, playing in 4 Spades doubled, receives the Club Ace lead from South, hoping for a Spade ruff.  North, seeing 10 Clubs between his hand and dummy easily deduces partner is looking for Club ruff.  Asking South to switch to a Heart, the high suit, North places a high Club, the C9.  Accordingly, East continues with the HJ, the top of a doubleton.  East is not thrilled about losing 5 tricks (1S, 2H, 2C), thus winning the HA.  Next comes a low Diamond to East’s stiff King.  Declarer East hopes to pitch a Heart by getting to dummy’s Spade J-9.  After leading a low Spade, South rises with the Ace and returns the H4 to North’s winning HQ.  North continues with the HK, knowing the Hearts split 5-3-3-2 (partner signaled high-low doubleton) and South pitches a low Diamond.  North continues, cashing the CK with South pitching another Diamond.  At this point, North leads a low Club and the plot thickens.

Our declarer East faces cards on the table saying, “The rest are mine.”  Here’s the remaining cards:

           --
           3 2
           Q
           J 8 7
J 9                   K Q 10 7 3
--                    6
A                     --
Q 6 5               --
           5
           --
           J 10 9 7 6
           --

But wait says South who calls the Director, pointing out he still holds the trump Spade 5.   The Director rules:

No mention was made of the outstanding spade in the defender’s hand. Declarer must ruff with the S3 and defender over ruffs with S5, therefore the result is: 4 Spades by East down three, E/W minus 500. (Law 70C)

Hmm, declarer East calls for an Appeal of the ruling, perhaps figuring it was “incontrovertible” that a player of his ability would win with a high trump and pull the remaining trumps (the player masterpoints were: East – 689, South – 1730, West – 6320, North – 1730).

Statements made by the appealing side: Declarer said when dummy went down he noted he had ten trump. He led one round with all following, which left one outstanding. When asked why he did not mention it, he said it was so obvious it didn’t merit a mention.

Finally the Appeals committee issued its ruling:

Law 70C gives the steps required before a trump trick should be awarded to an opponent. All must be met.

1. Claimer made no statement about that trump, and

2. It is at all likely that claimer at the time of his claim was unaware that a trump remained in an opponent’s hand, and

3. A trick could be lost by any normal* play.

*Normal includes play that would be careless or inferior for the class of player involved.

When the solons created this law, they would have left out #2 had they wanted directors to always rule that an opponent gets a trick(s) if conditions 1 and 3 are met. Ergo #2 must have meaning. In general, if declarer has adopted a reasonable line of play and has attempted to draw trump at every opportunity unless there is a valid bridge reason for not doing so, he is allowed to accurately count trump.

Conditions 1 and 3 have been met. When declarer got in he unblocked the diamond suit and led trump. Therefore the conditions of #2 were not met and the claim was upheld..

The result was changed to 4S by East down two, E/W minus 300.

So this time the mouse squeaked by (appealing declarer), enjoying the cheese.   Still, we should always be careful when making a claim to ensure we adhere to the criteria specified in Law 68:

For a statement or action to constitute a claim or concession of tricks under these Laws, it must refer to tricks other than one currently in progress . If it does refer to subsequent tricks:

A. Claim Defined

Any statement to the effect that a contestant will win a specific number of tricks is a claim of those tricks. A contestant also claims when he suggests that play be curtailed, or when he shows his cards (unless he demonstrably did not intend to claim).

B. Concession Defined

Any statement to the effect that a contestant will lose a specific number of tricks is a concession of those tricks; a claim of some number of tricks is a concession of the remainder, if any. A player concedes all the remaining tricks when he abandons his hand. Regardless of the foregoing, if a defender attempts to concede one or more tricks and his partner immediately objects, no concession has occurred; Law 16, Unauthorized Information, may apply, so the Director should be summoned forthwith.

C. Clarification Required for Claim

A claim should be accompanied at once by a statement of clarification as to the order in which cards will be played, the line of play or defense through which the claimer proposes to win the tricks claimed.

D. Play Ceases

After any claim or concession, play ceases. All play subsequent to a claim or concession shall be voided by the Director. If the claim or concession is acquiesced in, Law 69 applies; if it is disputed by any player (dummy included), the Director must be summoned immediately to apply Law 70 or Law 71, and no action may be taken pending the Director's arrival.

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