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file Optimal seatings : the return of the mutant

03 Dec 2018 09:09 - 04 Dec 2018 10:21 #92212 by Ankha
Replied by Ankha on topic Optimal seatings : the return of the mutant
And a new best optimal seating for 23 players :

R2: 19 20 15 6 2 | 8 23 1 16 11 | 10 3 13 21 18 | 5 17 7 12 | 4 9 22 14
R3: 18 2 22 11 7 | 21 9 12 1 19 | 23 13 4 17 6 | 15 5 16 10 | 14 3 8 20
N23
1. No pair of players repeat their predator-prey relationship. This is mandatory, by the VEKN rules.OK
2. No pair of players share a table through all two rounds, when possible. (N/A in some 2R event.)OK: 126 (once)
3. Available VPs are equitably distributed.KO. Absolute deviation is: 0,24952741020794 => 5, 14, 16, 17, 20, 22 have 13 VP | 3, 4, 7, 8, 9, 10, 12, 15, 18, 19, 21, 23 have 14 VP | 1, 2, 6, 11, 13 have 15 VP
5. A player doesn't sit in the fifth seat more than once.OK
6. No pair of players repeat the same relative position[*], when possible.OK
7. A player doesn't play in the same seat position, if possible.KO (player 2, table 1, position 2)
8. Starting transfers are equitably distributed. [NOAL]KO. Absolute deviation is: 0,635160680529301 => 3, 5, 8, 20, 21, 23 have 7 transfers | 1, 2, 4, 9, 13, 15, 16, 17, 18 have 8 transfers | 6, 7, 10, 11, 12, 14, 19, 22 have 9 transfers
Extra1. Inversions in the prey/predator relationshipOK

compared to the current one:
N23
1. No pair of players repeat their predator-prey relationship. This is mandatory, by the VEKN rules.OK
2. No pair of players share a table through all two rounds, when possible. (N/A in some 2R event.)KO (player 7 shares a table with player 8 on round 2): 96 (once), 15 (twice)
3. Available VPs are equitably distributed.KO. Absolute deviation is: 0,0982986767485822 => 8 have 13 VP | 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 have 14 VP
5. A player doesn't sit in the fifth seat more than once.OK
6. No pair of players repeat the same relative position[*], when possible.OK
7. A player doesn't play in the same seat position, if possible.KO (player 3, table 1, position 3)
8. Starting transfers are equitably distributed. [NOAL]KO. Absolute deviation is: 0,801512287334594 => 3, 5, 9, 11, 16, 19, 20, 23 have 7 transfers | 1, 4, 6, 10, 18, 22 have 8 transfers | 2, 8, 12, 13, 14, 15, 17, 21 have 9 transfers | 7 have 10 transfers
Extra1. Inversions in the prey/predator relationshipKO. Count: 3 => 17-23, 7-15, 9-10
Prince of Paris, France
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Last edit: 04 Dec 2018 10:21 by Ankha.

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04 Dec 2018 10:17 - 05 Dec 2018 13:50 #92237 by Ankha
Replied by Ankha on topic Optimal seatings : the return of the mutant
New best optimal seating for 27 players:
R2: 20 25 6 17 1 | 19 9 11 3 26 | 4 12 18 21 7 | 23 2 13 27 | 14 22 8 24 | 5 15 10 16
R3: 8 26 23 16 12 | 10 19 24 2 20 | 13 4 22 9 25 | 27 18 14 1 | 21 15 3 6 | 17 7 5 11
N27
1. No pair of players repeat their predator-prey relationship. This is mandatory, by the VEKN rules.OK
2. No pair of players share a table through all two rounds, when possible. (N/A in some 2R event.)OK: 144 (once)
3. Available VPs are equitably distributed.KO. Absolute deviation is: 0,288065843621399 => 27 have 12 VP | 5, 14, 15, 16, 17, 18, 21, 22, 23, 24 have 13 VP | 1, 2, 3, 6, 7, 8, 10, 11, 13, 19, 20, 25, 26 have 14 VP | 4, 9, 12 have 15 VP
5. A player doesn't sit in the fifth seat more than once.OK
6. No pair of players repeat the same relative position[*], when possible.OK
7. A player doesn't play in the same seat position, if possible.KO (player 20, table 1, position 1)
8. Starting transfers are equitably distributed. [NOAL]KO. Absolute deviation is: 0,592592592592593 => 20 have 6 transfers | 4, 8, 13, 17, 19, 21 have 7 transfers | 2, 5, 6, 7, 10, 11, 12, 14, 15, 18, 22, 23, 24, 25 have 8 transfers | 1, 16, 26, 27 have 9 transfers | 3, 9 have 10 transfers
Extra1. Inversions in the prey/predator relationshipOK

Current seating:

R2: 17 10 25 22 14 | 15 24 16 3 23 | 8 11 21 5 27 | 9 26 20 2 | 19 1 7 13 | 4 6 12 18
R3: 22 18 27 12 7 | 25 19 6 20 1 | 13 23 4 26 9 | 21 15 5 24 | 10 3 17 11 | 14 16 2 8
N27
1. No pair of players repeat their predator-prey relationship. This is mandatory, by the VEKN rules.OK
2. No pair of players share a table through all two rounds, when possible. (N/A in some 2R event.)KO (player 1 shares a table with player 19 on round 3): 132 (once), 6 (twice)
3. Available VPs are equitably distributed.KO. Absolute deviation is: 0,222222222222222 => 2, 16, 17, 18, 19, 20, 21, 24, 26 have 13 VP | 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 22, 23, 25, 27 have 14 VP
5. A player doesn't sit in the fifth seat more than once.OK
6. No pair of players repeat the same relative position[*], when possible.OK
7. A player doesn't play in the same seat position, if possible.OK
8. Starting transfers are equitably distributed. [NOAL]KO. Absolute deviation is: 1,18518518518519 => 6, 16, 17, 21, 25 have 6 transfers | 1, 10, 11, 15, 19, 24 have 7 transfers | 4, 8, 13, 20, 22 have 8 transfers | 2, 3, 7, 9, 12, 14, 18, 26 have 9 transfers | 23 have 10 transfers | 5, 27 have 11 transfers
Extra1. Inversions in the prey/predator relationshipKO. Count: 1 => 9-26
Prince of Paris, France
File Attachment:
Ratings Coordinator, Rules Director
Last edit: 05 Dec 2018 13:50 by Ankha.
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05 Dec 2018 13:42 - 05 Dec 2018 13:44 #92266 by Ankha
Replied by Ankha on topic Optimal seatings : the return of the mutant
For 31 players:

R2: 19 26 30 1 22 | 12 27 31 3 23 | 10 24 20 16 11 | 15 28 25 6 | 21 5 7 13 | 8 17 29 2 | 4 14 9 18
R3: 18 2 7 15 26 | 9 27 21 28 17 | 13 29 25 4 20 | 23 5 30 24 | 3 10 14 19 | 31 1 6 11 | 22 8 16 12
N31
1. No pair of players repeat their predator-prey relationship. This is mandatory, by the VEKN rules.OK
2. No pair of players share a table through all two rounds, when possible. (N/A in some 2R event.)OK: 162 (once), 0 (twice), 0 (thrice)
3. Available VPs are equitably distributed.KO. Absolute deviation is: 0,216441207075963 => 5, 6, 8, 14, 16, 17, 18, 19, 21, 22, 23, 24, 25, 28, 29, 30, 31 have 13 VP | 1, 2, 3, 4, 7, 9, 10, 11, 12, 13, 15, 20, 26, 27 have 14 VP
5. A player doesn't sit in the fifth seat more than once.OK
6. No pair of players repeat the same relative position[*], when possible.OK
7. A player doesn't play in the same seat position, if possible.KO (player 2, table 1, position 2)
8. Starting transfers are equitably distributed. [NOAL]KO. Absolute deviation is: 0,611862643080125 => 8, 21 have 6 transfers | 1, 10, 12, 24, 28, 29 have 7 transfers | 2, 3, 5, 6, 7, 9, 13, 16, 17, 18, 20, 22, 25, 27, 31 have 8 transfers | 4, 11, 14, 15, 19, 23, 26, 30 have 9 transfers
Extra1. Inversions in the prey/predator relationshipOK

Current seating:

R2: 25 20 12 8 4 | 5 6 21 18 28 | 26 11 19 7 31 | 23 1 29 13 | 14 16 2 30 | 9 24 17 3 | 27 10 15 22
R3: 17 27 14 1 30 | 2 22 9 16 29 | 13 3 24 10 23 | 31 18 6 11 | 7 26 4 20 | 12 19 5 21 | 8 15 28 25
N31
1. No pair of players repeat their predator-prey relationship. This is mandatory, by the VEKN rules.OK
2. No pair of players share a table through all two rounds, when possible. (N/A in some 2R event.)KO (player 2 shares a table with player 16 on round 3): 142 (once), 10 (twice), 0 (thrice)
3. Available VPs are equitably distributed.KO. Absolute deviation is: 0,216441207075963 => 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 have 13 VP | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 have 14 VP
5. A player doesn't sit in the fifth seat more than once.OK
6. No pair of players repeat the same relative position[*], when possible.OK
7. A player doesn't play in the same seat position, if possible.OK
8. Starting transfers are equitably distributed. [NOAL]KO. Absolute deviation is: 1,17169614984391 => 2, 6, 12, 17, 24, 26 have 6 transfers | 1, 7, 11, 16, 20, 25, 27 have 7 transfers | 5, 8, 9, 13, 14, 28 have 8 transfers | 3, 15, 18, 19, 21, 22, 23, 29, 31 have 9 transfers | 10 have 10 transfers | 4, 30 have 11 transfers
Extra1. Inversions in the prey/predator relationshipKO. Count: 1 => 13-23
Prince of Paris, France
File Attachment:
Ratings Coordinator, Rules Director
Last edit: 05 Dec 2018 13:44 by Ankha.
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17 Jun 2019 12:49 - 17 Jun 2019 13:09 #95421 by Ankha
Replied by Ankha on topic Optimal seatings : the return of the mutant
Back to business.

I tried to run the genetic seating generator with N=99. The thing is that above 75 players, the seating is done by taking the 50-players optimal seating, and adding the complementary N-50 seating. For instance, the 99-players seating is done with tables 1-10 matching the 50-players table, and tables 11-20 matching the 49-players seating.

It works, but it means that only half the tables truly have an optimal seating. By mixing all 99 players together, one can further smooth the irregularities and have a better seating.

I had to improve the genetic algorithm that would tend to give bad results on rules 5 and 7 because they had all-or-nothing scores. By refining the results (by giving a score matching the number of badly seated players), the algorithm works better.

Here's the seating for 99 players in the archon 1.5g
Round 1
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99



Round 2
14
10
 1
22
18
19
15
 6
 2
23
24
20
11
 7
 3
 4
25
16
12
 8
 9
 5
21
17
13
45
26
57
53
49
50
31
27
58
54
55
36
32
28
59
60
41
37
33
29
30
46
42
38
34
35
51
47
43
39
40
56
52
48
44
85
61
97
93
89
90
66
62
98
94
95
71
67
63
99
80
96
92
88
84
65
81
77
73
69
70
86
82
78
74
75
91
87
83
79
72
76
64
68



Round 3
12
23
 9
20
 1
13
24
10
16
 2
17
 3
14
25
 6
 7
18
 4
15
21
22
 8
19
 5
11
29
45
56
47
38
34
50
26
52
43
39
55
31
57
48
44
60
36
27
53
49
30
41
32
58
54
35
46
37
28
59
40
51
42
33
69
85
96
87
78
74
90
61
92
83
79
95
66
97
88
64
80
91
82
73
89
65
76
67
98
94
70
81
72
63
99
75
86
77
68
93
84
71
62





Score:





RuleResult



N99



1. No pair of players repeat their predator-prey relationship. This is mandatory, by the VEKN rules.OK



2. No pair of players share a table through all two rounds, when possible.  (N/A in some 2R event.)OK: 588 (once), 0 (twice), 0 (thrice)



3. Available VPs are equitably distributed.KO. Absolute deviation is: 0,0948882767064585 => 62, 64, 68, 71, 72, 76, 84, 93, 96, 97, 98, 99 have 14 VP | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 65, 66, 67, 69, 70, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95 have 15 VP



5. A player doesn't sit in the fifth seat more than once.OK



6. No pair of players repeat the same relative position[*], when possible.OK



7. A player doesn't play in the same seat position, if possible.OK



8. Starting transfers are equitably distributed. [NOAL]KO. Absolute deviation is: 1,35537190082645 => 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96 have 6 transfers | 7, 12, 17, 22, 24, 30, 35, 40, 45, 50, 55, 60, 65, 70, 72, 75, 80, 85, 90, 95 have 7 transfers | 1, 4, 6, 9, 11, 13, 14, 16, 19, 21, 64, 93 have 8 transfers | 3, 8, 10, 18, 23, 27, 29, 32, 34, 37, 39, 42, 44, 47, 49, 52, 54, 57, 59, 62, 67, 69, 74, 77, 79, 82, 87, 89, 92, 94, 97, 99 have 9 transfers | 2, 5, 15, 20, 25, 84 have 10 transfers | 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 98 have 11 transfers



Extra1. Inversions in the prey/predator relationshipOK





A better seating is:





Round 1
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99



Round 2
72
33
54
91
 1
39
96
50
 2
53
95
49
37
23
27
 4
74
 6
20
64
28
51
90
46
63
34
93
14
 8
21
29
79
32
67
87
24
99
66
55
76
82
15
 7
73
42
85
58
52
61
22
60
26
10
40
13
80
30
41
 5
57
89
94
25
17
48
65
18
59
97
86
38
88
71
62
77
 9
83
35
47
56
92
68
16
43
81
12
78
75
 3
36
84
44
69
98
11
70
45
19
31



Round 3
42
91
84
80
38
22
59
11
32
78
 8
90
47
60
24
73
25
45
16
96
79
13
49
81
18
40
98
95
72
82
87
53
77
26
41
17
50
 1
 6
58
35
 3
74
 7
68
48
70
 2
33
37
20
89
44
85
51
64
75
30
76
34
19
14
 9
88
61
55
10
67
28
92
43
29
57
12
83
 5
36
62
21
66
23
69
94
65
 4
99
31
27
52
39
15
46
97
71
93
54
63
56
86





Score:





RuleResult



N99



1. No pair of players repeat their predator-prey relationship. This is mandatory, by the VEKN rules.OK



2. No pair of players share a table through all two rounds, when possible.  (N/A in some 2R event.)OK: 588 (once), 0 (twice), 0 (thrice)



3. Available VPs are equitably distributed.KO. Absolute deviation is: 0,0948882767064585 => 19, 31, 45, 54, 56, 63, 70, 86, 96, 97, 98, 99 have 14 VP | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95 have 15 VP



5. A player doesn't sit in the fifth seat more than once.OK



6. No pair of players repeat the same relative position[*], when possible.OK



7. A player doesn't play in the same seat position, if possible.OK



8. Starting transfers are equitably distributed. [NOAL]KO. Absolute deviation is: 0,732782369146005 => 12, 15, 17, 22, 26, 29, 31, 36, 42, 46, 51, 70, 72, 79, 82, 87, 89, 91, 92, 96, 99 have 7 transfers | 1, 6, 8, 9, 11, 16, 19, 23, 28, 35, 38, 41, 43, 48, 54, 56, 66, 71, 73, 84, 95 have 8 transfers | 2, 3, 4, 5, 7, 10, 13, 14, 18, 20, 21, 24, 25, 27, 30, 32, 33, 34, 37, 39, 40, 44, 45, 47, 49, 50, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 74, 75, 76, 77, 78, 80, 81, 83, 85, 86, 88, 90, 93, 94, 97, 98 have 9 transfers



Extra1. Inversions in the prey/predator relationshipOK





This result was found in less than 3h.			


							

					

					


Prince of Paris, France

  

		
		
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		Last edit: 17 Jun 2019 13:09  by Ankha.			


	

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						17 Jun 2019 13:40		 -  17 Jun 2019 13:56		#95423
		by Ankha
	

	

		

			

				Replied by Ankha on topic Optimal seatings : the return of the mutant			


			

				If you want to contribute or to play with the seatings, you just have to download and unzip www.vekn.net/images/stories/downloads/VtesSeatings.zip



There are two programs:



1) genetics.exe

This command-line program tries to find the best seating for a given number of players.

To use it, you have to run it through a command line with two parameters:

- the first one is the number of players (eg., 51)

- the second one is the size of the "population"  that will breed and mutate to give the best results. Typical value is 1000.

The program will create a population for each of your logical processor. On my computer, it means 8*1000 individuals. If you have only 4 logical processors, you may want to double the population size. You can run the program in background since it has a very low priority and won't block your computer.





		
		
		File Attachment:

			






2/ RuleChecker.exe

You simply run it by double cliking on it. It always assume that the R1 seating is 1, 2, 3, ..., n so for 2R+F tournaments, you have to fill the first line only, and for 3R+F tournaments, two lines.

It can also import from your clipboard your seating if you copied it from the Archon file (by selecting the player numbers in the Optimal Seatings sheets) or from the Genetic program.

It will indicate if the rules are enforced or not.





		
		
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		Last edit: 17 Jun 2019 13:56  by Ankha.			


			
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						17 Jun 2019 14:47				#95427
		by Ankha
	

	

		

			

				Replied by Ankha on topic Optimal seatings : the return of the mutant			


			

				51 players



Archon 1.5g:





Round 1
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51



Round 2
 5
36
22
28
43
46
 4
37
11
29
12
47
10
38
24
15
16
39
 6
48
30
40
17
49
34
35
44
41
18
50
23
31
45
42
51
19
 1
26
 8
 9
20
27
 2
25
 3
32
13
14
21
 7
33



Round 3
47
35
36
27
 7
33
23
48
37
13
49
19
 2
45
38
20
39
40
50
 1
51
 9
21
41
 3
29
 8
44
25
42
43
26
14
32
46
28
 6
11
17
18
 5
30
12
10
34
15
22
 4
24
16
31





Score:





RuleResult



N51



1. No pair of players repeat their predator-prey relationship. This is mandatory, by the VEKN rules.OK



2. No pair of players share a table through all two rounds, when possible.  (N/A in some 2R event.)OK: 282 (once), 0 (twice), 0 (thrice)



3. Available VPs are equitably distributed.KO. Absolute deviation is: 0,0645905420991926 => 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 have 14 VP | 23, 29, 35 have 15 VP



5. A player doesn't sit in the fifth seat more than once.OK



6. No pair of players repeat the same relative position[*], when possible.OK



7. A player doesn't play in the same seat position, if possible.OK



8. Starting transfers are equitably distributed. [NOAL]KO. Absolute deviation is: 1,15340253748558 => 16, 21, 23, 26, 36, 40, 44 have 6 transfers | 1, 4, 5, 6, 9, 12, 19, 20, 31, 35, 47, 49 have 7 transfers | 10, 11, 14, 15, 18, 28, 30, 33, 46, 48 have 8 transfers | 2, 3, 7, 8, 17, 22, 25, 27, 29, 32, 37, 39, 41, 43, 45, 51 have 9 transfers | 24, 34 have 10 transfers | 13, 38, 42, 50 have 11 transfers



Extra1. Inversions in the prey/predator relationshipOK





New seating:





Round 1
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51



Round 2
20
43
47
32
28
45
30
 9
 1
38
46
18
 5
36
26
37
50
15
16
42
39
33
48
22
14
34
51
41
21
 7
13
40
49
 2
44
25
 6
12
27
 3
10
19
11
29
23
17
31
 4
35
24
 8



Round 3
35
15
25
17
46
24
47
36
41
50
32
29
39
45
12
43
 8
27
44
 3
19
42
31
 6
49
38
11
34
48
23
10
 4
51
40
37
14
 1
 7
26
28
16
21
13
22
 9
 2
18
30
 5
20
33





Score:





RuleResult



N51



1. No pair of players repeat their predator-prey relationship. This is mandatory, by the VEKN rules.OK



2. No pair of players share a table through all two rounds, when possible.  (N/A in some 2R event.)OK: 282 (once), 0 (twice), 0 (thrice)



3. Available VPs are equitably distributed.KO. Absolute deviation is: 0,0645905420991926 => 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 have 14 VP | 15, 32, 34 have 15 VP



5. A player doesn't sit in the fifth seat more than once.OK



6. No pair of players repeat the same relative position[*], when possible.OK



7. A player doesn't play in the same seat position, if possible.OK



8. Starting transfers are equitably distributed. [NOAL]KO. Absolute deviation is: 0,726643598615917 => 1, 4, 6, 10, 11, 16, 22, 29, 30, 32, 35, 37, 40, 43, 45 have 7 transfers | 3, 13, 19, 20, 21, 24, 25, 28, 31, 34, 36, 38, 39, 46, 48 have 8 transfers | 2, 5, 7, 8, 9, 12, 14, 15, 17, 18, 23, 26, 27, 33, 41, 42, 44, 47, 49, 50, 51 have 9 transfers



Extra1. Inversions in the prey/predator relationshipOK



			


							

					

					


Prince of Paris, France

  

		
		
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