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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. |
