file Optimal seatings changes

03 Nov 2014 08:44 - 13 Mar 2017 10:06 #67154 by Ankha
Please disregard those results, for some of them are wrong due to a flaw in the validation.

From now on, I strongly recommand not to use the version 1.5e but version 1.5f :

Excel: www.vekn.net/images/stories/downloads/thearchon1.5f.xlsx
LibreOffice: www.vekn.net/images/stories/downloads/thearchon1.5f.ods


I've been working recently on the 2R+F optimal seatings of the archons, and I've found some more "optimal" seatings than the current ones. The search has been done through exhaustive computations so I doubt there will be better results.
Of course, there's more than one seating that is optimal, but they're all equivalent. For instance, for 10 players:

T1: 4 9 2 7 1 T2: 10 3 5 6 8
and
T1: 4 8 2 6 1 T2: 10 5 9 3 7

are the same in respect to rules 1 to 8. They both violate rule 2 (2. No pair of players share a table through all two rounds, when possible. (N/A in some 2R event.)).
Starting transfers can't be equitably distributed (rule 8) because there are 28 transfers to divide between 10 players.

Nevertheless, in the first case, we have an absolute deviation of 0,72: 1, 2, 3, 4, 6, 10 have 5 transfers | 5, 8 have 7 transfers | 7, 9 have 6 transfers
In the second case, an absolute deviation of 0,72 too: 1, 2, 4, 6, 8, 10 have 5 transfers | 3, 9 have 7 transfers | 5, 7 have 6 transfers.

Basically, some players swap their positions. We'll choose arbitrarily one of the optimal seatings as the official one.

The current optimal seating for 10 players is:

T1: 10 1 4 7 3 T2: 5 6 9 2 8

Which gives us an absolute deviation of 1,28: 1, 6 have 3 transfers | 2, 7 have 6 transfers | 3, 4, 8, 9 have 7 transfers | 5, 10 have 5 transfers
which is worse (we have 2 players with 3 transfers).

The optimal seatings will be updated in the next version of the archon, here's the current "best" optimal seatings:
(NB: in some cases, rule "3. Available VPs are equitably distributed." is violated too, when the tables have different sizes. The optimal seating is the one with the smaller absolute deviation on the vps).

10 players: 4 9 2 7 1 | 10 3 5 6 8
Rule 2 KO (player 1 shares a table with player 2): 24 (once), 8 (twice)
Rule 8 KO. Absolute deviation is: 0.72 => 1, 2, 3, 4, 6, 10 have 5 transfers | 5, 8 have 7 transfers | 7, 9 have 6 transfers
(Current seating has an absolute deviation of 1.28)

11 players: no calculated, it should be avoided anyway

12 players: 4 11 9 5 | 8 3 1 10 | 12 7 2 6 (fixed in 1.5f)
Rule 2 KO (player 1 shares a table with player 3): 30 (once), 3 (twice)
Rule 8 KO. Absolute deviation is: 0.333333333333333 => 1, 4, 6, 7, 8, 9, 10, 11 have 5 transfers | 2, 12 have 6 transfers | 3, 5 have 4 transfers
(Current seating has an absolute deviation of 0.5)

13 players: 4 13 6 12 7 | 3 8 2 10 | 11 5 9 1 (fixed in 1.5f)
Reverted back to 1.5a seating, until we find a better seating.

14 players: 5 3 12 7 11 | 9 13 2 8 1 | 14 10 4 6 (fixed in 1.5f)
Rule 2 KO (player 1 shares a table with player 2): 42 (once), 5 (twice)
(Current seating is: 40 once, 6 twice)
Rule 3 KO. Absolute deviation is: 0,476190476190476 => 1, 4, 6, 8, 11, 12, 13, 14 have 9 VP | 2, 3, 5, 7, 9, 10 have 10 VP
(Current seating has the same absolute deviation)
Rule 8 KO. Absolute deviation is: 0,836734693877551 => 1, 3 have 4 transfers | 2, 12, 14 have 6 transfers | 4, 5, 6, 7, 8, 11, 13 have 5 transfers | 9 have 7 transfers | 10 have 8 transfers
(Current seating has the same absolute deviation)

15 players: 9 13 7 11 1 | 14 5 12 6 2 | 15 4 10 8 3 (fixed in 1.5f)
Rule 2 KO (player 2 shares a table with player 5): 48 (once), 6 (twice)
Rule 8 KO. Absolute deviation is: 0,72 => 1, 6, 7, 9, 11, 12, 13, 14, 15 have 5 transfers | 2, 4, 5 have 6 transfers | 3, 8, 10 have 7 transfers
(Current seating has an absolute deviation of 1.09)

16 players: 16 11 6 1 | 12 15 2 5 | 8 3 14 9 | 4 7 10 13
All rules are OK!
(Current seating is OK too!)

17 players: 5 3 7 14 10 | 4 12 15 6 | 9 16 11 1 | 17 13 2 8 (fixed in 1.5f)
Rule 2 KO (player 3 shares a table with player 5): 54 (once), 1 (twice)
(Current seating is KO, 46 once, 5 twice)
Rule 3 KO. Absolute deviation is: 0,617647058823529 => 1, 2, 4, 7, 10, 14 have 9 VP | 3, 5 have 10 VP | 6, 8, 9, 11, 12, 13, 15, 16, 17 have 8 VP
(Current seating has a better absolute deviation: 0,5 => 1, 2, 3, 4, 5, 6, 8, 11, 13, 17 have 9 VP | 7, 9, 10, 12, 14, 15, 16 have 8 VP)
Rule 8 KO. Absolute deviation is: 0,311418685121107 => 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17 have 5 transfers | 8 have 7 transfers | 13 have 6 transfers
(Current seating has an absolute deviation of 0.93)

18 players: 9 5 7 15 11 | 4 13 16 6 1 | 10 17 12 2 | 18 8 14 3 (fixed in 1.5f)
Rule 2 KO (player 1 shares a table with player 4): 60 (once), 2 (twice)
(Current seating has 48 once, 8 twice)
Rule 3 KO. Absolute deviation is: 0,555555555555556 => 1, 4, 5, 6, 7, 9 have 10 VP | 2, 3, 8, 10, 11, 13, 15, 16 have 9 VP | 12, 14, 17, 18 have 8 VP
(Current seating has a better absolute deviation of 0,1111)
Rule 8 KO. Absolute deviation is: 0,518518518518519 => 1, 4, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18 have 5 transfers | 2, 5 have 6 transfers | 3, 14 have 7 transfers
(Current seating has an absolute deviation of 0.74)

19 players: 4 18 7 11 6 | 19 9 12 3 1 | 15 13 17 2 8 | 14 10 5 16 (fixed in 1.5f)
Rule 2 KO (player 1 shares a table with player 3): 66 (once), 3 (twice)
(Current seating is: 56 once, 8 twice)
Rule 3 KO. Absolute deviation is: 0,552631578947368 => 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 15 have 10 VP | 5, 10, 14, 17, 18, 19 have 9 VP | 16 have 8 VP
(Current seating has a better absolute deviation: 0,5)
Rule 8 KO. Absolute deviation is: 0,648199445983379 => 1, 4, 6, 7, 11, 12, 13, 14, 15, 16, 17, 18, 19 have 5 transfers | 2, 9, 10 have 6 transfers | 3, 5, 8 have 7 transfers
(Current seating has an absolute deviation of 0.69)

20 players: 9 4 12 16 11 | 14 18 7 2 6 | 19 10 17 13 1 | 20 15 5 8 3
Rule 2 KO (player 3 shares a table with player 5): 72 (once), 4 (twice)
(Current seating is: 58 once, 11 twice)
Rule 8 KO. Absolute deviation is: 0,72 => 1, 6, 7, 9, 11, 12, 14, 16, 17, 18, 19, 20 have 5 transfers | 2, 4, 10, 15 have 6 transfers | 3, 5, 8, 13 have 7 transfers
(Current seating has an absolute deviation of 0.76)

21 players: 13 20 7 15 1 | 9 16 2 18 | 4 12 19 14 | 21 8 17 10 | 5 3 11 6
Rule 2 KO (player 3 shares a table with player 5): 66 (once), 1 (twice)
(Current seating is: 58 once, 11 twice)
Rule 3 KO. Absolute deviation is: 0,533333333333333 => 1 have 10 VP | 2, 3, 4, 5, 7, 13, 15, 20 have 9 VP | 6, 8, 9, 10, 11, 12, 14, 16, 17, 18, 19, 21 have 8 VP
(Current seating has a better absolute deviation: 0.495)
Rule 8 KO. Absolute deviation is: 0,258503401360544 => 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 19, 20, 21 have 5 transfers | 15 have 6 transfers | 17 have 7 transfers
(Current seating has the same absolute deviation)

22 players: 18 21 16 19 1 | 22 17 12 2 6 | 9 13 7 15 | 4 8 10 11 | 14 5 20 3
Rule 2 KO (player 3 shares a table with player 5): 66 (once), 5 (twice)
(Current seating is: 60 once, 8 twice)
Rule 3 KO. Absolute deviation is: 0,472727272727273 => 1, 2, 6 have 10 VP | 3, 4, 5, 7, 8, 9, 10, 12, 16, 17, 18, 19, 21, 22 have 9 VP | 11, 13, 14, 15, 20 have 8 VP
(Current seating has a better absolute deviation: 0,254)
Rule 8 KO. Absolute deviation is: 0,446280991735537 => 1, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 have 5 transfers | 2, 5 have 6 transfers | 3, 10 have 7 transfers
(Current seating has the same absolute deviation)

23 players: 23 18 21 11 16 | 19 22 17 12 6 | 9 13 7 20 1 | 14 4 2 8 | 15 5 10 3
Rule 2 KO (player 2 shares a table with player 4): 72 (once), 6 (twice)
(Current seating is 76 once, 4 twice, which is better)
Rule 3 KO. Absolute deviation is: 0,382608695652174 => 1, 6, 7, 9, 11, 12, 13 have 10 VP | 2, 3, 4, 5, 8, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 have 9 VP
(Current seating has the same absolute deviation)
Rule 8 KO. Absolute deviation is: 0,578449905482042 => 1, 2, 6, 7, 9, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 have 5 transfers | 3, 8, 10 have 7 transfers | 4, 5, 12 have 6 transfers
(Current seating has an absolute deviation of 0.87)
Note also that rule 7. "A player doesn't play in the same seat position, if possible." is violated in the current seating (player 3, table 1, position 3)

24 players: 19 23 17 21 16 | 24 18 22 11 6 | 14 20 12 1 7 | 4 9 2 13 8 | 15 10 5 3
Rule 2 KO.
Rule 3 KO. Absolute deviation is: 0,466666666666667 => 1, 2, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 20 have 10 VP | 3, 5, 10, 15, 21, 22, 23, 24 have 9 VP
(Current seating has the same absolute deviation)
Rule 8 KO. Absolute deviation is: 0,666666666666667 => 1, 2, 4, 6, 11, 12, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24 have 5 transfers | 3, 5, 8, 13 have 7 transfers | 7, 9, 10, 20 have 6 transfers
(Current seating has an absolute deviation of 0.95)


25 players*: 10 14 22 18 1 | 15 19 2 23 6 | 20 24 7 3 11 | 25 4 12 8 16 | 5 9 17 13 21 (seating was done manually)
Rule 2 OK.
(Current seating is 84 once, 8 twice)
Rule 8 KO. Absolute deviation is: 0,72 => 1, 2, 4, 6, 9, 11, 12, 15, 16, 17, 19, 21, 22, 23, 24 have 5 transfers | 3, 5, 8, 13, 18 have 7 transfers | 7, 10, 14, 20, 25 have 6 transfers
(Current seating has an absolute deviation of 0.72)


26 players: 26 21 24 19 11 | 22 25 20 16 12 | 14 17 7 23 | 4 13 2 15 | 18 8 5 6 | 9 3 10 1
Rule 2 KO.
Rule 3 KO. Absolute deviation is: 0,410256410256411 => 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 19, 20, 21, 23, 24, 25, 26 have 9 VP | 12, 13, 14, 16, 17, 22 have 8 VP
(Current seating has an absolute deviation of 0.51)
Rule 8 KO. Absolute deviation is: 0,390532544378698 => 1, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 have 5 transfers | 2, 4 have 6 transfers | 3, 5 have 7 transfers
(Current seating has an absolute deviation of 1.34)

27 players: 19 26 17 24 11 | 27 22 25 20 1 | 23 18 21 16 6 | 14 9 12 7 | 4 13 2 8 | 15 10 5 3
Rule 2 KO.
Rule 3 KO. Absolute deviation is: 0,111111111111111 => 1, 6, 11 have 10 VP | 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 have 9 VP
(Current seating has an absolute deviation of 0.40)
Rule 8 KO. Absolute deviation is: 0,518518518518518 => 1, 2, 4, 6, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 have 5 transfers | 3, 5, 8 have 7 transfers | 7, 9, 10 have 6 transfers
(Current seating has an absolute deviation of 1.38)

29 players*: 24 28 22 26 21 | 29 23 27 16 11 | 19 14 17 6 1 | 4 18 12 7 2 | 25 9 20 13 8 | 15 10 5 3
Rule 2 KO.
Rule 3 KO. Absolute deviation is: 0,425287356321839 => 1, 2, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 have 10 VP | 3, 5, 10, 15, 26, 27, 28, 29 have 9 VP
(Current seating has an absolute deviation of 0.42)
Rule 8 KO. Absolute deviation is: 0,677764565992866 => 1, 4, 6, 11, 12, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29 have 5 transfers | 2, 7, 9, 10, 14 have 6 transfers | 3, 5, 8, 13, 20 have 7 transfers
(Current seating has an absolute deviation of 1.33)

30 players*: 24 28 22 26 21 | 29 23 27 16 11 | 19 14 17 6 1 | 4 9 12 7 2 | 30 25 20 18 13 | 15 10 5 8 3
Rule 2 KO.
Rule 8 KO. Absolute deviation is: 0,72 => 1, 4, 6, 11, 12, 15, 16, 17, 19, 21, 22, 23, 24, 26, 27, 28, 29, 30 have 5 transfers | 2, 7, 9, 10, 14, 25 have 6 transfers | 3, 5, 8, 13, 18, 20 have 7 transfers
(Current seating has an absolute deviation of 1.52)

31 players: 23 26 29 25 28 | 27 30 21 24 17 | 31 22 19 20 18 | 14 8 12 16 | 4 13 7 11 | 9 5 2 6 | 15 3 10 1
Rule 2 KO.
Rule 3 KO. Absolute deviation is: 0,16589861751152 => 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 have 9 VP | 16 have 8 VP
(Current seating has an absolute deviation of 0.55)
Rule 8 KO. Absolute deviation is: 0,468262226847034 => 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31 have 5 transfers | 5, 17, 25 have 6 transfers | 10, 18, 19 have 7 transfers
(Current seating has an absolute deviation of 1.32)


Computing results for 30+ players in progress...

* didn't perform an exhaustive search

Prince of Paris, France
Ratings Coordinator, Rules Director
Last edit: 13 Mar 2017 10:06 by Ankha.
The following user(s) said Thank You: Pascal Bertrand, Lönkka, BenPeal, D-dennis, self biased

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03 Nov 2014 08:52 #67155 by BenPeal

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03 Nov 2014 13:09 - 03 Nov 2014 13:09 #67170 by Ankha
Replied by Ankha on topic Re: Optimal seatings changes
Seating for 17 players is interesting: the current archon has a better absolute deviation for VPs, and a worse one for transfers.
And no, you can't have both :)

Question is: would you favor the transfers so they are more equitably distributed, or the VPs (ie: how many times you sit at a 4-players table)?

Prince of Paris, France
Ratings Coordinator, Rules Director
Last edit: 03 Nov 2014 13:09 by Ankha.

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03 Nov 2014 13:11 #67172 by BenPeal

Question is: would you favor the transfers so they are more equitably distributed, or the VPs (ie: how many times you sit at a 4-players table)?


I would rather the VPs be more equitably distributed than the transfers.

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03 Nov 2014 13:23 - 03 Nov 2014 13:23 #67173 by Timo
Replied by Timo on topic Re: Optimal seatings changes

Question is: would you favor the transfers so they are more equitably distributed, or the VPs (ie: how many times you sit at a 4-players table)?


I would rather the VPs be more equitably distributed than the transfers.


I guess you have to balance your data.

Because going from 0.5 to 0.56 for the VP is no big deal but going from 0.93 to 0.31 for transfers is more important (IMO).
Last edit: 03 Nov 2014 13:23 by Timo.

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03 Nov 2014 13:24 - 03 Nov 2014 13:25 #67174 by Ankha
Replied by Ankha on topic Re: Optimal seatings changes

Question is: would you favor the transfers so they are more equitably distributed, or the VPs (ie: how many times you sit at a 4-players table)?


I would rather the VPs be more equitably distributed than the transfers.


I guess you have to balance your data.

Because going from 0.5 to 0.56 for the VP is no big deal but going from 0.93 to 0.31 for transfers is more important (IMO).

I'll do a test and keep only the best deviation for VPs (0.5) and see what we obtain as transfer deviation.
Another thing is: would you like to play your 2 rounds on a 4 players table and have more transfers, or play a 5-players and a 4-players tables with "slightly" less transfers ("slightly" being the big unknown).

Prince of Paris, France
Ratings Coordinator, Rules Director
Last edit: 03 Nov 2014 13:25 by Ankha.

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