Tournament blocks: Difference between revisions

Tournament blocks (view source)

Revision as of 01:17, 4 October 2015

2,266 bytes added , 4 October 2015

I'm working on this to include more matchups, and what to do with some that may end up deleted. WIP, comment to me but don't muck the tables.

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Senechal

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 The general formula is that table t consists of players [t, t + n/4, t + 2n/4, t + 3n/4] in hanchan 0 {mathematically speaking so the formula works}, and for future hanchan h, tables consist of [t, ((t + 1*h) % n/4) + n/4, ((t + 2*h) % n/4) + 2n/4, ((t + 3*h) % n/4) + 3n/4]. Its usefulness can be demonstrated as soon as there are 44 or more participants, and preferably not a multiple of 3. Heavily composite numbers of players will lead to collisions when tables = h * factor. The 2014 WRC had 120 players over 30 tables: as 120 (as well as 30) is divisible by 10, it would lead to a collision when h = 10, making the 11th hanchan place naively two players who met before across all 30 tables. It is also divisible by 5, but for larger events, a collision cannot occur if 1*factor, 2*factor or 3*factor does not equal or surpass the number of tables.
-===== Blocks of 4 =====
+==== Tested blocks of 4 ====
-{| class="wikitable"
+These blocks should be as close to optimal as humanly possible. Tournaments aiming to run only 4 rounds may require using a different set of tables as balancing may require different pairings to obtain a specific goal at 4 rounds which is potentially unattainable in a solution aimed for 5 or more rounds. Comments and sources included when possible.
+Format is in CSV with extra spaces between tables when possible.
+{| class="mw-collapsible mw-collapsed wikitable"
+|-
+! 16 Players !! Round !! Out of !! Raw data !! Balanced data
+|-
+| 16 || 1 || 4/5 || 01,05,09,13,  02,06,10,14,  03,07,11,15,  04,08,12,16 || AEIM BFJN CGKO DHLP
+|-
+| 16 || 2 || 4/5 || 07,04,13,10,  06,01,16,11,  05,02,15,12,  08,03,14,09 || GDMJ FAPK EBOL HCNI
+|-
+| 16 || 3 || 4/5 || 09,15,06,04,  10,16,05,03,  13,11,02,08,  14,12,01,07 || IOFD JPEC MKBH NLAG
+|-
+| 16 || 4 || 4/5 || 12,13,03,06,  11,14,04,05,  15,10,08,01,  16,09,07,02 || LMCF KNDE OJHA PIGB
+|-
+| 16 || 5 ||   5 || 01,02,03,04,  05,06,07,08,  09,10,11,12,  13,14,15,16 || ABCD EFGH IJKL MNOP
+|-
+|colspan=5| '''Notes:''' In 4 rounds, players 13 and 15 will have to play the same table 3 times. In 5 rounds, add players 4, 6, 11 and 14. This is unavoidable, the alternative being that players will play 4 times on a table.<br/>
+'''Balances achieved:''' Opponent, Wind, Table. This match-up is solved.<br/>
+'''Source:''' Pegg, adapted by [[User:Senechal]].
+|}
+{| class="mw-collapsible mw-collapsed wikitable"
 |-
-! Players !! Block !! Of !! Raw data !! Balanced data
+! 20 Players A !! Round !! Out of !! Raw data
+|-
+| 20 || 1 || 6/7 || 01,02,03,04,  05,06,07,08,  09,10,11,12,  13,14,15,16,  17,18,19,20
+|-
+| 20 || 2 || 6/7 || 14,03,06,17,  18,04,10,13,  16,05,09,19,  15,08,01,11,  20,07,12,02
+|-
+| 20 || 3 || 6/7 || 12,17,16,01,  03,11,13,05,  08,20,14,10,  19,15,04,07,  06,09,02,18
 |-
-| 16 || 1 || 4/5 || AEIM BFJN CGKO DHLP || AEIM BFJN CGKO DHLP
+| 20 || 4 || 6/7 || 18,11,07,03,  04,12,20,06,  17,13,02,15,  14,01,05,09,  10,16,08,19
 |-
-| 16 || 2 || 4/5 || AFKP BELO CHIN DGJM || FAPK EBOL HCNI GDMJ
+| 20 || 5 || 6/7 || 08,19,12,13,  20,15,09,03,  07,01,18,14,  11,06,04,16,  02,05,17,10
 |-
-| 16 || 3 || 4/5 || AGLN BHKM CEJP DFIO || NLAG MKBH JPEC IOFD
+| 20 || 6 || 6/7 || 07,09,13,01,  15,19,10,06,  02,08,16,18,  05,20,11,17,  03,04,14,12
 |-
-| 16 || 4 || 4/5 || AHJO BGIP CFLM DEKN || OJHA PIGB LMCF KNDE
+| 20 || 7 || 7/7 || 04,17,08,09,  12,18,05,15,  11,14,19,02,  06,13,01,20,  10,16,03,07
 |-
-| 16 || 5 || 5 || ABCD EFGH IJKL MNOP || ABCD EFGH IJKL MNOP
+|colspan=4| '''Notes:''' This is not a solution to the Social Golfer Problem but it does balance out fairly well to get players to play against almost everyone.<br/>
+'''Balances achieved:''' Wind, Table. This match-up is imperfect. 20 Players B is a simple Dutch cycle of players, more suitable for 4 or 5 rounds.<br/>
+'''Source:''' [[User:Yazphier]], balanced by [[User:Senechal]].
+|}
+{| class="mw-collapsible mw-collapsed wikitable"
+|-
+! Players !! Block !! Of !! Raw data !! Balanced data
 |-
 | 20 || 1 || 5 || ABCD EFGH IJKL MNOP QRST ||
@@ Line 155: / Line 190: @@
 Considering that league blocks contain 5 players, the counting mechanism has to be recalculated almost from scratch. These numbers are to satisfy 6-session events or seasons. For all Dutch cycles, as well as some non-Dutch SGP blocks can drop the last fifth in order to make groups of 4, expanding the solved ranges of players from as low as 80% to 100% of the maximal solutions. Considering all our solutions for 25+ are good for 6+ sessions, solutions for larger numbers can concatenate smaller groups with the minimum amount of sessions needed to make a larger group that satisfies that lower bound. The solution for 25 players in 6 sessions can drop one player, the solution for 40 present below can drop 5, although it may be possible that a solution allowing to drop 8 exists.
-{| class="wikitable"
+{| class="mw-collapsible mw-collapsed wikitable"
 |-
 ! Players !! Round !! Of !! Match-ups