SUMMARY OF
PROBLEMS
Detailed 76 tables about all smallcard 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 23(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 23(4) in this
defensive problem:

J976 

1. xx
2. xxx
3. Qxx 

AK108 

1. Qxx 2. Qx 3. xx 

Using the indicators ♫ ♪ in Problem 23(4) there are four groups
of systems:

Indicators 



Efficiency 
_{ } 
I_{0} 
I_{1} 
II_{0} 
II_{1} 
II_{2} 
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
M_{0} did not occur at all.
Additional successes of the type ♫ for signal M_{1} occured as follows:
I_{0} 
I_{1} 
II_{0} 
II_{1} 
II_{2} 
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 (S_{S}) has not been taken into account as two
systems differing only in S_{S} have identical indicators.
SUMMARY OF 23(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 23(5) in this
defensive problem:

J109 

1. xx
2. xxx
3. Qxx 

AK107 

1. Qxxx 2. Qxx 3. xxx 


Indicators 


Efficiency 
_{ } 
I_{0} 
I_{1} 
II_{0} 
II_{1} 
II_{2} 
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
M_{0} did not occur at all.
Additional successes of the type ♫ for signal M_{1} occured as follows:
I_{0} 
I_{1} 
II_{0} 
II_{1} 
II_{2} 
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 (S_{S}) has not been taken into account as two
systems differing only in S_{S} have identical indicators.
SUMMARY OF 34(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 34(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 
_{ } 
I_{0} 
I_{1} 
II_{0} 
II_{1} 
II_{2} 
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 34(4) the signal M_{0} only appears a few times, and then is always linked with signal M_{1}, or has no negative effect.
Additional successes of the type ♫ for signal MM_{1} occurred only in the system MM and comprised: 1 in I_{0} and 1 in I_{1}.
After reducing the advantage of M_{1} from 17% to 10.5% (see summary of
problems 23) 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 smallcard 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 

Rev 


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 34(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 34(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 M_{0} and M_{1} is the same as that in Problem 34(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 45(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 23(5) in this
defensive problem:

J987 

1. xxxx 2. xxxxx 3. Qxxx 4. Qxxxx 

AK10 

1. Qx 2. Q 3. xx 4. x 

Signals M_{0} and M_{1} only appear in the system MM; M_{0} having no negative influence while the
advantage of M_{1} relates to two
successes of the type ♫ in columns I_{0} I_{1}. 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 56(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 23(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 M_{0} and M_{1} is the same as that in Problem 45(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 +