SUMMARY OF PROBLEMS

Detailed 76 tables about all small–card systems are not placed here (too much work to do).

You may view these in the scan at  Systems in Defence.pdf.

Here are only summaries.

 

SUMMARY OF 2–3(4)

In this problem there are three basic possibilities:    xx  xxx  Hxx     generating 16 possibilities in all.

The hidden hands contain 4 lowest cards:   5 4 3 2

An illustration of Problem 2–3(4) in this defensive problem:

 

J976

 

  1. xx

  2. xxx

  3. Qxx

 

AK108

 

 1. Qxx

 2. Qx

 3. xx

 

 

Using the indicators ♫ ♪ in Problem 2–3(4) there are four groups of systems:

 

Indicators

 

 

Efficiency

 

I0

I1

II0

II1

II2

    Systems

 

77.57%

15

16

16

16

16

  Combine  QM  MMQ  MML

 

 

11

12

16

16

16

75.35%

15

16

16

16

16

 Jou  Cla 

LLQ  QQL  LLM  QQM   MQ

10

10

13

13

16

74.17%

12

14

15

16

16

  Rev  MUD  BT 

LQ  ML  QL  QLQ   LQL  MLM

10

10

13

13

16

64.17%

13

13

16

16

16

   LM  LML

8

8

12

12

12

The signal  M0 did not occur at all.

Additional successes of the type for signal M1 occured as follows:

I0

I1

II0

II1

II2

  for systems:

2

2

2

2

2

Combine  MM  QM

1

1

2

2

2

LM

This correspond to a 17% advantage over L and Q which, as the author has admitted in the third edition, is somewhat excessive.

After reducing this to the more reasonable value of 40.5% (see “Evaluation of signals”) we get the following efficiences:

 

1)

75.30%

Cla  Jou     MQ  QQ  LL

 

 

2)

74.17%

Rev  MUD  BT      ML  QL  LQ

 

3)

73.75%

Combine  MM QM

 

4)

61.62%

LM

N.B.

In the summaries the third part of the name (SS) has not been taken into account as two systems differing only in SS have identical indicators.

 

SUMMARY OF 2–3(5)

 

In this problem there are three basic possibilities:    xx  xxx  Hxx     generating 30 possibilities in all.

The hidden hands contain 5 lowest cards:   6  5 4 3 2

An illustration of Problem 2–3(5) in this defensive problem:

 

J109

 

  1. xx

  2. xxx

  3. Qxx

 

AK107

 

 1. Qxxx

 2. Qxx

 3. xxx

 

                     

 

Indicators

 

Efficiency

 

I0

I1

II0

II1

II2

    Systems

75.51%

28

28

30

30

30

  Combine  QM  QMQ  MML MMQ

20

20

23

23

23

72.44%

28

28

30

30

30

 Jou  Cla 

QQL QQM LLQ LLM MQ MQM

18

18

24

24

24

71.56%

26

26

30

30

30

  Rev  MUD  BT 

ML MLM QL QLQ LQ LQL

18

18

24

24

24

64.44%

24

24

30

30

30

   LM  LML

15

15

23

23

23

The signal  M0 did not occur at all.

Additional successes of the type for signal M1 occured as follows:

I0

I1

II0

II1

II2

  for systems:

2

2

3

3

3

Combine  MM  QM

1

1

3

3

3

LM

This correspond to a 17% advantage over L and Q which, as the author has admitted in the third edition, is somewhat excessive.

After reducing this to the more reasonable value of 40.5% (see “Evaluation of signals”) we get the following efficiences:

 

1)

72.73%

Combine  MM  QM

 

2)

72.44%

Cla Jou  MQ QQ  QL

 

3)

71.56%

Rev MUD BT  QL LQ ML

 

4)

62.74%

LM

N.B.

In the summaries the third part of the name (SS) has not been taken into account as two systems differing only in SS have identical indicators.

 

SUMMARY OF 3–4(4)

In this problem there are 4 basic possibilities:    xx  xxx  Hxx  Hxxx   generating 15 possibilities in all.

The hidden hands contain 4 lowest cards:   5 4 3 2

An illustration of Problem 3–4(4) in this defensive problem:

 

876

 

  1. xxx

  2. xxxx

  3. Qxx

  4. Qxxx

 

AJ109

 

 1. KQx

 2. KQ

 3. Kxx

 4. Kx

 

 

 

Indicators

 

Efficiency

 

I0

I1

II0

II1

II2

    Systems

84.07%

14

15

15

15

15

  Combine 

10

12

14

15

15

83.48%

14

15

15

15

15

  MMQ  MML

10

12

13

15

15

82.36%

13

15

15

15

15

  QM  QMQ    LM  LML

10

12

13

15

15

79.70%

13

15

15

15

15

  Rev

        MQ  MQM   ML  MLM

10

12

12

12

15

77.19%

15

15

15

15

15

  QQL  QQM   LLQ  LLM

9

11

12

12

15

76.59%

15

15

15

15

15

  Cla

9

11

11

12

15

68.00%

12

12

15

15

15

  BT

          QL  QLQ   LQ  LQL

8

8

12

12

15

66.96%

13

15

15

15

15

  Jou

7

8

11

12

15

66.56%

14

15

14

15

15

  MUDs

8

8

9

9

15

 

In Problem 3–4(4) the signal M0 only appears a few times, and then is always linked with signal M1, or has no negative effect.

Additional successes of the type for signal MM1 occurred only in the system MM and comprised: 1 in  I0  and  1 in I1.

After reducing the advantage of M1 from 17% to 10.5% (see summary of  problems 2–3) the efficiency of system MM is reduced to 82.12%.

The final order is:

 

1)  84.07%  COMBINE

6)  76.59%  CLA

 

2)  82.96%  QM  LM

7)  68.00%  BT  QL  LQ

 

3)  82.12%  MM

8)  66.96%  JOU

 

4)  79.70%  REV  MQ  ML

9)  65.56%  MUD

 

5)  77.19%  QQ  LL

 

 

FOR THOSE WHO HAVE NO CONFIDENCE IN STATISTICS

The efficiency of small–card systems, expressed as a percentage, is based on several parameters (see page 34== and 35==) whose values have been assigned largely intuitively (without exact documentation). However, the order of systems in a given problem can generally be

established without using percentages, but relying solely on the indicators *+ *. .

For example, look at the tables of successes for systems Combine and Rev:

Combine

14

15

15

15

15

10

12

14

15

15

Rev

13

15

15

15

15

10

12

12

12

15

 

Since every indicator for Combine is ≥ the  corresponding indicator for Rev (and there are, in this case, no extra successes for the greater value of signal M1), Combine is better than Rev, irrespective of the value of the parameters.

Similarly it can be shown that:

        Combine > QM = LM > Rev

        QQ > Cla > MUD ...etc.

The order of systems thus established is only marginally different from the order using percentages, was the case in the first edition.

 

SUMMARY OF 3–4(5)

 

In this problem there are 4 basic possibilities:    xx  xxx  Hxx  Hxxxx   generating 35 possibilities in all.

The hidden hands contain 5 lowest cards:   6 5 4 3 2

An illustration of Problem 3–4(5) in this defensive problem:

 

987

 

  1. xxx

  2. xxxx

  3. Qxx

  4. Qxxx

 

AJ10

 

 1. KQxx

 2. KQx

 3. Kxxx

 4. Kxx

 

 

The situation regarding M0 and M1 is the same as that in Problem 3–4(4).

Reducing the advantage of M1 from 17% to 10.5% gives a reduction in the efficiency of MM of 0.58% to 70.47%, the final order being:

1)   73.75%    Combine

2)   71.87%    QQ  LL

3)   70.67%    QM  LM

4)   70.47%    MM

5)   69.65%    Rev  MQ  ML

6)   68.95%    Cla

7)   67.40%    BT  QL  LQ

8)   66.79%    MUD

9)   59.87%    Jou

 

SUMMARY OF 4–5(5)

 

In this problem there are 4 basic possibilities:    xxxx  xxxxx  Hxxx  Hxxxx   generating 21 possibilities in all.

The hidden hands contain the fourth lowest cards:   6  5 4 3 2

An illustration of Problem 2–3(5) in this defensive problem:

 

J987

 

  1. xxxx

  2. xxxxx

  3. Qxxx

  4. Qxxxx

 

AK10

 

 1. Qx

 2. Q

 3. xx

 4. x

 

 

Signals M0 and M1 only appear in the system MM; M0 having no negative influence while the advantage of M1 relates to two successes of the type in columns I0 I1. Reducing this from 17% to 10.5% gives us an efficiency of 88.96% for MM, the final order being:

 

1)

95.13%

COMBINE  ML

6)

85.82%

QM

 

2)

94.76%

BT   QL  LQ

7)

85.40%

QQ LL

 

3)

88.96%

MM

8)

85.03%

MQ

 

4)

88.36%

MUD  LM

9)

84.60%

Rev

 

5)

87.94%

Cla

10)

78.68%

Jou

 

 

SUMMARY OF 5–6(6)

In this problem there are 4 basic possibilities:    xxxxx  xxxxxx  Hxxxx  Hxxxxx   generating 28 possibilities in all.

The hidden hands contain 6 lowest cards:   7 6 5 4 3 2

An illustration of Problem 2–3(5) in this defensive problem:

 

Q108

 

  1. xxxxx

  2. xxxxxx

  3. Kxxxx

  4. Kxxxxx

 

AJ9

 

 1. Kx

 2. K

 3. xx

 4. x

 

The situation regarding M0 and M1 is the same as that in Problem 4–5(5), except it applies to BT as well as MM.

Both their percentages are reduced by 1.46%, which makes the final order:

        1)  97.78%    Combine  MQ  ML

        2)  90.92%    BT

        3)  90.48%    QL  LQ

        4)  89.81%    MM

        5)  89.37%    QM  LM

        6)  87.46%    Jou  QQ  LL

        7)  83.17%    Cla

        8)  81.83%    MUD

        9)  80.00%    Rev

N.B. Combine is slightly better than ML and MQ as there are more +

 

 

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