SUMMARY
As a result of the analysis so far, we have a rough idea of the relative
merits of various systems. If a system is at the top of the order in a problem, it is certainly a good one (eg
Combine, MM); if it is near the bottom it is not so good (eg MUD, Jou). But to
compare systems effectively we must calculate the average value of the
efficiency of each system.
Frequency of problems
Assuming that the 6 problems analysed comprise 100% of all occurrences,
their frequency is as follows:
|
2–3 (4) |
= |
19.35% |
38.03% |
3–4 (4) |
= |
19.65% |
43.88% |
|
|
2–3 (5) |
= |
18.68% |
3–4 (5) |
= |
24.23% |
|||
|
4–5 (5) |
= |
13.98% |
|
5–6 (6) |
= |
4.11% |
|
Final efficiency of systems
Using the above frequencies as weightings, we calculate the final
efficiencies of systems as follows:
1) 79.56%
COMBINE
2) 77.75%
ML (Mixed–Length)
3) 77.20%
MM (Mixed)
4) 76.94%
QM (Quality–Mixed)
5) 76.56%
MQ (Mixed–Quality)
6) 76.23%
QQ (Quality) LL
(Length)
7) 75.58%
Cla (Classical)
8) 75.37%
Rev (Reverse)
9) 74.40%
BT (Blue Team)
10) 74.38%
QL (Quality–Length) LQ
(Length–Quality)
11) 73.09%
LM (Length–Mixed)
12) 72.50%
MUD
13) 70.37%
Jou (Journalist)
So we can see that Combine is significantly better than the rest, and
other new systems figure in the leading places (except LM QL LQ). It should be
added that, apart from defining source S, systems QQ, LL and QL are not totally
new, as:
QQ is based on giving quality signals
LL is based on giving length signals
QL is in principle the same as BT
When it comes to traditional and well–known systems it is surprising not
so much that they occupy the bottom half of the table, but that the newer the
discovery, the lower the efficiency !! The oldest one (Classical) is the best,
and the newest (Journalist) is the worst. Also, the first classical system was
probably QQ, which means that introducing fourth–highest leads was not an
improvement, but a step backwards !
The theory of small–card systems presented here enables us to avoid this
kind of apparent improvement; every new discovery should be subjected to
statistical analysis. As an example, let us analyse the idea of using classical
leads from honours and reverse leads from small cards, or:
|
|
|
|
This idea arose through a misunderstanding. In 1975 the author tried playing
the small–card system QM, which can be described as follows:
from small cards: QL*
from honours: QL
This was often explained somewhat inaccurately to opponents, ie:
from an honour: normal (length)
from small cards: reverse (length)
which was inaccurate as it only explained So,omitting SF.
Having explained the origin of the system "normal–reverse",
let us now calculate its efficiency. It is equivalent to:
in problem 2–3: LM
in problem 3–4: atypical
in problem 4–5: Reversed
in problem 5–6: Reversed
So we have to construct a table for problem 3–4; this will give us
efficiencies of 66.96%; 61.84%. Using this and the figures obtained from the
tables in preceding chapters we get an overall efficiency of 67.71% – the worst
system of all ! It is doubtful whether we would have noticed this without the
help of statistical analysis, even after years of playing it.
The genesis of Combine
In 1974 I began work on the theory of systems, which ended successfully
with the discovery of the Mixed Signal, the formulation of a general theory and
the classification of small–card systems. From January 1975 onwards I started
testing the system QM (which I felt was the best of
the classifiable ones) in practice, simultaneously commencing a
statistical analysis, the aim of which was to discover the optimum system. This
analysis covered many different systems, not all of which have been mentioned
in this book. On completion of the analysis in June 1975, I called the best of
the systems Combination Leads, which I changed to Combine Leads in 1978.
Combine, then, is the result of research, so its first place is not
surprising. It is worth noting that
Combine would still take first place (followed by ML and MQ) even if the signal M1 is given the
value of 50%.
END OF PART TWO
PART THREE |
The COMBINE |
|
HONOUR COMBINE
Leads from sequences
from a two–card sequence – the highest from a broken sequence – the
middle from an interior sequence – the lowest
from a full sequence – the middle
or the highest |
|
HH HHh Hhh HHH |
From a full sequence the lead is:
|
the middle honour – when you want to emphasize possession of the
lowest honour. the highest honour – when the lowest honour is deemed unimportant. |
A similar possibility exists when leading from a broken sequence:
|
From a broken sequence the highest honour can be led if there is no need to signal possession of the lowest honour |
From a broken sequence the highest honour can be led if there is no need to signal possession of
the lowest honour.
Leads from a doubleton sequence:
|
From a doubleton sequence (AK, KQ, QJ, J10, 109) against a suit contract the
lower honour is led. |
This suggests the possession of a third
honour, so partner will tend to return the suit, thus increasing the chances of
obtaining a ruff.
Leads from a doubleton honour
From the doubletons Ax Kx Qx Jx 10x 9x the honour is led, but against
suit contracts the small card is led from 10x and 9x.
The reason for this is explained in the next chapter.
The scheme of playing small cards is this:
|
from small cards |
|
|
when
the highest small card could
be working |
|
from honours |
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
|
|
|
|
|
|
The plays in the third column would be used with these holdings: 10 7 3,
9 6 4 2, 10 8 7 6 3 etc.
It should be borne in mind, however, that it is not only the rank of a
small card which decides whether or not it is working, but also the expected
distribution of the suit (based on the course of he auction). Also, as
mentioned on earlier, the terms "honour" and "small card"
should be used flexibly. For example: from a suit such as Jxxxx or Qxxxxx,
against a suit contract, it may be right to lead as though the suit was xxxxx
or xxxxxx. On the other hand, against no–trumps even the nine in a suit of
9xxxx may be treated as an honour.
THE MEANING OF LEADS
Let us now analyse the meaning of Combine leads from the point of view
of the leader's partner.
Honour leads (AKQJ)
These show either a singleton or doubleton honour or these sequences:
|
|
|
(1) |
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
|
A |
= |
AK |
|
|
|
|
AKQ |
AKJ |
|
K |
= |
KQ |
AK |
AKJ |
|
AKQ |
KQJ |
KQ10 |
|
Q |
= |
QJ |
KQ |
KQ10 |
|
KQJ |
QJ10 |
QJ9 |
|
J |
= |
J10 |
QJ |
QJ9 |
AQJ |
QJ10 |
|
|
The above possibilities are arranged in columns, starting with the most
probable:
1) From a two–card sequence
2) From a doubleton sequence against a
suit contract
3) From a broken sequence
4) From an interior sequence
5)
6) From a full sequence
7) From a broken sequence (occasionally)
Leads of the 10 and 9
The 10 and 9 can be treated in two ways: either as honours or as small
cards, depending on the situation. Their meanings, then, consist of
possibilities from both Combine – Honour and Small–card:
|
|
|
From
at least three
small cards |
From
an interior sequence |
From a
doubleton in
no–trumps |
|
|
10 |
= |
10xx... |
AJ10 KJ10 |
10x |
|
|
9 |
= |
9... |
A109 K109 Q109 |
9x |
|
Leads of small cards
Remember that the 10 and 9 are also treated as small cards, albeit high
ones.
|
First small card (F), or the first card played |
|
||
|
low (L) |
= |
aggressive lead (xx or Hxx....) |
|
|
high (H) |
= |
passive lead (xxx....) |
So the first small card is, as you can see, something in the nature of
encouragement/discouragement in the suit led.
Second small card (S) has different meanings depending on the type of
lead.
|
Second small card after a passive lead (xxx...) |
|
||
|
low (L) |
= |
aggressive lead (xx or Hxx....) |
|
|
high (H) |
= |
passive lead (xxx....) |
|
Is always lower than the first one (order D) |
|
|
|
|||
|
Its rank transmits a reverse length signal (L*): |
|
|
||||
|
high(H) |
= |
odd number of cards |
||||
|
low (L) |
= |
even number of cards |
||||
Combine using normal length signals would be equally effective here.
|
Second small card after an aggressive lead |
|
|
|||
|
Is always the lowest! The only source of further information
is comparison of the rank of the two cards (order). This order transmits a
mixed signal (M): |
|
|
|||
|
upwords (A) |
= |
even number of small cards |
|||
|
downwards (D) |
= |
odd number of small cards |
|||
SIGNALS
It would be desirable for signals when following suit to be identical to
leads, even if only to lessen the amount of memory work. As yet, however, this
possibility has not been examined thoroughly enough by the author. Perhaps
readers could experiment with it? In the meantime it is recommended to use the
following signals when playing Combine:
Mixed Signal (preferred)
Quality Signal Reverse Smith Peters
Reverse Length Signal Lavinthal
Use of signals
This is only defined in certain circumstances. In the remaining
situations a common–sense rule applies:
Give that signal which,
in your opinion, partner needs.
Mixed Signal
Preferred and so most often used:
A or L
= even number of small cards
D or H
= odd number of small cards
If the quality of the suit is known, then the Mixed Signal becomes a
length signal:
normal for a suit of good quality
reverse for a suit of bad quality
If the length of the suit is known, then the Mixed Signal becomes a
quality signal:
normal for an odd number of cards
reverse for even number of cards
The advantage of the Mixed Signal over length and quality signals has
been already demonstrated.
Quality Signal
This is only used when it is clear that partner needs information about
quality:
A or L
= good quality (encouragement)
D or H
= bad quality (discouragement)
N.B.
This method is popularly known as "reverse", but, as the
author has already shown, it is really "normal".
Reverse Length Signal
This is used only when it is clear that partner needs information about
length:
A or L
= even number of cards
D or H
= odd number of cards
N.B.
Reverse length signals are mistakenly thought of by many players as the
same as the Reverse System, because of the similarity of their names. In fact,
a reverse length signal (just like any other signal) should be given clearly as
possible, ie beginning with the extreme (lowest or highest) small card:
Reverse Smith Peters
In the situation in the first suit led by the defence is not yet clear,
then in the first suit declarer plays, the opening leader plays:
A or L
= encouragement (continue)
D or H
= discouragement (switch)
Lavinthal
This is used whenever:
1) It is clearly necessary
2) No other signal makes sense
END OF PART THREE
AFTERWORD
In spite of the mass of theory it
contains, this book has no means covered all the new possibilities in the field
of defence. For example, you could give
information as to both sequences and number of cards simultaneously. Although the author has not
fully developed this idea, one simple
sequential-length system called
“SEQUEL" is:
Leads from
sequences depend on the number of cards in the suit:
odd : H H H H h H h h (Combine)
even: H H H H h H h h (anti–Combine !)
If you enjoy experimenting, try it.
|