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Issue 12: January 2010 BridgeHands Newsletter

Losing Trick Count, Part II - Cover Cards

October 2010

Dear Bridge Friend,

Welcome to Bridgehands eMag Newsletter, Issue 12. In this issue, we continue our exploration of advanced hand evaluation using Losing Trick Count (LTC).  Having looked at opener’s LTC methods, we will turn our attention to responder’s hand evaluation methodology and opener’s follow-up bidding.  Recall that making suit contracts is all about suit length and quick tricks with primary controls (Aces and Kings).  While LTC calculations still works for responder, we will learn using “Cover Cards” is a far quicker method to effectively evaluate bids. And Cover Card hand evaluation is particularly effective when considering game and slam bids.  Quiz yourself here on Cover Cards.

Also in this newsletter, we will check out an Appeal at the Washington DC NABC.  And like our last newsletter, again we will focus on what can go wrong when declarer makes a generalized claim without stating a specific line of play.

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Cover Cards – Less counting is more fun for responder, too!

Okay, traditional 4-3-2-1 High Card Point hand evaluation is simple enough. And we certainly know how to value short side suits using our favorite approach to count dummy distribution points.  In our last article on Losing Trick Count, we learned to appreciate the value of quick tricks and side suit length to improve our bidding accuracy.  Recall that holding Aces and Kings we can quickly go about our business before the pesky opponents develop their own tricks. Following the approach in Ron Klinger’s book, "Modern Losing Trick Count”  once partnership has identified a suit fit of 8+ cards, each suit may be evaluated as containing between 0 to 3 losers.  Here’s a recap of LTC hand evaluation once the partnership finds an 8+ card trump fit:

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 Queens, 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, i.e. 2 Hearts or 2 Spades
To see more about various game and slam LTC calculations, please refer to LTC Part I.

Now we will turn our attention to responder’s LTC calculations.  After opener makes a typical opening bid of 1 Heart or 1 Spade promising 5 cards and responder has a 3+ card fit, the partnership can consider Losing Trick Count to determine the best contract.  Of course, in most situations the responder will have far more losers than the declarer.  Declarer’s opening hands are usually 7 or less LTC, so counting losers is a fairly straight forward and quick process.

Not so for the responder, whose hand may contain up to 9 or 10 losers.  So an easier LTC analysis for responder is to count winners rather than losers.  In the 1970s, George Rosencrantz championed the concept of “Cover Cards” as part of his Romex system.  Cover Cards are defined as Aces and Kings in each suit, cards that “cover” opener’s losers and can quickly take tricks. In an ideal world responder’s cover cards would be located in opener’s bid suit, opener’s rebid suit.  Of course Bridge bidding is all too often more an art than a science. So while we may count our side suit Kings, we do so with the realization that the holding may be dependent on a finesse.  But then that’s Bridge – sometimes we must roll the dice and take our chances. Here’s a question to ponder until later in this lesson.  Which contract is a riskier adventure with a side suit King – playing in game or slam?  And what about Queens?  On an unbid side suit, forget it – she is not worthy to be called a cover card.  Yet a well placed Queen in one of partner’s bid suits, well that’s a horse of another color.  So supporting side suit Queens are indeed promoted to Cover Card status.

How about supporting side suit Jacks?  Sure, with adequate length in a supporting side suit (combined 8 card fit), a well placed Jack should count for one-half of a Cover Card.  But wait, there’s more.

With adequate trump support, a side suit singleton or void certainly covers losers in partner’s long suit/s.  Finally, holding a fourth trump is also worth one-half of a Cover Card.  Wait a minute – if we count for side suit shortness and trump length, aren’t we double counting?  If we are not careful, YES!  But if we restrict ourselves to one-half a cover for the fourth trump and one or two covers for a side suit singleton or void, we are taking a reasonable position. When in doubt, upgrade your position holding Aces and Kings. Downgrade holding Queens and Jacks as partial covers since these holding yield slower tricks – consider counting these as partial stoppers, especially in high level contracts.  Here’s an illustrative example: holding a hand of “Quackers” (Queens and Jacks) with a side suit singleton you get a bit too frisky counting the short suit and place partner in a high level contract.  The opening leader begins with a trump Ace, trump King and a small trump.  Rather suddenly the sparkle of your side suit singleton seems to have lost its luster!  Now do you see what we mean?  Use caution counting shortness without holding primary honors (Aces and Kings).

When we are trying to make a game or slam contract, it’s all about taking tricks.  Below are two hands that illustrate the responder’s benefit of counting Cover Cards.  First we will go through some arduous arithmetic calisthenics to illustrate responder’s challenge to use LTC.  Then we will discuss the elegance of Cover Cards for responder.  So if doing math proofs in school wasn’t your favorite subject, skim the LTC stuff and jump ahead one page.  Okay, here we go . . .

The bidding begins with partner opening 1 Spade and we hold 12 High Card Points on both hands below.  Openers usually hold 7 or less LTC, counted after responder supports opener’s major.  As you will recall, we subtract the combined LTC between opener and responders hand from the number 24 to determine the combined LTC.  For those curious about the seemingly magic number 24, it’s based on a maximum of 12 losers per hand. Why not 13 since a player holds 13 cards?  Well, according to LTC the maximum losers are 3 in a given suit, so the maximum number of losers is 12.  That’s 24 LTC for the partnership – bingo, the number 24.

To make a 4 level major suit contract, the combined LTC requirement is 14 LTC or less (24 total tricks minus 10 tricks to make game).

1S - ?

Responder Hand 1:
S  A 10 3 2   Losers:1.5  Covers:  1.5*
H  A 2          Losers:   1  Covers: 1
D  A 4 3 2     Losers:   2  Covers: 1
C  10 9 2      Losers:   3  Covers: 0
Total                       7.5              3.5
*  1 for Ace, .5 for fourth trump

Responder Hand 2:
S  Q J 5 4     Losers: 1.5  Covers: 2**
H  Q J           Losers: 2    Covers: 0
D  K 7 6 5     Losers: 2    Covers: 1
C  Q J 3        Losers: 2    Covers: 0
Total                      7.5               3.0
**  1 for trump Queen, .5 for trump Jack, .5 extra trump

Using LTC, the responder seems to have 7.5 LTC on either hand.  Thus:

Declarer 7 LTC (or less)
Responder 7.5 LTC
Total LTC = 14.5
24 total deck losers – 14.5 = 9.5 tricks total

Whew, that’s quite a bit of mathematical gyrations that would be difficult for a non-seasoned player to quickly perform at the table.  And considering hand 2 is full of “slow tricks” it seems responder’s LTC evaluation should require a compensating offset.  Notice how hand 2 is full of “Quackers.”  Perhaps there’s a quicker and more accurate responder method to evaluate losing tricks.

Let’s look at the same two hands using the Cover Card concept.

Hand 1:
Declarer 7 LTC (or less).
Responder can cover 3.5 losers.
Thus, the total losers are 7 – 3.5 = 3.5, .5 too many.
Since declarer can lose 3 tricks in a major suit game,
3.5 – 3 = .5, so declarer should have 6.5 LTC to make game.

Hand 2:
Declarer 7 LTC (or less).
Responder could optimistically cover 3 losers, but with only one primary honor we should probably downgrade at least one-half cover.  2.5 covers looks safer with this hand.
Thus, the total losers are 7 – 2.5 = 4.5, 1.5 too many.
Declarer can lose 3 tricks for game, so declarer should have 5.5 LTC for game.

As you can see, it’s far easier for responder to count Cover Cards than compute the aggregate losing trick count.   Also notice that on hand 2, Cover Card hand evaluation is not as “generous” to award merit for hands without primary honors – Aces and Kings (1 trick variance).  Let’s ponder a deeper meaning here.  Were you able to contrast the subtle difference between Losing Trick Count and Cover Cards?  Essentially, once the partnership finds a trump fit opener includes all Aces, Kings and Queens as non-losers.  Recall that for our Cover Card theory, responder does not value Queens and Jacks except in supporting suits with partner.  Mind you we are not knocking LTC hand evaluation for opener – an opening hand often has twice the valuation as responder’s hand.  Thus opener’s aggregate honors, including “working Queens” useful in finesse and promotion plays, are usually worth counting.  Taking a ruff cut with poetic license:

Farewell thee, our stranded Queens.
Welcome back, my supporting Jacks.
We honor thy Queen, in supported suits.
For all are covers, with trump suit length.

Earlier we mentioned opener’s initial opening bid should be 7 LTC or less.  How much less?  Well certainly not a 3 LTC hand – opener should normally make a strong opening bid with such fine values.  So opener should hold 7 LTC with a minimum hand, up to 4 LTC when holding a maximum 1 level opener (19-21 points).  Here’s a few examples based on opener’s rebid:

1H – 2H;
3D           Opener’s help suit game try always promises 6 LTC

1H – 1S;
3H           Opener has a very nice 6 card suit and 6 LTC

1D – 1S;
2H           Opener’s reverse shows 4-5 LTC – forcing

(1D) – X – (P) – 1S;
(P)   - 2D   Overcalling partner’s double and new suit shows 4-5 LTC

1H – 1S;
3C             Opener’s strong jump shift promises great suits and 4 LTC – forcing game

2C - ?        Assuming a trump fit, opener has 0-4 LTC

See our Encyclopedia for more on LTC evaluation based on bidding.

Okay, since we’re touting the benefits of responder using Cover Card theory, buckle up and we will put this into action.  Moving up into thinner air, Cover Cards hand evaluation is especially powerful when exploring slam contracts.  Let’s say this time opener bids 1 Heart, responder bids 1 Spade and opener makes a strong jump shift to 3 Clubs showing a 3-4 LTC hand.  As responder, we hold 10 HCP for both hands.

1H – 1S;
3C - ?

Responder Hand 3:
S  10 9 3 2    Covers: .0 (not a suit with a fit)
H  A J 2         Covers: 1.5
D  5              Covers: 1 (singleton)
C  A J 9 2      Covers: 2.0,
Total:                       4.5

Declarer shows 4 LTC after strong jump shift
Responder can cover 4.5 losers (all honors working)
Thus, the total losers are 4 minus 4.5 = Grandslam! (bid Blackwood)

Responder Hand 4:
S  K J 3 2      Covers: 1.0 (but honor may not be working in slam)
H  Q 5 4        Covers: 1.0
D  Q J           Covers:    0
C  J 4 3 2      Covers: 1.0 (but soft values if pushing to slam)
Total:                      3.0 (on a good day, but don’t be too optimistic)

Declarer shows 4 LTC after strong jump shift
Responder can cover up to 3.0 losers (that side suit King may not be helpful)
Thus, the total losers are 4 minus 2 to 3 = maybe a small slam; do you feel really lucky?

Over the years, we’ve come to appreciate the value of controls - Aces and Kings are boss when exploring slams.  And as we’ve seen above, a supporting suit Queen and side suit shortness with trump length both bolster responder’s Cover Card count.  Responder’s Cover Card hand evaluation offers a quick and accurate methodology to explore game and especially slam auctions. 

On the next auction, responder will count Cover Cards after opener’s reverse, implying 4-5 LTC (assuming responder has an 8 card fit).

1C – 1S;
2H - ?

Hand 5:
S  9 8 7 4 2     Covers:   0
H  A K 6 5       Covers: 2.5
D  9                Covers: 1.0
C  A K 4          Covers: 2.0

Hand 6:
S  K Q 9 7 4     Covers: 1.0 (slow trick, opener could be void)
H  K 6 5 4        Covers: 1.5
D  J                 Covers: 1.0
C  A J 3            Covers: 1.5

Both hands have 14 HCP and 6 LTC. Forgetting the math for a moment, just take a look at the solid controls on hand #5.  No one will contest the 5 covers for the working Aces and Kings in all the right places – partner’s bid suits!  And the accompanying fourth trump is as good as gold, surely worth an extra .5 covers.  However hand #6 is a much thornier hand evaluation, isn’t it?  The off suit Spade King-Queen is great, but on another hand on another day – partner is likely to be very short in Spades so this honor combo is questionable. To be fair, the Club Ace-Jack is nice and the Heart King with a four card suit is lovely.  But what a difference quick tricks make, especially in supported suit when playing slam contracts!

So how does Cover Card theory compare to LTC when the partnership has a double fit? Let’s say the opener makes a Strong Jump Shift (4 LTC) with the following bidding sequence:

1C – 1D;
2H - ?

Hand 7:     Cover Cards
S  8                1.0
H  K Q 3 2       2.5
D  9 8 7 6          0
C  A J 5 4        2.0

Holding 10 HCP (13 distribution points), the responder clearly has a double-fit with opener’s Club and Heart suits – at least 9 Clubs and 8 Hearts. Using Cover Card evaluation, after checking for Aces, a Heart slam or grandslam looks quite likely; 4 LTC minus 5.5 Cover Cards = all the tricks and then some!  At the table and without the benefit of kibitzing these hands, evaluating double fits in two suits can be a bit of a tricky prospect.  On a good day, declarer pulls trump, sets up a side suit going about one’s slam or grandslam business.  But on those “other days” the mouse gets the cheese – poor declarer has mirrored values with 4-4 and 2-2 side suits, unable to promote or ruff suits.  Our advanced players will recognize the opportunity to consider and endplay with such holdings but that’s another story.  By the way, if you were defending against 7 Hearts and held 3 or 4 Clubs I’m sure you couldn’t wait to lead the Club suit – declarer’s side has 9+ Clubs, so with your 4 Clubs lead one and show partner just how smart you really are!

Finally, let’s see how our Cover Card evaluation works when opener has made a preemptive bid.   For our last example, let’s assume our disciplined partner preempts with a weak 2 Spade call in second seat, vulnerable versus non-vulnerable.  If ever, in this situation with adverse vulnerability and in second seat, partner should be making a disciplined call with a decent trump suit.  The classic weak two opener contains two of the top three trump honors and perhaps little else.  On this hand, partner has some extras when opening 2 Spades:

S  K Q 9 6 4 2
H  9 3 2
D  8 6
C  K 6 4

Granted opener’s bid was not made with a self-sustaining suit, but assuming a modest responder fit we can estimate opener’s losing trick count.  On the above hand opener has 8 LTC. With a four card side suit or singleton, the opener may hold 7 LTC; 6 LTC hands should not normally be opened preemptively in first or second seat.  For a 3 level preempt, opener’s count would be 6-7 LTC.  Okay, back to opener’s weak 2 Spade bid, now let’s compare two nice responder hands that we would normally open 1 Notrump with 17 HCP:

Hand 8:    Cover Cards
S  A 8              1
H  A K 7           2
D  9 7 5 2        0
C  A Q 7 5        1+

Hand 9:
S  A J               1
H  K Q 7           1
D  K J 7 5         1 ?
C  Q J 7 5         0

On hand 8, responder holds an excellent hand with 4+ Cover Cards and a good chance to bring home a 4 Spade contract.  However, on hand 9 it’s clear that responder’s 3 Cover Cards are at least two fewer than required to make game and side suit King may not be helpful. 
Back to hand 8, responder can query opener with a 2 Notrump asking bid.  Playing either Feature Ask or Ogust, after learning opener’s rebid, the responder will be ready to accept a 4 Spade game.  Also see our eMag issue on preemptive opener rebids.

In conclusion, once the partnership has a trump fit, Losing Trick Count is a very useful hand evaluation tool to improve the opener’s accuracy finding games.  And responder’s Cover Card hand evaluation can result in easier and more accurate hand evaluation to explore game and slam contracts (over LTC or many other methods).

For more, see our Losing Trick Count write-up in our online Bridge Encyclopedia.  And for those eMag newsletter subscribers going back to December 2005, we briefly covered LTC in our first Intermediate-Advanced newsletter.  You can Quiz yourself on Cover Card here.



The Claim, the Law, the Appeal and the Verdict

The beat: Washington North American Bridge Championship, July 30, 2009

It’s board 16 playing in the first session of the Mixed Board A Match team game.  No one is vulnerable, North is dealer and the auction proceeds:

  S     W      N      E
                 1N - (2D!);
  P – (2H!) – P – (2S);
 4H - (P) -    P – (P);

East’s 2D was alerted as a long unspecified suit.  West’s 2H was alerted, a puppet bid asking East to identify long suit. Not deterred, North belatedly jumped to 4H which ended the auction.

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

The opening lead was the Spade 6 to dummy’s 2, Jack to declarer’s Queen.  Next declarer led a Club to the dummy’s Ace with RHO playing the Queen.  The declarer switched to dummy’s Heart 10, with the finesse failing to LHO’s Heart King.  LHO then led the Spade 3 to RHO’s Ace who dutifully returned a low Spade which the declarer won with the Heart Queen. 

With the declarer on lead, the players held:

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

At this point North claimed the remaining tricks saying, “I’ll throw my losers on Dummy’s high black cards.” West immediately objected and called the director.  No mention was made of how the Club suit would be played. 

Per Law 70A and E, the director disallowed the claim and awarded one trick to E/W thus adjusting the result to 4 Hearts by declarer making four.

North/South appealed the director’s decision.  The declarer stated he always had club finesse in his mind. RHO noted that he might have false-carded, holding the Club Queen – Ten doubleton.

The Decision: Law 70E says you may not play one opponent for a specific card unless one opponent has or will show out on normal play or unless it would be irrational to do otherwise. The committee thought the declarer would likely have finessed the club ten but that the play of the club king would not be irrational. Therefore the committee ruled as the director had, setting a score of 4 Hearts by North making four, N/S plus 420 for both sides.

As we have discussed in the last newsletter, neither Bridge directors nor appeals committees are impressed by declarer’s assertion it is “incontrovertible” that a player of his ability would draw the last trump and continue with the seemingly marked Club finesse.

Remember that 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.

BridgeHands Back Issues

If you missed a back issue of a BridgeHands Intermediate-Advanced eMag newsletters, here are the links:

Issue 0 - Finesses
Issue 1 - Forcing Pass
Issue 2 - Leads on Notrump Doubled contracts
Issue 3 - Opener Reverses
Issue 4 - Reverses, Part II - Responder Rebids
Issue 5 - Psyches, Part I
Issue 6 - Psyches, Part II
Issue 7, Street Smart Bridge Player, Part I
Issue 8, Street Smart Bridge Player, Part II
Issue 9, Street Smart Bridge Player, Part III
Issue 10, Street Smart Bridge Player, Part IV

Issue 11, Losing Trick Count, Part I

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