Kaleidoscope Series Lesson #4
The Law Of Total Tricks
-----------------------
The Law Of Total Tricks ("LOTT") is a very
simple theory. It postulates that in a competitive
or pre-emptive auction the total number of tricks
available on any given hand is equal to the total
number of TRUMPS that the two pairs have in their
respective longest suits.
Hand A | Hand B
|
S- AQxx | S- AQxx
H- xxx | H- xxx
D- KJx | D- KJx
C- Axx | C- Axx
S- xxx S- Kx | S- Kxx S- xx
H- AJ109 H- KQxx | H- AJ109 H- KQxx
D- xxx D- Axxx | D- xxx D- Axxx
C- Qxx C- J10x | C- Qxx C- J10x
S- J109x | S- J109x
H- xx | H- xx
D- Qxx | D- Qxx
C- Kxxx | C- Kxxx
In the above example, both sides have an eight
card fit. This means that there should be (8 + 8)
sixteen tricks to be had in total. In the case of
Hand A, N-S can make 2S while E-W can make eight
tricks in Hearts. By switching the S-King to the
"onside" position N-S can make 3S while E-W can
only make seven tricks in Hearts. The total number
of tricks remains the same; only the distribution
of those sixteen tricks changes.
----- The Arithmetics of LOTT -----
Before we can appreciate LOTT, we need to
consider how it works in regards to the scoring
methods. We will look at it from the point of
view of a pair considering a sacrifice in 4S
over the opponents' 4H.
Consider this scale, where "F" means Favourable
vulnerability (them vul, us not), "B" means Both
are vul, "N" means Neither vul and "U" means
Unfavourable vulnerability (us vul, them not):
Trick | Tricks for | Scores for | 4S IMP
Total | Them Us | 4H 4S | Result
| | |
16 | 10 6 | F: +620 vs -800 | -6
16 | 10 6 | B: +620 vs -1100 | -10
16 | 10 6 | N: +420 vs -800 | -9
16 | 10 6 | U: +420 vs -1100 | -12
| | |
16 | 9 7 | F: -100 vs -500 | -12
| | |
17 | 10 7 | F: +620 vs -500 | +3
17 | 10 7 | B: +620 vs -800 | -5
17 | 10 7 | N: +420 vs -500 | -2
17 | 10 7 | U: +420 vs -800 | -9
| | |
17 | 9 8 | F: -100 vs -300 | -9
| | |
18 | 10 8 | F: +620 vs -300 | +8
18 | 10 8 | B: +620 vs -500 | +3
18 | 10 8 | N: +420 vs -300 | +3
18 | 10 8 | F: +420 vs -500 | -2
| | |
18 | 9 9 | F: -100 vs -100 | -5
| | |
19 | 10 9 | F: +620 vs -100 | +11
19 | 10 9 | B: +620 vs -200 | +9
19 | 10 9 | N: +420 vs -100 | +8
19 | 10 9 | U: +420 vs -200 | +6
| | |
19 | 9 10 | F: -100 vs +420 | +8
19 | 9 10 | B: -100 vs +620 | +11
19 | 9 10 | N: -50 vs +420 | +9
19 | 9 10 | U: -50 vs +620 | +11
The bottom line is that with 16 total trumps
sacrificing is NEVER profitable. It is only
marginally profitable with 17 total trumps when
we are not vulnerable versus vulnerable opponents.
At 18 trumps, the scales tip in favour of the 4S
sacrificers, who will lose only at unfavourable
vulnerability. With 19 or more trumps, sacrificing
is automatic. With 20 trumps, BOTH sides may be
able to make game!
Our biggest problem is that we don't always
know how many trumps the opponents have. Hence, we
often go by a more "simplified" (some would say
"oversimplified") Law Of Total Tricks: bid to
your level of trumps. We compete or pre-empt one
trick for each trump that we have. Hence, with NINE
Hearts between Partner and ourselves we might
compete/pre-empt as far as 3H...but no further.
----- Questions -----
1. I want to know how many tricks WE can take. Why
should I care about how many BOTH sides can take?
2. As Advancer, I hold: S-Axx H-Jxxx D-xxxx C- Kx.
Playing SAYC, after 1D-2D-Pass, knowing that Partner's
2D is Michaels showing both majors, should I bid 3H?
3. I'm an impatient type. I want the bottom line NOW!
Does this "trumps = tricks" formula really WORK?
4. Is there some way to TEST this theory before
investing a few thousand IMPs or MPs in TRYING it?
----- LOTT versus "Got More? Bid More!" ------
There are two schools of thought regarding
the basis for making bidding decisions. The
traditional method is to use what is euphemistically
called "bridge judgement", following a "got more,
bid more" approach. The number of trumps that the
pair holds plays a significant but not central role
for traditionalists. Factored equally into their
calculations are texture, overall shape, position,
cover cards, trump suit symmetry, non-trump suit
asymmetry, High Card Points, and, yes, the number
of trumps that the pair has.
LOTT, on the other hand, uses the total number
of trumps that BOTH sides have as the principle
guideline. Other considerations are "adjustments"
(to use the LOTT terminology) to the total number
of tricks we expect.
Hand C
S- AK10xxx
H- xxx
D- x
C- xxx
S- Q S- xxx
H- xxx H- Q
D- KJxxx D- AQxx
C- AQxx C- KJxxx
S- Jxx
H- AKJ109x
D- xxx
C- x
Here E-W outgun N-S 24-16 in HCPs. The
total number of trumps is (9 + 9) 18.
Still, both sides can make ELEVEN tricks!
That means that LOTT is "wrong" by (22 - 18)
FOUR tricks in an auction which is bound to
be hotly contested. Again, LOTTers would
say that the Total Number Of Tricks has to
be "adjusted" upwards because of the double
fits for both sides. Skeptics would say that
FOUR tricks is a HUGE "adjustment".
----- A LOTT of Adjustments -----
While traditionalists consider Mike Lawrence's
"Hand Evaluation" the definitive work on bridge
bidding judgement, LOTTers regard "Following the Law",
"Points Schmoints" and "To Bid or Not to Bid" as
sacred texts. If we read any of the literature on
LOTT we will see that the total number of tricks
available "occasionally" has to to be "adjusted"
upwards or downwards based on certain criteria.
These criteria are essentially the same ones
developed by traditionalist: texture, overall shape,
position, cover cards, trump suit symmetry, non-trump
suit asymmetry. Only High Card Points ("HCPs") are
removed from the equation. In a PRE-EMPTIVE situation
HCPs are considered irrelevant because, by definition,
we are conceding that THEY hold the majority of strength
and we are NOT bidding to make. We are simply trying to
obstruct. In a COMPETITIVE situation HCPs are
disregarded by LOTTers since they are presumed to break
about 20-20 between the two pairs.
In Hand C we saw a case where the existence of
a double fit increases the total number of tricks
that the sides can make. Double fits, then, would
require an "upward adjustment". In the coming
sections we will examine the effects of the other
critieria on the total number of tricks available.
----- Questions -----
1. If both schools use essentially the same
criterion in their competitive decisions, what
is the DIFFERENCE between them?
2. LOTTers rely on the number of trumps that
BOTH sides have. But how do they calculate
this without knowing for sure how many the
OPPONENTS have?
3. LOTT relies on knowing how many trumps PARTNER
holds. Does this mean that LOTTers, with a
SIX card suit, are more inclined than non-LOTTers
to jump overcall with decent hands? Would they
bid TWO Hearts over RHO's 1D opening with:
S- xxx H- AKJ10xx D- x C- Qxx ?
----- Texture and Mesh -----
The term "suit texture" refers to whether our
long suits are supported by high cards--including
good spot cards. "Hand texture" describes whether
or not our High Card Points are in "controls" (Aces
and Kings) or "secondary honours" (Queens and Jacks).
Aces and Kings are considered "hard" values while
Queens and Jacks are regarded as "soft" values.
This assignation changes, though, once the bidding
reveals how useful these values are likely to be.
Only after we have heard a few bids can we
make an estimate of how our High Cards will "mesh"
with Partner's hand. According to Mike Lawrence's
"In and Out" theory, Queens and Jacks in our long
suits are "gold". Queens and Jacks in the OTHER
suits are liable to be useless if we end up
declaring the hand--especially in a suit contract.
Mike ("O_Bones" on OKBridge) Dorn Wiss refers to
such secondary honours outside our long suits as
"QUACKS" ("QUeens and jACKS"), reminding us of
their doubtful value to us declaring in any suit
contract. Our S-QJx opposite Partner's S-xx will
not help prevent them from cashing tricks in that
suit, as the S-Kx or the S-Ace might. Similarly,
a King may be wasted opposite Partner's singleton.
Even an ACE may be wasted if opposite Partner's
void, but at LEAST it will give us one pitch.
While S-QJx opposite our S-xx might not help
OUR chances of making, say, 4H, it may well prevent
THEM from making 4S. Such secondary honours reduce
the number of TOTAL tricks by reducing the opponents'
expectations without enhancing ours. LOTTers call
this a "downward adjustment". Non-LOTTers call these
QUACKS "defensive values".
Hand D: S- Axxx H- QJxx D- x C-Axxx
The above hand is FAR stronger in support of
Hearts than either black suit. Indeed, were Partner
to overcall their 1D with 1H we would force to game.
After 1H-1S-Pass, though, the dubious value of the
Heart QUACKS reduces this to an invitational hand.
After 1S-2H-2S Advancer's S-Ace is considered a
"pure" value opposite Overcaller's likely singleton.
Similarly, S-xxxx would be a good holding for offence
in that it would indicate that none of our overall
values are liable to be wasted if we play in Hearts.
S-Kxxx, though, would be of questionable merit on
offence after 1S-2H-2S.
For decades there existed the myth that Aces
and Kings were better for suit contracts, while
Queens and Jacks were better for No Trump contracts.
This is ONLY true if BOTH hands are flat. If we
are bidding No Trump based on a long (likely
minor) suit we will need ACES--not Kings, Queens
OR Jacks--in the other suits. In general, then,
Aces and Kings are best for DECLARING, Queens and
Jacks better for DEFENDING.
----- Overall Distribution -----
Flat hands require a downward adjustment, while
double fits--which may include POSSIBLE double fits--will
require an upward adjustment in the total number of
tricks. In non-LOTTer parlance, we don't over-compete
with flat hands.
Hand E: S- Q10xxx H- QJx D- xx C- Qxx
Over 1S-Dble, at equal or favourable vulnerability
most would simply leap to 4S. Ten trumps, ten tricks,
4S. However, the flat distribution is considered a
downward adjustment; we should consider 3S as the
limit of our hand's competitive potential.
Hand F: S- J10xx H- x D- KQxxx C- xxx
Here, after 1S-Dble the possibility of a double fit
in the pointed suits (Diamonds and Spades) would require
an UPWARD adjustment. LOTTers might wish to check for
Diamond support from Opener and, if it is present, go to
4S on this hand. The methods used to check for such a
double fit may vary from partnership to partnership.
Hand G: S- J10xx H- x D- A10xxxx C- xx
Here, even a shortness in Diamonds in Opener's
hand may allow us to set the suit up with ruffs. Bid
4S here. LOTTers might consider the 6th Diamond an
upward adjustment.
When competing or when considering a sacrifice
we should consider a doubleton in the opponents' suit
a "death holding". Even "xxx" is less obscene than
"xx", since it raises the possibility of Partner
having shortness in their suit. Holding "xxx", if
the opponents are competing vigourously we should
assume that they have 9 trumps; this marks Partner
with a singleton--ONE loser in that suit for us.
Holding "xx" in our hand, though, the opponents
will have to have a TEN card fit before Partner
can have a singleton and hold our losers to one.
Hence, tend to DEFEND with a doubleton in their suit.
If they have just sacrificed, double.
----- Position -----
Having STRENGTH in RHO's suits is good, since
the chances of these cards taking tricks increases
as long as we apply the "play small towards big"
rule from Rainbow Lesson #12. Having LENGTH in
RHO's suits is also good, since Partner can over-ruff
LHO (who, along with partner, is likely short in
this suit). Length or strength in LHO's suit should
be devaluated.
Position of our lengths behind RHO (which is
GOOD for us) or in front of LHO (which is BAD for
us) does not affect the total number of tricks,
generally. It simply shifts them from one pair
to the other.
--- Cover Cards and the 4-Point Principle ---
Any card which will cover one of partner's
losers is a "cover card". An Ace opposite a void
MAY or MAY NOT cover one of partner's losers
(depending on whether partner can cash this Ace
before the opponents cash their winners). A King
opposite a singleton is NOT a cover card.
Consistent with the "In and Out" theory above,
secondary honours in partner's long suit should
be viewed as cover cards.
It is a rule of thumb in bidding that we
will take Partner for ONE such cover card for every
FOUR HCPs that partner has shown in the auction.
This is called the "4-Point Principle". For
example, if Partner opens 1NT, we would play hir
for (16 / 4 = ) FOUR such cover cards, since 16 HCPs
is an average 1NT opening (15-17). Similarly, after
1H:2H, Opener might guess that Responder will hold
about (8 / 4 = ) TWO "cover cards", since 8 points
is about average for such a raise. Note: this
4-Point Principle is useful in CONSTRUCTIVE auctions
as well as competitive ones. Because it is part
of the "got more, bid more" approach and does not
affect the total number of tricks, it is NOT
generally known or practiced by LOTTers. It DOES
help us determine how many tricks WE can take,
though.
----- Trump Suit Symmetry -----
Consider this common theme:
Hand H
Opener: S- AKQxx H- KJxx D- Ax C- xx
Responder: S- J10xx H- AQxx D- xxx C- Ax
This pair can make 6H on a 3-2 trump break by
pitching a Club loser from Responder's hand on the
fifth Spade. 5S is the limit if SPADES are trump,
since we will NOT have any pitches. Hence, at
higher levels especially, the balanced (4-4 here)
fit is superior over the unbalanced (5-3 here) one.
This explains the popularity of jumping to
game in Partner's 5-card major with 5 of them
ourselves. Even if either of us *does have* a
second suit, it will rarely be any more balanced
than our major suit fit.
In competition, then, it may be worthwhile
to investigate the chances of a second, balanced
fit via negative or Snapdragon doubles, rather
than jumping on the first fit that comes along.
If the auction started with 1S-2C or 1S-2D on
the above hand, then, a negative double might
work out far better than any quick raise or cuebid.
LOTTers will note that choosing Hearts
instead of Spades on the above hand will REDUCE
the number of actual trumps, but INCREASE the number
of TOTAL tricks by boosting OUR potential to 12.
LOTT uses the longest suit, though (9 Spades in
this case), even if that suit is NOT chosen as
trumps.
----- Plain Suit Symmetry -----
The more asymmetrical our plain (i.e. non-trump)
suits are, the more tricks we can take. On Hand "H"
in the above section slam in Hearts made because we
choose Spades to be the NON-trump suit, where its
asymmetry (5-4 rather than 4-4) permitted a pitch
that would be unavailable in 6S. This same theme
popped up in Hand C, repeated here for convenience:
Hand C (repeated) | Hand C (revised)
|
S- AK10xxx | S- AK10xxx
H- xxx | H- xxx
D- x | D- xx
C- xxx | C- xx
S- Q S- xxx | S- Q S- xxx
H- xxx H- Q | H- xxx H- Q
D- KJxxx D- AQxx | D- KJxxx D- AQxx
C- AQxx C- KJxxx | C- AQxx C- KJxxx
S- Jxx | S- Jxx
H- AKJ109x | H- AKJ109x
D- xxx | D- xx
C- x | C- xx
If N-S were vulnerable versus non-vulnerable
opponents we would have to infer that our 3-1 minor
suit distribution might allow 5H or 5S to make, given
the opponents' vigorous bidding the minors. The one
bidding 5H or 5S would have to conclude that their
partner is SHORT in their THREE card minor. In the
revised case on the right, though, with FOUR "death
holdings" (i.e. doubletons) in the minor suits between
them, N-S would have to AVOID bidding 5H or 5S.
This is more than simply competing more with
unbalanced hands--a theme that both groups embrace.
After all, both the 2-2 and 3-1 minor suit distributions
would make the hands unbalanced, and would amount to
the same number of Short Suit Points (i.e. two) in
both the North and South hands. It is a matter of
recognizing that Partner is likely short in our 3-card
minor suit and that doubletons are grim holdings.
----- Pre-Empting with LOTT -----
Many non-LOTTers would be surprised to learn that
the tendency to pre-empt at the TWO level with a SIX
card suit, at the THREE level with SEVEN, is an
application of LOTT. Consider this: you have SIX
Spades. There are SEVEN outstanding. Divide them
equally and Partner rates to have 2 1/3 Spades--closer
to two than three. This means that, on average, we
have EIGHT trumps in that suit. Hence, we open 2S
as a weak 2-bid with the appropriate overall strength.
With SEVEN cards in, say, Hearts, we should expect
the outstanding six Hearts to divide 2-2-2 on average.
Hence, we should expect NINE Hearts in total (7 + 2),
and will therefore bid with 3H.
In responding to such a pre-empt, we will often
raise briskly to the appropriate level. For example,
opposite Partner's non-vulnerable 2S opening we might
bid 3S with ANY hand of 0-17 HCPs that has THREE
Spades! With FOUR Spades we would venture to 4S if
our point total is 0-14; only with 15-17 will we
balk at the notion of taking a likely minus against
a game which is not a favourite to make.
Among the many modifications to modern bidding
structures that have been inspired by LOTT is the
Bergen raise. 1H:3H and 1S:3S become pre-emptive
while responses of 3C or 3D show 4-card support
for 1H or 1S Opener's major. The cost of this
approach is that the declaration of a NINE card
fit so early in the auction assures the opponents
of a similar fit of their own. This hand featured
may of the themes discussed here, along with an
inspired Defensive SnapDragon Double by Advancer:
Hand I | IMPs, Both Vul. Dlr: N
|
S- AQ10xx | South West North East
H- xx | 1S Pass
D- Jxx | 3D* Dble 3S Dble*
West C- AQJ East | Pass 4H Pass Pass
S- xxx S- x | Pass
H- J10xx H- AKxx |
D- AK10xx D- Qxx | 3D* was a constructive
C- x C- 10xxxx | raise, 8-10, 4 Spades.
S- KJxx | Double of 3S was "Defensive
H- Qxx | Snapdragon", showing 4+ Hearts
D- xx | Diamond tolerance and defensive
C- Kxxx | values (see Lesson #3).
The knowledge that N-S had NINE Spades allowed West
to double 3D here (or bid 3D if South had bid 3C instead)
with virtual impunity. When the opponents have a NINE
card fit we are GUARANTEED an EIGHT card fit and will
USUALLY have EITHER a 9-carder ourselves or two 8-carders.
This result was a rare +620 for E-W in 4H while many N-S
pairs were able to buy this one in TWO Spades. LOTTers,
then, must always ask themselves if the knowledge that
Partner has FOUR trumps (rather than 3+ trumps) is more
valuable to US than to THEM.
----- Discussing LOTT with Partner -----
It is a good idea for any pickup partnership to
discern how closely wedded to LOTT they and their
opponents are. Many pairs mention LOTT in their
stats (e.g. "Out, Law" versus "Law Abider") and/or
on their convention cards. Since this is a matter
of STYLE, it *is* possible for a LOTTer and non-LOTTer
to play TOGETHER as long as both they and their
opponents are aware of who does what in this critical
regard.
----- In Closing -----
Few controversies make this game more
interesting than LOTT. One might make the mistake
of presuming that LOTTers prefer to play against
others of their ilk so that they can accurately assess
the total number of trumps/tricks during competitive
auctions. Not true! Ask any LOTTer and they will
tell you that they prefer playing against critics
of the theory. As for the skeptics, they will
respond with one voice: "Sit yourselves down,
LOTTers, and DEAL THEM PASTEBOARDS!" :)
The beauty of the Law Of Total Tricks cannot
be found in the prose describing it. Rather, it
lies in the theory's inherit simplicity. As the
Romans would say: "Simplex signum veritae."
No theory in ANY game has ever caused such
a revolution in popular thinking. Even the greatest
of its critics may find themselves COUNTING THEIR
TRUMPS in close competitive auctions. :)
---- Final Quiz -----
1a. Holding: S- Kxxx H- xxx D- x C- Kxxxx what would
you rebid as Responder after 1S-P-2S-3D-P-P ?
1b. Holding: S- Kxx H- xx D- Kxxx C- xxxx what would
you rebid as Responder after 1S-P-2S-3D-P-P ?
1c. Holding: S- Kxx H- Axx D- Q10x C- xxxx what would
you rebid as Responder after 1S-P-2S-3D-P-P ?
1d. Holding: S- Kxx H- K109xxx D- x C- xxx what
would you rebid as Responder after 1S-P-2S-3D-P-P ?
2a. S-KQxx H-xx D-Qxx C-xxxx None vul, IMPs. Partner
opens 1S and the auction proceeds: 1S-2H-2S-3H-P-P
back to Responder. What is a LOTTer liable to do here?
2b. S-KQxx H-xx D-Qxx C-xxxx None vul, IMPs. Partner
opens 1S and the auction proceeds: 1S-2H-2S-3H-P-P
back to Responder. What will anyone who has read
KaleidoScope Lesson #2 (Maxi-Flex) do here?
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The KaleidoScope Series, at 8:00 A.M. and either 3:00 P.M. (Monday and Wednesday) or 7:00 P.M. (Tuesday and Thursday) PST from Monday to Thursday, is a lecture program on a variety of subjects: Bidding Light, Maximum Flexibility, Defensive Doubles, LOTT versus "Got More, Bid More" and Squeezes. Unlike the FireSide and 5th Chair sessions mentioned above, the Kaleidoscope Series is a semi-private lesson program for our students. Nevertheless, you are invited to stop by and participate. The KaleidoScope Series, directed more at that intermediate player than the Rainbow and Spectrum, has quickly become one of our most popular. For $60 for five invaluable lessons ($100 for two series, $150 for all three series) this may be the best bridge instruction available anywhere!  CLICK HERE to email your registration. In the meantime, why not click on the lessons below and start learning now ? |
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