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:

x

x

 

 

 

 

x

x

x

 

 

 

x

x

x

x

 

 

x

x

x

x

x

 

x

x

x

x

x

x

 

 

 

 

 

 

 

H

x

x

 

 

 

H

x

x

x

 

 

H

x

x

x

x

 

H

x

x

x

x

x

 

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

 

 

 

combine

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

 

x

x

 

 

 

 

x

x

x

 

 

 

x

x

x

x

 

 

x

x

x

x

x

 

x

x

x

x

x

x

 

 

 

 

 

 

 

 

x

x

x

 

 

 

x

x

x

x

 

 

x

x

x

x

x

 

x

x

x

x

x

x

 

 

 

 

 

 

 

H

x

x

 

 

 

H

x

x

x

 

 

H

x

x

x

x

 

H

x

x

x

x

x

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.

 

 

Content

Writings