Tournament blocks: Difference between revisions

Tournament blocks (view source)

Revision as of 20:25, 25 March 2017

1,310 bytes added , 25 March 2017

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Senechal

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 ==== Simplest solution: Dutch cycles ====
 {| class="wikitable" style="float:right; margin-left: 10px; width: 30%;"
+|-
+! Round !! Table !! East !! South !! West !! North
+|-
+| 1 || 1 || 01 || 02 || 03 || 04
+|-
+| 2 || 1 || 32 || 35 || 38 || 41
+|-
+| 3 || 1 || 23 || 16 || 37 || 30
+|-
+| 4 || 1 || 22 || 33 || 44 || 11
+|-
+| 5 || 1 || 29 || 14 || 43 || 28
+|-
+| 6 || 1 || 12 || 31 || 06 || 25
+|-
+| 7 || 1 || 19 || 40 || 21 || 42
+|-
+| 8 || 1 || 44 || 26 || 19 || 01
+|-
+| 9 || 1 || 34 || 17 || 24 || 07
+|-
+| 10 || 1 || 13 || 26 || 39 || 08
+|-
+| 11 || 1 || 36 || 27 || 18 || 09
+|- bgcolor=#cccccc
+| 2 || 5 || 04 || 07 || 10 || 13
+|- bgcolor=#cccccc
+| 3 || 9 || 11 || 04 || 18 || 25
+|- bgcolor=#cccccc
+| 4 || 2 || 26 || 37 || 04 || 15
+|- bgcolor=#cccccc
+| 5 || 6 || 05 || 34 || 19 || 04
+|- bgcolor=#cccccc
+| 6 || 10 || 04 || 23 || 42 || 17
+|- bgcolor=#cccccc
+| 7 || 3 || 27 || 04 || 29 || 06
+|- bgcolor=#cccccc
+| 8 || 7 || 14 || 41 || 04 || 31
+|- bgcolor=#cccccc
+| 9 || 11 || 09 || 22 || 35 || 04
+|- bgcolor=#cccccc
+| 10 || 4 || 04 || 39 || 30 || 21
+|- bgcolor=#cccccc
+| 11 || 8 || 43 || 04 || 33 || 38
+|-
+|colspan=6| '''Notes:''' This is a sample of the table matching for a 44-person tournament. Players are assigned in a linear manner to the tables in Round 1. In further rounds, note the players on Table 1 being backfilled by the people at higher tables in Round 1, and the numerical step downward. Also note the tables that Player 4 will be at in subsequent rounds, also with the numerical step upward.<br/>
+'''Balances achieved:''' Opponent, Wind, Table. This match-up is solved '''if''' the number of players is sufficiently large or prime. Works for 7 (maybe more) hanchan for 28, 44, 52, 56, 64, 68, 76++. Works for 6 hanchan with 72. Works for 5 hanchan with 20, 40, 60. Do not use with 24, 32, 36, 48.<br/>
+'''Source:''' [[User:Senechal]].
+|}
+<!-- {| class="wikitable" style="float:right; margin-left: 10px; width: 30%;"
 |-
 ! Round !! Table !! East !! South !! West !! North
@@ Line 67: / Line 117: @@
 | 7 || 7 || 24 || 41 || 01 || 18
 |-
-| 8 || 8 || 44 || 26 || 19 || 01
+|colspan=6| '''Notes:''' This is an old table for a 44-person tournament. The numbering system is by block as opposed to linear.<br/>
-|-
+'''Balances achieved:''' Same as above, except that the winds are imperfectly balanced. Balance is achieved but the player starting with East would have a speed advantage in any indivisible number of rounds (1 is obvious, 2 and 3 would always give East an advantage).<br/>
-| 9 || 9 || 01 || 20 || 28 || 36
-|-
-| 10 || 10 || 21 || 01 || 39 || 30
-|-
-| 11 || 11 || 32 || 42 || 01 || 22
-|-
-|colspan=6| '''Notes:''' This is a sample of the table matching for a 44-person tournament. As players are evenly divided in 4 blocks of shifting players, when a block exceeds the size allotted, players shuffle back. E.g.: On table 5 above, the 4th block comprises of playres 34 to 44. One group is moving forward in steps of 3, and 43+3 is 46. Naturally, there is no player 46 to take that seat and is filled with the 2nd player (44+2) of that block, player 35.<br/>
-'''Balances achieved:''' Opponent, Wind, Table. This match-up is solved '''if''' the number of players is sufficiently large or prime. Works for 7 (maybe more) hanchan for 28, 44, 52, 56, 64, 68, 76++. Works for 6 hanchan with 72. Works for 5 hanchan with 20, 40, 60. Do not use with 24, 32, 36, 48.<br/>
 '''Source:''' [[User:Senechal]].
 |}
+-->
 Dutch cycles (also called ____) serve a purpose of fairly distributing players across a set number of games, all while reducing/preventing repeats between pairs of players. This system works best when prime factors are in play, but breaks down when composite factors are used. Large player bases can mitigate some issues.