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Tournament blocks: Difference between revisions
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=== Tournament blocks === | === Tournament blocks === | ||
==== Simplest solution: Dutch cycles ==== | |||
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. | |||
The obvious flaw with this solution is that players are segregated into blocks. The method is fair as long as players draw from one pool with all entries mixed AND that the draw occurs fairly, in the presence of all players, or failing that, that the location and time of draw be published beforehand with a fair chance for all to attend. Both NMB tournaments (2011 in Utrecht) and the 2014 WRC used this method, however they both had flaws in their implementation. | |||
The general formula is that table t consists of players [t, t + n/4, t + 2n/4, t + 3n/4] in hanchan 1, 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 6. | |||
{| class="wikitable" | |||
|- | |||
! Players !! 4H !! 6H !! 8H !! 10H !! 12H !! Comment | |||
|- | |||
| 16 (4*4) || 3 / Other || Other (5) || no || no || no || Different block solution for 5 hanchan. | |||
|- | |||
| 20 (5*4) || Yes || Other (5) || no || no || no || | |||
|- | |||
| 24 (6*4) || 3 / Other || Other || Other (7) || no || no || | |||
|- | |||
| 28 (7*4) || Yes || Yes || 7 || Other (9) || no || | |||
|- style="background:#ccf" | |||
| 40 (10*4) || Yes || 5 / unkn. || unkn. || unkn. || no || | |||
|- | |||
| 44 (11*4) || Yes || Yes || Yes || Yes || 11 || | |||
|- | |||
| 52 (13*4) || Yes || Yes || Yes || Yes | 13 || | |||
|- | |||
| 68 (17*4) || Yes || Yes || Yes || Yes || 17 || | |||
|} | |||
Notes: | |||
[http://www.mathpuzzle.com/MAA/54-Golf%20Tournaments/mathgames_08_14_07.html Mathpuzzle.com] has a few non-Dutch solutions for the "Social Golfer Problem".<br /> | |||
1. For 16P in 5H: ABCD EFGH IJKL MNOP, AEIM BFJN CGKO DHLP, AFKP BELO CHIN DGJM, AGLN BHKM CEJP DFIO, AHJO BGIP CFLM DEKN.<br /> | |||
2. For 20P in 5H: ABCD EFGH IJKL MNOP QRST, AEIM BFJQ CGNR DKOS HLPT, AFOT BELR CIPS DGJM HKNQ, AJPR BHMS CEKT DFIN GLOQ, ALNS BGIT CHJO DEPQ FKMR. <br /> | |||
3. For 24P in 7H: ABKU IJSE QRCM DGFX HLNO PTVW, ACLV IKTF QSDN EHGR BMOP JUWX, ADMW ILUG QTEO FBHS CJNP KRVX, AENX IMVH QUFP GCBT DJKO LRSW, AFOR INWB QVGJ HDCU EKLP MSTX, AEPS IOXC QWHK BEDV FJLM NRTU, AHJT IPRD QXBL CFEW GKMN OSUV.<br /> | |||
4. For 28P in 9H: ABCD EFGH IJKL MNab cdef ghij klmn, AEgk BFMc Ndhl GIem HJai CKbn DLfj, AFjn BEae bfim HKcl GLMh CINk DJdg, AIci BJNn EKMj FLdm begl CGaf DHhk, AGbd BHgm ELNi achn FKfk CJej DIMl, AKeh BLbk FIag EJfl Ncjm CHMd DGin, AHNf BGjl FJbh Meik EIdn CLcg DKam, ALal BKdi GJck Mfgn HIbj CEhm DFNe, AJMm BIfh CFil DEbc GKNg HLen adjk.<br /> | |||
5. For 32P in 10H: ABCD EFGH IJKL MNPO abcd efgh ijkl mnop, AEIm BgcH DFKp kPdf Maei ChbG jNoL lJnO, Alof Bhkm DNGi FaLO MbHK CPeJ Ejcp gIdn, AciL BjdK DkbJ FgoP fGOp CIla EhMn NeHm, AgNK BElP DIoH hdiO beLp Cjfm FMcJ kaGn, AhJp BFin DcmO INbf leGK CMod EgkL jPaH, AFde BoGJ DEaf hlNc PiKm CHLn gjbO IkMp, APbn BNap DglM koce fHiJ CEKO FhIj dGLm, AjMG BIeO DhPL gaJm cfKn CFkN Eobi ldHp, AkHO BMfL Djen Flbm IPcG Cgip ENdJ hoaK. This solution also has the property that there is a pairwise exclusion: Two pots could be used to guarantee that any two players will play with everone else but not with each other. | |||
=== League play blocks === | === League play blocks === | ||