WOW! LTC is now SHARP.
LTC BASICS
Suited
contracts only
Maximum of
3 losers per suit and any missing A K or Q in the suit is a loser. Qxx is 3
losers. QJx is 2 losers. Qx DBT and Kx DBT
count as 2 and 1 losers. K or Q SGTs are 1 loser. Non-trump suit voids are 0
losers (providing there are some trumps with which to ruff). Short trumps impose additional losers. Add a
loser if no ace in the hand.
Each hand
has a maximum of 12 losers. Add the losers of both hands and subtract total
from 24 to get the number of tricks you can expect to make. The minimum opening
requirement is 7 losers, and the minimum response is 9 losers. 24-9-7=8, so you
expect to make a two level contract.
INNER WORKINGS
Declarer’s
ultimate objective in play is to make one of the hands good or as good as
possible and normally that is the concealed hand. With some sort of trump fit
in place declarer looks at dummy and sees two basic types of real winners
- Independent winners
declarer can use to ditch losers from the concealed hand
- Those where
the requirement of play dictates a real dummy winner is played on a real
winner in declarer’s hand; the usual
requirement is to collect trumps but it is a common situation in
the side suits as well .
Setting aside real defence for the moment, if all declarer’s losers can be
aligned with free accessible winners in dummy
then all the tricks will be made. LTC
calculates the apparent losers in the two hands, partial suit by partial suit
(no losers beyond the third), without considering any relationship between the
suits. The loser sum is subtracted from 26 to obtain a count of available
winners (but not tricks yet!).
The graphic
shows two hands where a small slam can make. There is one real loser pair as a blue L.
Where a winner in one hand is matched to a loser in the other a black link is used, otherwise, that
winner must land on a winner in the other hand and that is a red
link. The adventitious winners (those cards beyond the third in a
suit) may fail to establish in the course of play or may not be independent
(loser-ditching) winners, and then they become tied to other winners. In a side
suit adventitious winners are coded U=unresolved, but trumps are coded as
(presumed) winners. To determine the trick taking potential of the combined
hands, the count based on 26 must be revised for the occurrences of winners on
winners (wows).
A wow cancellation drops a winner from
both sides (2 lost from the trick pot) and a single winner is returned (1 back
to the pot). With the trumps considered
as available winners in the trick pot, two rounds are used to collect
opposition trumps. That is 2 wow
cancellations. So 4 winners are removed from the pot and 2 put back in. A provisional trick estimate is obtained by
subtracting the loser count of the side
suits from 24 and not 26. The trump wows are split between the two hands so
that 12 is the maximum losers for any hand.
But LTC still has to guess about the occurrences of wow cancellations relating to the adventitious side suit winners in the pot. If a ruff has to be used to establish a long suit then that is wow cancellation. If suits are of equal length say 4, then that is wow cancellation. LTC applies one wow cancellation to each side suit. 1 winner per partial side suit is discounted in each hand (so 6 removed from the pot) and 3 returned. The provisional tricks in the trick pot are 24 -3 - side suit losers.The trumps are still the in pot as apparent winners and the combined LTC for trumps (if there are no holes between the two hands) is 3. Instead of subtracting 3 in the formula above, the LTC for the trumps is subtracted. So the pot contents or expected tricks become the familiar
24 –LTC all suits (trumps are LTC’ed along
with all side suits)
This has
the benefit to correct for holes in trumps as with any other suit and the 24
neatly matches the LTC counting maximum of 3 losers per partial suit. Nevertheless, it is only neatness.
Not
surprisingly, LTC is sensitive to those wow
cancellations; 2 are core within the formula and 3 built-in as part of the
(LTC)ounting across the side suits.
Although the wow cancellations
are buried in usual presentation of the
LTC method, these cancellations dull what could be sharp tool. Moreover, the loser count is determined
with a broad brush, although that I
suspect is the appeal of LTC.
Consider
the impact of 3 rounds of trump winners on winners to collect trumps. An
anticipated independent loser-ditching winner is lost, so the overall return is
ONE TRICK LESS than that predicted by LTC. But since most suit contracts are
based on hands that are unbalanced, opportunities arise in the course of play
to upgrade adventitious winners to real tricks. Long suits can come good or a
suit splitting 3-3 establishes the 13th.
In addition, a loser can be converted by an endplay or a squeeze. The effect is
the winner deficit is recovered. The more unbalanced the hands, the greater are
the opportunities to discount an uncounted
side suit wow cancellation.
LTC is effective as a guide to trick expectancy for the range of common hand distributions where the wow model applies, however there are situations to be wary of. If you are in slam and have a real uncounted trump loser (10 or J), then by definition, LTC has not seen it. You cannot throw away a trump loser on side suit. Your options to play around the problem are limited since you need all (or almost all) the tricks but sometimes there is a chance to save the day. Moreover, there is the classic irony that LTC can indicate that you can make 12 tricks despite missing 2 ACES.
SHARP LTC
Shapely two suited distributions with holed suits often present a low LTC value despite a deficit of high card winners due to two short side suits with just one or two losers. LTC assumes a maximum of 3 losers in each suit and automatically recruits adventitious winners of the longer suits (including trumps) without any specific assessment. Often the contract makes. Of greater concern is where there are already sufficient obvious winners and there is an adventitious winner that is uncounted and materializes. If it is compensation for an uncounted loser equity is restored. However a gain of a trick above those estimated by LTC may result in a missed game or slam.
It
is important to think of the losers associated with the two provisioned trump
wow cancellations and the 3 built-in counting wow cancellations are like adventitious winners – their states are
only implied. Often there is compensation - a natural uncounted realisable winner somewhere,
or a cancellation can be avoided. The
most obvious avoidance is the
The
recommendation is drop a loser (just one between both hands), assuming there is
one adventitious uncounted winner in
the wash: However, you have no way to
mitigate a real trump loser, so trump control is a pre-requisite of the pushed
loser drop. If there is a good trump support, responder drops not declarer. The loser is not dropped because
there is no counted loser in the trump suit; instead, it is an unspecified
all-purpose loser drop somewhere, but if there is a contra-indication of trump
control then it is prudent to hold off.
Also take
into account that as the high card strength goes down so top honours go missing
then more adventitious winners are counted in to backfill the LTC implied
winner set. Insufficient adventitious
winners then remain to support the unspecified loser drop. So there is a concept of holding off the
loser drop if point weak.
COUNTING RULES
Adjustments
to the LTC calculation, (cf. Rules Table
below) seek to obtain a realistic loser count of responder’s trumps bearing in
mind the sirenous nature of the ‘unspecified loser’ drop. Also, there is reference to the loser
balancing option.
A side suit
Qxx or Qxxx suit is “loser balanced” by a floating side suit ace as an Ax or Axx combination elsewhere in the hand.
There is a mindset that a loose ace is worth say a 1/3 more than a whole winner
and that a roaming Qxx is worth 1/3 of a winner. Taken together the Q, normally counted as a
loser, is effectively only a loser 1/3 of the time. There is a possible
conflict if the balancing ace is
located in a side suit of 4 or more. The
recommended unspecified loser drop could materialise as an adventitious suit
winner in that side suit so the ace there is not floating free. The guide is do
the loser balancing or a non-specific loser drop but not both.
HALF LOSER SHARP
|
Half Losers are a concept and not part of the
count |
The modern style of loss weighted jump overcalls and
high-level sacrifices has pushed the direct immediate game raise to be slightly pre-emptive,
a half loser short of
game. This increases the likelihood that an opponent’s
sacrificial overcall is false. Correspondingly, the minimum surfeit for a delayed game raise is consequently reduced from a loser above game
values to a half loser. The honest
7loser 12-13pt responder has to slot-in to this schema. To delay the game raise a 7loser responder has to conjure up a half
loser. Opener, with a loser under-the-hood, would have advanced to 4NT
after a DGR but the schema imposes a supplemental half loser requirement
because responder may not be the full loser ahead. The suggestion is that opener use a raise rebid to 5S (or 5H) to be the
cautious LTC limit of the combined hands. Responder only goes up to level6 with
an honest 6loser. Tied to this level5 rebid is a recommendation that the DGR is
not used with an honest 7loser if just one ace is held. This provides
a margin of protection against the partnership pursuing slams where a real ace
loser has been sharpened out of existence. The half
loser is applied when a system procedural decision is
required and is not to be included in the determination of trick expectancy
contrary to the language used.
Say there is a minimum overcall of opener and responder has AQ10 in
the suit. Opposite opener’s xxx or xx
the LTC combined is 4 or 3 respectively. On average 3½ losers. However should opener have four (xxxx), the
suit is a liability:
However, probability wise the sharp LTC has already counted in such
possibilities within the recommended unspecified loser drop. The nature of LTC is
such that a half loser comes ‘good’ some of the time, but it often just diverts
an adventitious winner on loser match to become
a wow cancellation elsewhere rather than a loser dropped altogther; no
trick benefit accrues. As a guess, the
half loser , 1/2 the time, makes a difference
1/3 of time = 1/6 of a LTC loser.
The half
loser is a decision guide, not a measure
of trick expectancy.
POINT WEAK HANDS
Consider an
extreme – the responding hand contains 5trumps and another 5suit; there are
only 3 counted losers outside the two suits.
The bidding
starts, 1D P
1S P 2N
P 3C
♠ A K Q ♠
10 9 8 7 6
♥ LLL ♥LL
♦ LLLL ♦L
♣ A KQ ♣
10 9 8 7 6
LTC offers
no excuse for responder to bid 1S with the right hand
|
So it has to be part of the system. A courtesy bid, nothing to with LTC. The
right-hander is not using LTC, so after
the hand is played out there is little purpose in analysing the actions of the weak hand
from the perspective of LTC. |
The
18+pointer, with spades as trumps, is the supporting hand and is the arbiter of
whether to drop the unspecified loser. The right side apparent 9 loser
(actually 10, one is added for no ace), may only have a 4trumps. On the left,
you do not drop the loser for the moment and counting your hand as 7 losers the combined loser sum
is 16, 24-16=8 tricks can be made. If
you as left raise to 2S, even as semi-forcing asking, partner can pass and a probable game is missed. So either you
drop the loser and raise to 3S (3-4 fit at worst) or, rebid 2C/3C or, rebid 2NT
which is fair description and best.
Partner is less worried about his 5-6pts all classified as losers
and tries an escape to 3C (but now looks
like an 8loser with lots of black cards).
On the left, you can force with
3H. Depending on your partnership FSF method, a 3S response should confirm a 5
suit and 4S is inevitable. You had 7losers, partner implied 8 with the 3C bid,
and together with a loser drops makes 14.
LTC predicts 24-14=10 tricks. There is also the added bonus of that your
ashen faced partner is clearly in your debt when the 18pts goes down on the table. I think the room
would or should overcall the 1D opening or make a TOX. Nevertheless, if
non-vulnerable the weak hand still worth a 1S response because there is a real
opportunity to be successful at variance to the room. If there is a jump overcall after the 1S
response then the big hand may speculatively go to 3S. This is unfortunate
because a double would allow the right hand to slip in a free escape bid of 4C.
After 3S, the weak hand should say no more, unless the big hand later doubles.
Should the 3S stand but 4 make, the
principle is for you as right side to be able to say ‘the 1S was a courtesy and
system endorsed, but with a 10loser without including a loading for being point
weak and without any defensive trick, then I am grateful that +170 will net some match point fishes ’. If all the good players in the room have
reached and made 4S when there has been competitive bidding, think about
playing their systems.
POINT WEAK OVERCALLS and RESPONSES
I mention
the point weak loser loading above because it crops up with overcalls of 1
level openings. If partner overcalls, I want there to be something behind it. A
simple overcall, depending on agreement, ranges 8 to 15pts, but 2 queens and 4
jacks is not what I want in partner’s hand. I want to see something
‘resembling’ a 7-loser opener but the hand can be as low as 10 points with a
sensible 5-card suit.. With
8 points, the bidding becomes more a test of character and not theory. In addition, partner’s hand should not qualify for a
MICHAELS cue. These would do it.
|
♠ A 10 9 8 7 6 |
|
♠ A Q J 9 8 |
|
♥ X |
|
♥ Q X |
|
♦ X X |
|
♦ X X X |
|
♣ A 10 9 8 |
|
♣ A Q 8 |
The first
is on the wire and not a sensible vulnerable overcall. As a point-weak hand, it
is 8loser and THAT PRESUMES THERE IS A FIT.
The 6 suit is mandatory at this point count and the suit must have
structure should only limited support exist in partner’s hand.
|
Without the fit LTC means nothing. All you will have done is psyched an overcall with 8pts. The decision to overcall is based on the
premise that with partner holding Hx there is enough of a fit to allow LTC to
work. (To raise with10x is a push else xxx is minimum required.) |
Here the interior
sequence is convincing. A raise by partner with just Hx in spades would provide
enough for there to be a fit and the 8-loser count to the stand.
Similarly
the 5 trumps in the 15ptr are also convincing. Otherwise with 12pts+ it
is better to double regardless of the heart implication. 1(2)H is likely to
be bid by the opponents immediately
after a double to dispel confusion and with 15 maybe a thin 1N overcall is
better.
Pushing
opponents bidding to the edge of their trick taking potential so you can mount
a defence pre-supposes that you have a
defence. One reason for the Kx sparse raise is to have your suit in amongst
the opponent’s cards hopefully as losers. However if partner is a weak extreme
overcall, 2S requires a sparse raise that is robust enough to be an
8-loser in another suit! So 1N (1/2
guard) is standard, 2S is 9pts max with Hx,
2D cue a
robust 2S raise, and still keep the principle
of abandonment. With more, the supporting hand advances after the cue.
The cue skips over the problem of opener doubling a spade raise.
This is a
minimum robust cue,
♠ K 5 (2 losers, must load the count with short trumps)
♥ K J X (2)
♦ J X (2)
♣ K 7 6 5 4 (2)
+ (1 acelessness)
A jump 2NT
is spade game try and may be declined with 3S.
A 3S jump is pre-emptive - not encouraging. If I do not bid the cheapest
cue or jump 2NT, the response is not LTC.
In fourth
position with everyone else having bid partner should assume that your raise is
thin air and a double is robust or better.
Losing Trick Count Rules
|
Not
trumps |
Count |
|
Trumps |
Count |
||
|
Void |
0 |
xxx |
3 |
|||
|
A AK |
0 |
Axx |
2 |
|||
|
Singleton |
1 |
Kxx |
2 |
|||
|
Ax-Kx |
1 |
Qxx |
2 |
|||
|
AQ KQ |
1 |
Ax1
Kx1 Qx1 |
2
|
|||
|
AJT |
1 |
xx1 |
3
|
|||
|
AQx AQJ |
1 |
AK1-AQ1-KQ1 |
1 |
|||
|
Axx Kxx |
2 |
A2
– |
2 |
|||
|
xxx |
3 |
x2 |
3 |
|||
|
Jxx |
3 |
|
|
|||
|
Qxx# |
3 |
|
|
|||
|
(# )Drop Loser if Q
can be balanced i.e. paired with an side suit Axx combo elsewhere Or the
Suit Is Trumps Or is QJx |
-1 |
(1)
(2) Virtual Trump Losers added |
+1 or +2 |
|||
|
Drop
a Loser if you have 4card support for Partner But
then don’t do (# ) |
-1 |
|||||
|
Add Loser if hand Aceless |
+1 |
Axx
Ax Kx Qx Kxx Qxx AK-AQ-KQ Drop
a Loser If Partner known to have 6 (1S-3S) and there is no requirement to
ruff in the Short Hand |
-1 |
|||
|
|
||||||