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Tournament blocks: Difference between revisions
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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.
m (→Blocks of 4: 28 block, first 5.... eh, closest thing to perfect balance. Try to do better.) |
(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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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. | 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. | ||
==== | ==== 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 !! | ! 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 | |||
|- | |- | ||
| | | 20 || 4 || 6/7 || 18,11,07,03, 04,12,20,06, 17,13,02,15, 14,01,05,09, 10,16,08,19 | ||
|- | |- | ||
| | | 20 || 5 || 6/7 || 08,19,12,13, 20,15,09,03, 07,01,18,14, 11,06,04,16, 02,05,17,10 | ||
|- | |- | ||
| | | 20 || 6 || 6/7 || 07,09,13,01, 15,19,10,06, 02,08,16,18, 05,20,11,17, 03,04,14,12 | ||
|- | |- | ||
| | | 20 || 7 || 7/7 || 04,17,08,09, 12,18,05,15, 11,14,19,02, 06,13,01,20, 10,16,03,07 | ||
|- | |- | ||
| | |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 || | | 20 || 1 || 5 || ABCD EFGH IJKL MNOP QRST || | ||
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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. | 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 | ! Players !! Round !! Of !! Match-ups | ||