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Tournament blocks: Difference between revisions
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=== League play blocks === | === League play blocks === | ||
This section may receive heavy | This section may receive heavy edits or be deleted in the future. It is not worth the effort to consider the league issues until a far off future. | ||
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. | ||
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==== WAML-relevant summary ==== | ==== WAML-relevant summary ==== | ||
If we can get player blocks of 25♥, 30♥, 35, 40♥, 45♥, 50♥, 55 or sums of their multiples (60♥ = 25♥ + 35; 65 = 25♥ + 40; 70 = 35 + 35; 75yes; 80yes; 85♥♥yes; 90yes; 95yes; 100♥yes; ...) or a number significantly close, with 80%-100% range (or 100% -1 per heart), then we can cover the whole span from <!-- [24, 25], [28, 35], [39,40], [44, 55], [48, 50], [52, 60], [52, 65], [56, 70]... --> 48+ if we stop forming asymmetrical groups after 4 are made. <!-- up to 55 is covered by waiting, 56 is doable with 4 groups of 4 out of 13 [56, 65] ... two 35s [60, 70] ... 35 and 40 for [64, 75] ... 40s [68, 80] --> A fifth group can be drawn at 57 with no dificulty. | If we can get player blocks of 25♥, 30♥, 35, 40♥, 45♥, 50♥, 55 or sums of their multiples (60♥ = 25♥ + 35; 65 = 25♥ + 40; 70 = 35 + 35; 75yes; 80yes; 85♥♥yes; 90yes; 95yes; 100♥yes; ...) or a number significantly close, with 80%-100% range (or 100% -1 per heart), then we can cover the whole span from <!-- [24, 25], [28, 35], [39,40], [44, 55], [48, 50], [52, 60], [52, 65], [56, 70]... --> 48+ if we stop forming asymmetrical groups after 4 are made. <!-- up to 55 is covered by waiting, 56 is doable with 4 groups of 4 out of 13 [56, 65] ... two 35s [60, 70] ... 35 and 40 for [64, 75] ... 40s [68, 80] --> A fifth group can be drawn at 57 with no dificulty. | ||
==== 2021 Canada WRC options ==== | |||
With the 2020 pandemic forcing a lot of play online, newer interest has been developing into launching a balanced league. | |||
Some new results have come up allowing more flexibility in league play, within reason. The parameters involve a 5-session season, with an intended minimum group size of 16. Data provided in braces, 0-indexed, if differing from above solutions. General descriptors without data remain 1-indexed. | |||
{| class="wikitable" | |||
|- | |||
! Min. Players !! Max Players !! Mechanism !! Comment | |||
| 16 || 19 || 4P perfect + AABBB + BBCCD + CCAAC || First 16 players play each other without repeats. Players 17-19 have between 6-9 duplicates, no triplicates. | |||
|- | |||
| 20 || 25 || Dutch cycle for 20 + CCABD + AEDCA + BDBDC + DBCEE + EAEAB || 20 and 21 have zero duplicates. 22-25 have 5 duplicates, and no triplicates. | |||
|- | |||
| 26 || 27 || Mix and randomize || {TBD.} | |||
|- | |||
| 28 || 28 || Use 4P || | |||
|- | |||
| 29 || 30 || Use 5P || For 29 players, ignore 30th player in grid, those sessions are 4P | |||
|- | |||
| 31 || 35 || Use 5P grid for 35 || | |||
|- | |||
| 36 || 40 || Use 5P grid for 40 || Grid can ignore last 5 players. | |||
|} | |||
== External links == | == External links == | ||