Optimal seatings changes 3R+F

I've added the result for 21 players.

The current seating violates rule 7 ("A player doesn't play in the same seat position") but has a better deviation (one less player with 6 transfers and 9 transfers, one more with 7 and 8 transfers). Which one is better?

I fixed the results for 18 (bad paste).

We used the new seatings to our last tournament (17 players), and many players had the feeling the met the same players often.

I gave a look to the seating used, and I can confirm that this feeling was true. Among all the possible seatings that are "optimal" (ie. with the lowest vp/transfers deviation), there are variations about how many times player X met player Y.

For instance, the current (non-optimal) seating has 13 pairs of players that meet twice, and 58 pairs of players that meet once during the 3 rounds.

The seating I took among the list of optimal seatings was: 9 14 10 15 7 | 5 12 4 2 | 3 13 17 6 | 16 1 11 8 / 13 8 6 11 16 | 15 5 14 3 | 7 4 1 12 | 2 17 9 10

It contains 1 pair of players that meet thrice (14 and 15), 14 pairs twice, 53 pairs once.

But there are other optimal seatings that seem "better": 17 pairs twice, 50 pairs once, or 15 pairs twice, 54 pairs once.

I think we should value more the seatings with the most "meet once" pairs.

But what if it increases the number of players that meet thrice?

For instance, the seating with the most "meet once" pairs is: 63 once, 6 twice, 3 thrice

The seating with the most "meet once" pairs AND no "meet thrice" pairs is: 60 once, 12 twice

Which seating is "better"?

I'm redoing the computations because rule 2 had been taken out of the equation.

I've corrected the algorithm to take rule 2 into account. The algorithm will now return the results that minimize the number of times each player meet other players, and will exclude any results where the players would meet on the three rounds.

I takes a lot of computation power to get the results, so if you have a PC that runs Windows, and some spare CPU, you can help!

1/ download www.veknfrance.com/tmp/seatings19calculator.7z
2/ extract the files in it into an empty folder
3/ run the command line: ConsoleApplication5.exe X Y
or double-click on ConsoleApplication5.exe and input the interval

X and Y define the boundaries of the computation interval. For my part, I've already calculated the results from 1 to 127000 (over 228550), so try to take intervals of size 10000 starting from 150000. If you do, please leave a message here before launching the computation and indicate what interval you are going to computeso that other people don't compute the same thing.

4/ in the folder, files will appear: seating3r-19.txt-$$$$-$$$$-$$$$-$$$$$$$$$$-value
When the computation is over, please create a zip with those files and send me that archive.

Beware! It's a pretty heavy computation that will take all your powerhorses, making it laggish. The best thing to do is to take small intervals and make it run nightly.

Here's the list of contributors:
Ankha: 1 - 144 000
Ankha (azure81): 144 000 - 144 999
Ankha (132): 145 000 - 150 000
Ankha (build8): 150 001 - 159 999
Lestat: 180 000 - 190 000
Lestat: 190 000 - 200 000
Ankha (build8): 200 000 - 210 000 OK
Mimmy: 210 000 - 220 000
Apolokia final: 220 000 - 228 550