1751:, etc.; to ensure fairness, this must alternate between rounds since competitor 1 is always on the first row. If, say, competitors 3 and 8 were unable to fulfil their fixture in the third round, it would need to be rescheduled outside the other rounds, since both competitors would already be facing other opponents in those rounds. More complex scheduling constraints may require more complex algorithms. This schedule is applied in chess and draughts tournaments of rapid games, where players physically move round a table. In France this is called the
401:
to play out their remaining games. Thus games are played late in the competition between competitors with no remaining chance of success. Moreover, some later matches will pair one competitor who has something left to play for against another who does not. It may also be possible for a competitor to play the strongest opponents in a round robin in quick succession while others play them intermittently with weaker opposition. This asymmetry means that playing the same opponents is not necessarily completely equitable.
3652:
40:
289:
429:, having qualified for the next round, were ejected from the competition for attempting to lose in the round robin stage to avoid compatriots and better ranked opponents. The round robin stage at the Olympics was a new introduction, and these potential problems were readily known prior to the tournament; changes were made prior to the next Olympics to prevent a repeat of these events.
421:
Further issues arise where a round-robin is used as a qualifying round within a larger tournament. A competitor already qualified for the next stage before its last game may either not try hard (in order to conserve resources for the next phase) or even deliberately lose (if the scheduled next-phase
2040:
This schedule can also be represented as a (n-1, n-1) table, expressing a round in which players meets each other. For example, player 7 plays against player 11 in round 4. If a player meets itself, then this shows a bye or a game against player n. All games in a round constitutes a diagonal in the
1758:
The schedule can also be used for "asynchronous" round-robin tournaments where all games take place at different times (for example, because there is only one venue). The games are played from left to right in each round, and from the first round to the last. When the number of competitors is even,
400:
Other issues stem from the difference between the theoretical fairness of the round robin format and practice in a real event. Since the victor is gradually arrived at through multiple rounds of play, teams who perform poorly, who might have been quickly eliminated from title contention, are forced
365:
Moreover, in tournaments such as the FIFA or ICC World Cups, a first round stage consisting of a number of mini round robins between groups of 4 teams guards against the possibility of a team travelling possibly thousands of miles only to be eliminated after just one poor performance in a straight
349:
In theory, a round-robin tournament is the fairest way to determine the champion from among a known and fixed number of contestants. Each contestant, whether player or team, has equal chances against all other opponents because there is no prior seeding of contestants that will preclude a match
392:
The main disadvantage of a round robin tournament is the time needed to complete it. Unlike a knockout tournament where half of the participants are eliminated after each round, a round robin requires one round less than the number of participants. For instance, a tournament of 16 teams can be
1925:
positions. This schedule is easily generated manually. To construct the next round, the last player, number 8 in the first round, moves to the head of the table, followed by player 9 against player 7, player 10 against 6, until player 1 against player 2. Arithmetically, this equates to adding
437:
Another disadvantage, especially in smaller round-robins, is the "circle of death", where teams cannot be separated on a head-to-head record. In a three-team round-robin, where A defeats B, B defeats C, and C defeats A, all three competitors will have a record of one win and one loss, and a
1759:
this schedule performs well with respect to quality and fairness measures such as the amount of rest between games. On the other hand, when the number of competitors is odd, it does not perform so well and a different schedule is superior with respect to these measures.
358:
The system is also better for ranking all participants, not just determining the winner. This is helpful to determine the final rank of all competitors, from strongest to weakest, for purposes of qualification for another stage or competition as well as for prize money.
92:. The term is rarely used when all participants play one another more than twice, and is never used when one participant plays others an unequal number of times, as is the case in almost all of the major North American professional sports leagues.
354:
since one or two bad performances need not ruin a competitor's chance of ultimate victory. Final records of participants are more accurate, in the sense that they represent the results over a longer period against the same opposition.
404:
There is also no scheduled showcase final match unless (by coincidence) two competitors meet in the last match of the tournament, with the result of that match determining the championship. A notable instance of such an event was the
522:
377:
Round-robins can suffer from being too long compared to other tournament types, and with later scheduled games potentially not having any substantial meaning. They may also require tie-breaking procedures.
696:
609:
362:
In team sports, the round-robin major league champions are generally regarded as the "best" team in the land, rather than the cup winners, whose tournaments usually follow a single-elimination format.
426:
4754:"C. General Rules and Technical Recommendations for Tournaments / 05. General Regulations for Competitions / General Regulations for Competitions. Annex 1: Details of Berger Table /".
4282:
The pairing tables were published as an annex concerning the arrangements for the holding of master tournaments. Schurig did not provide a proof nor a motivation for his algorithm.
369:
In the circle of death it is possible that no champion emerges from a round-robin tournament, even if there is no draw, but most sports have tie-breaker systems which resolve this.
3686:
venue = 1 ββββββββββββββββββββββββββββββββββββββββββββββββββββββ 1βΟ >>> 2β13 >>> 3β12 >>> 4β11 >>> 5β10 >>> 6β9 >>> 7β8
1564:
1036:
1951:
1923:
384:
attempt to combine elements of the round-robin and elimination formats, to provide a worthy champion using fewer rounds than a round-robin, while allowing draws and losses.
114:
leagues in the world are organized on a double round-robin basis, in which every team plays all others in its league once at home and once away. This system is also used in
2035:
2003:
1745:
574:
1065:
4832:
4795:
4005:
3833:
3807:
3781:
3753:
1636:
1590:
1488:
1428:
1368:
1348:
1288:
1145:
4277:
3979:
3727:
1971:
1699:
1676:
1656:
1610:
1528:
1508:
1468:
1448:
1408:
1388:
1328:
1308:
1268:
1248:
1228:
1205:
1185:
1165:
1125:
1105:
1085:
1003:
980:
957:
653:
633:
542:
472:
397:
tournament format requires 30 (or 31) matches, but a round-robin would require 15 rounds (i.e. 120 matches) to finish if each competitor faces each other once.
366:
knockout system. The top one, two, or occasionally three teams in these groups then proceed to a straight knockout stage for the remainder of the tournament.
768:
Next, one of the competitors in the first or last column of the table is fixed (number one in this example) and the others rotated clockwise one position:
4445:
4007:
in the previous table (the last row is populated with numbers from the first row in the original table), but in the reverse order (from right to left).
174:
decided in 2005 and in 2007 on an eight-player double round-robin tournament where each player faces every other player once as white and once as black.
241:
306:
4641:
188:
LIDOM (Baseball Winter League in the
Dominican Republic) plays an 18-fold round robin as a semi final tournament between four classified teams.
95:
In the United
Kingdom, a round-robin tournament has been called an American tournament in sports such as tennis or billiards which usually have
410:
1704:
If there are an odd number of competitors, a dummy competitor can be added, whose scheduled opponent in a given round does not play and has a
4671:
4340:
883:
825:
770:
712:
3701:
If the number of players is odd, the player in the first venue gets a bye. If the number is even, an added player (Ο) becomes the opponent.
237:
959:
of competitors this algorithm realizes every possible combination of them (equivalently, that all pairs realized are pairwise different).
206:
88:
schedule, each participant plays every other participant once. If each participant plays all others twice, this is frequently called a
4677:
4498:
477:
4940:
4532:
4428:
4279:
is alternatingly substituted for the first and second positions, whereas if the number of competitors is odd a bye is used instead.
328:
4566:
3698:
2βΟ >>> 3β1 >>> 4β13 >>> 5β12 >>> 6β11 >>> 7β10 >>> 8β9 Οβ9 >>> ...
658:
55:
is a competition format in which each contestant meets every other participant, usually in turn. A round-robin contrasts with an
710:
to create a schedule for a round-robin tournament. All competitors are assigned to numbers, and then paired in the first round:
579:
4291:
191:
310:
4583:
4524:
How to succeed in tennis without really trying: the easy tennismanship way to do all the things no tennis pro can teach you
3809:
horizontal rows. Then he populates it starting from the top left corner by repeating the sequence of numbers from 1 up to
261:
115:
4935:
442:, where all four teams finished with a record of one win, one draw, and one loss. This phenomenon is analogous to the
439:
185:
plays a 16-fold round robin, with each of the 10 teams playing each other 16 times for a total of 144 games per team.
1898:
This constitutes a schedule where player 14 has a fixed position, and all other players are rotated counterclockwise
346:
The champion in a round-robin tournament is the contestant that wins the most games, except when draws are possible.
4335:
4323:
123:
299:
4317:
4311:
1708:. The schedule can therefore be computed as though the dummy were an ordinary player, either fixed or rotating.
1038:
of times the rotation has to be carried out in order that one competitor arrives at the position the other had.
171:
4320:, a variation of the Swiss system that incorporates pre-tournament rankings to prevent early lopsided pairings
3692:Οβ8 >>> 9β7 >>> 10β6 >>> 11β5 >>> 12β4 >>> 13β3 >>> 1β2
1658:
pair at the same position. Clearly, these pairs are pairwise different. The conclusion is that every distance-
1747:
will generate a complete schedule. The upper and lower rows can indicate home/away in sports, white/black in
4460:
381:
4366:
351:
245:
56:
1536:
1008:
230:
4894:
3651:
110:
In sports with a large number of competitive matches per season, double round-robins are common. Most
39:
4630:
4351:
4297:
111:
28:
4332:, a series of tournament formats that combine features of single- and double-elimination tournaments
1929:
1901:
4658:
4361:
4345:
3683:
To easily remember this method, the following mnemonic can be used. Starting from the first round,
406:
4826:
4789:
4721:
4703:
1775:, are widely used in the planning of tournaments. Berger published the pairing tables in his two
394:
210:
139:
96:
3668:
422:
opponent for a lower-placed qualifier is perceived to be easier than for a higher-placed one).
4872:
4814:
4777:
4667:
4528:
4494:
4424:
443:
249:
234:
226:
201:
are conducted on a round-robin basis. Examples with single round-robin scheduling include the
127:
4486:
194:
usually go by number of matches won and drawn, with any of a variety of tiebreaker criteria.
4713:
4473:
American
Tournament: A tournament in which each player must meet in turn every other player.
4356:
3660:
1712:
611:
games can be run concurrently, provided there exist sufficient resources (e.g. courts for a
275:
Season ending tennis tournaments also use a round robin format prior to the semi on stages.
143:
2008:
1976:
1718:
547:
4329:
1044:
269:
265:
4912:
Ahrens, Wilhelm (1901). "XIV Anordnungs
Probleme, Β§ 1 Anordnungen im Kreise, Aufgabe 2".
4421:
Standardizing
Terminology for Better Communication: Practice, Applied Theory, and Results
3984:
3812:
3786:
3758:
3732:
1615:
1569:
438:
tiebreaker will need to be used to separate the teams. This famously happened during the
135:
4913:
4611:
4555:
1473:
1413:
1353:
1333:
1273:
1130:
962:
First, the algorithm obviously realizes every pair of competitors if one of them equals
881:
This is repeated until when the next iteration would lead back to the initial pairings:
4845:
4738:
4262:
3964:
3712:
3672:
1956:
1781:
1684:
1661:
1641:
1595:
1513:
1493:
1453:
1433:
1393:
1373:
1313:
1293:
1253:
1233:
1213:
1190:
1170:
1150:
1110:
1090:
1070:
988:
965:
942:
638:
618:
527:
457:
202:
119:
4259:
Then the first column is updated: if the number of competitors is even, player number
221:) in the Southern Hemisphere during its past iterations as Super 12 and Super 14 (but
4929:
1772:
131:
102:
A round-robin tournament with four players is sometimes called "quad" or "foursome".
4725:
4588:
1705:
350:
between any given pair. The element of luck is seen to be reduced as compared to a
4881:
17:
4522:
4403:
4390:
Webster's Third New
International Dictionary of the English Language, Unabridged
288:
218:
214:
59:, wherein participants are eliminated after a certain number of wins or losses.
4717:
3961:
Then to get the opponents a second table is constructed. Every horizontal row
257:
253:
198:
178:
159:
4876:
4818:
4781:
4694:
Suksompong, Warut (2016). "Scheduling asynchronous round-robin tournaments".
4918:(in German). Leipzig: B. G. Teubner. pp. 259β272. ark:/13960/t2w37mv93.
4811:
Schach-Jahrbuch fΓΌr 1899/1900: Fortsetzung des Schach-Jahrbuches fΓΌr 1892/93
3663:
in as a recreational mathematics puzzle. Lucas, who describes the method as
707:
155:
1752:
182:
167:
151:
4863:
Schurig, Richard (1886). "Die
Paarung der Theilnehmer eines Turniers".
3648:
The above schedule can also be represented by a graph, as shown below:
1768:
313: in this section. Unsourced material may be challenged and removed.
256:
leagues outside the United States, including the regular season of the
163:
4467:. English Amateur Billiards Association. February 1912. Archived from
612:
474:
is the number of competitors, a pure round robin tournament requires
393:
completed in just 4 rounds (i.e. 15 matches) in a knockout format; a
4755:
1779:(Chess Annals), with due reference to its inventor Richard Schurig.
4708:
4584:"Eight Olympic badminton players disqualified for 'throwing games'"
3650:
1748:
147:
38:
4468:
3705:
Original construction of pairing tables by
Richard Schurig (1886)
1230:) can only be taken by competitors of a fixed distance. In round
4666:(in French). FΓ©dΓ©ration FranΓ§aise des Γchecs. 2008. p. 56.
517:{\displaystyle {\begin{matrix}{\frac {n}{2}}\end{matrix}}(n-1)}
99:(or "knockout") tournaments, although this is now rarely done.
4348:, where each member of one team plays each member of the other
4326:, a type of single-elimination tournament featuring four teams
282:
3671:. Lucas also included an alternative solution by means of a
691:{\displaystyle {\begin{matrix}{\frac {n-1}{2}}\end{matrix}}}
4369:, for round robin implications of different scoring systems
4744:, examples of round robin schedules up to 30 participants.
604:{\displaystyle {\begin{matrix}{\frac {n}{2}}\end{matrix}}}
4449:. New York: Harper & Brother Publishers. p. 786.
3667:, attributes the solution to Felix Walecki, a teacher at
244:(which currently has 9 members). The group phases of the
698:
games, and one competitor having no game in that round.
43:
Example of a round-robin tournament with 10 participants
4901:(in French). Paris: Gauthier-Villars. pp. 161β197.
4461:"A Glossary of Terms Used in Connection with Billiards"
663:
584:
482:
4419:
Strehlov, Richard A; Wright, Sue Ellen, eds. (1993).
4265:
3987:
3967:
3815:
3789:
3761:
3735:
3715:
2011:
1979:
1959:
1932:
1904:
1721:
1687:
1664:
1644:
1618:
1598:
1572:
1539:
1516:
1496:
1476:
1456:
1436:
1416:
1396:
1376:
1356:
1336:
1316:
1296:
1276:
1256:
1236:
1216:
1193:
1173:
1153:
1133:
1113:
1093:
1073:
1047:
1011:
991:
968:
945:
661:
641:
621:
582:
550:
530:
480:
460:
4882:
4408:. Vol. 2. New York: The Editors. pp. 1, 3.
77:('ribbon'). Over time, the term became idiomized to
3835:. Here is an example table for 7 or 8 competitors:
1210:In a round, a non-leftmost position (not including
252:are contested as a double round-robin, as are most
4271:
3999:
3973:
3827:
3801:
3775:
3747:
3721:
2029:
1997:
1973:. When the result of the addition is greater than
1965:
1953:to the previous row, with the exception of player
1945:
1917:
1739:
1693:
1670:
1650:
1630:
1604:
1584:
1558:
1522:
1502:
1482:
1462:
1442:
1422:
1402:
1382:
1362:
1342:
1322:
1302:
1282:
1262:
1250:of the example, in the second position competitor
1242:
1222:
1199:
1179:
1159:
1139:
1119:
1099:
1079:
1059:
1030:
997:
974:
951:
690:
647:
627:
603:
568:
536:
516:
466:
4640:. Mount Saint Mary College: GRAPH THEORY DAY 48.
4631:"Designing Schedules for Leagues and Tournaments"
3659:Both the graph and the schedule were reported by
4858:
4856:
4314:, mathematical model of a round-robin tournament
233:, major Twenty-20 Cricket tournament, and many
4612:"UC Berkeley Quiz Bowl: How To Make Schedules"
1005:competitors, let their distance be the number
1767:Alternatively Berger tables, named after the
1711:Instead of rotating one position, any number
8:
3755:of competitors, Schurig builds a table with
72:
4556:"An Introduction to USCF-Rated Tournaments"
4294:, including details of tie-breaking systems
264:has used a double round-robin for both its
225:in its later 15- and 18-team formats), the
27:For the application to voting methods, see
4831:: CS1 maint: location missing publisher (
4794:: CS1 maint: location missing publisher (
4423:. Vol. 1166. ASTM. pp. 336β337.
3981:is populated with the same numbers as row
260:(as well as its former Top 16 phase); the
4707:
4660:Le livre de l'arbitre : Γ©dition 2008
4446:Brewer's Dictionary of Phrase & Fable
4385:
4383:
4264:
3986:
3966:
3814:
3788:
3765:
3760:
3734:
3714:
2010:
1978:
1958:
1933:
1931:
1905:
1903:
1720:
1686:
1663:
1643:
1638:rounds and they all realize one distance-
1617:
1597:
1571:
1546:
1538:
1515:
1495:
1475:
1455:
1435:
1415:
1395:
1375:
1355:
1335:
1315:
1295:
1275:
1255:
1235:
1215:
1192:
1172:
1152:
1132:
1112:
1092:
1072:
1046:
1018:
1010:
990:
967:
944:
827:Round 3. (1 plays 12, 13 plays 11, ... )
772:Round 2. (1 plays 13, 14 plays 12, ... )
666:
662:
660:
640:
620:
587:
583:
581:
549:
529:
485:
481:
479:
459:
329:Learn how and when to remove this message
4300:, a balanced tournament design of order
4135:
4009:
3837:
3020:
2047:
885:Round 13. (1 plays 2, 3 plays 14, ... )
714:Round 1. (1 plays 14, 2 plays 13, ... )
4915:Mathematische Unterhaltungen und Spiele
4647:from the original on February 23, 2022.
4572:from the original on February 23, 2022.
4392:(1971, G. & C. Merriam Co), p.1980.
4379:
1755:-Berger system (Système Rutch-Berger).
1330:, this position is held by competitors
427:2012 Olympics Women's doubles badminton
4824:
4813:(in German). Leipzig. pp. 21β27.
4787:
4776:(in German). Leipzig. pp. 26β31.
4683:from the original on January 19, 2013.
122:and the continental tournaments (e.g.
4341:List of round-robin chess tournaments
1390:, etc. Similarly, the next position (
199:pool stages within a wider tournament
7:
311:adding citations to reliable sources
2043:
1559:{\displaystyle k<{\frac {n}{2}}}
1031:{\displaystyle k<{\frac {n}{2}}}
207:UEFA European Football Championship
4629:Dinitz, Jeff (November 13, 2004).
4563:The United States Chess Federation
118:for major tournaments such as the
25:
4493:. Allied Publishers. p. 38.
3655:Round Robin Schedule Span Diagram
1701:, hence, every pair is realized.
4491:Chambers 21st Century Dictionary
287:
71:is derived from the French term
4292:Group tournament ranking system
3689:the next round is constructed:
1510:, etc.) can only hold distance-
298:needs additional citations for
177:In a more extreme example, the
2024:
2012:
1992:
1980:
1946:{\displaystyle {\frac {n}{2}}}
1918:{\displaystyle {\frac {n}{2}}}
1734:
1722:
706:The circle method is a simple
563:
551:
511:
499:
142:). There are also round-robin
1:
4405:Official Lawn Tennis Bulletin
4402:Orcutt, William Dana (1895).
982:(the non-moving competitor).
4774:Schach-Jahrbuch fΓΌr 1892/93
4696:Operations Research Letters
440:1994 FIFA World Cup Group E
4957:
4336:Duplicate bridge movements
4324:Shaughnessy playoff system
4150:
4147:
4144:
4141:
4024:
4021:
4018:
4015:
3852:
3849:
3846:
3843:
411:between Uruguay and Brazil
192:Group tournaments rankings
124:UEFA European Championship
26:
4899:RΓ©crΓ©ations MathΓ©matiques
4895:"Les jeux de demoiselles"
4718:10.1016/j.orl.2015.12.008
4638:Home Page for Jeff Dinitz
4318:McMahon system tournament
4312:Tournament (graph theory)
4240:
4223:
4206:
4189:
4172:
4155:
4138:
4133:By merging above tables:
4114:
4097:
4080:
4063:
4046:
4029:
4012:
3942:
3925:
3908:
3891:
3874:
3857:
3840:
3598:
3554:
3510:
3466:
3422:
3378:
3334:
3290:
3246:
3202:
3158:
3114:
3070:
3029:
2949:
2881:
2813:
2745:
2677:
2609:
2541:
2473:
2405:
2337:
2269:
2201:
2133:
2056:
1870:
1865:
1862:
1836:
1810:
1784:
544:is even, then in each of
213:(2004β2009) in football,
34:Type of sports tournament
4941:Chess tournament systems
382:Swiss system tournaments
172:World Chess Championship
4893:Lucas, Edouard (1883).
4809:Berger, Johann (1899).
4772:Berger, Johann (1893).
4521:Mead, Shepherd (1977).
1370:, also having distance
985:Next, for pairs of non-
53:all-play-all tournament
4865:Deutsche Schachzeitung
4527:. McKay. p. 130.
4367:Three points for a win
4273:
4001:
3975:
3829:
3803:
3777:
3749:
3723:
3656:
2031:
1999:
1967:
1947:
1919:
1741:
1695:
1672:
1652:
1632:
1606:
1586:
1560:
1524:
1504:
1484:
1464:
1444:
1424:
1404:
1384:
1364:
1344:
1324:
1304:
1284:
1264:
1244:
1224:
1201:
1181:
1161:
1141:
1121:
1101:
1081:
1061:
1041:In the example given (
1032:
999:
976:
953:
692:
649:
635:is odd, there will be
629:
605:
570:
538:
518:
468:
262:United Football League
246:UEFA club competitions
73:
57:elimination tournament
49:round-robin tournament
44:
4565:. February 23, 2006.
4487:"American tournament"
4274:
4002:
3976:
3830:
3804:
3778:
3750:
3724:
3654:
3022:Round Robin Schedule
2032:
2030:{\displaystyle (n-1)}
2000:
1998:{\displaystyle (n-1)}
1968:
1948:
1920:
1742:
1740:{\displaystyle (n-1)}
1696:
1681:This holds for every
1673:
1653:
1633:
1607:
1587:
1566:, there are exactly
1561:
1525:
1505:
1485:
1465:
1445:
1425:
1405:
1385:
1365:
1345:
1325:
1305:
1285:
1265:
1245:
1225:
1202:
1182:
1162:
1142:
1122:
1102:
1082:
1062:
1033:
1000:
977:
954:
693:
650:
630:
606:
571:
569:{\displaystyle (n-1)}
539:
519:
469:
231:Indian Premier League
136:CONMEBOL Copa AmΓ©rica
42:
4616:www.ocf.berkeley.edu
4298:Combinatorial design
4263:
3985:
3965:
3813:
3787:
3759:
3733:
3713:
3665:simple and ingenious
2009:
1977:
1957:
1930:
1902:
1719:
1685:
1662:
1642:
1616:
1596:
1570:
1537:
1514:
1494:
1474:
1454:
1434:
1414:
1394:
1374:
1354:
1334:
1314:
1294:
1290:, their distance is
1274:
1254:
1234:
1214:
1191:
1171:
1151:
1147:and it has distance
1131:
1111:
1091:
1071:
1060:{\displaystyle n=14}
1045:
1009:
989:
966:
943:
939:With an even number
659:
639:
619:
580:
548:
528:
478:
458:
450:Scheduling algorithm
307:improve this article
112:association football
4362:Condorcet criterion
4346:Scheveningen system
4000:{\displaystyle x+1}
3828:{\displaystyle n-1}
3802:{\displaystyle n-1}
3776:{\displaystyle n/2}
3748:{\displaystyle n-1}
3709:For an even number
3023:
2050:
1631:{\displaystyle n-1}
1585:{\displaystyle n-1}
886:
828:
773:
715:
407:1950 FIFA World Cup
238:college conferences
4936:Tournament systems
4471:on March 3, 2022.
4269:
3997:
3971:
3825:
3799:
3783:vertical rows and
3773:
3745:
3719:
3657:
3021:
2048:
2027:
1995:
1963:
1943:
1915:
1737:
1691:
1678:pair is realized.
1668:
1648:
1628:
1602:
1592:pairs of distance
1582:
1556:
1520:
1500:
1483:{\displaystyle 11}
1480:
1460:
1440:
1423:{\displaystyle 12}
1420:
1400:
1380:
1363:{\displaystyle 12}
1360:
1343:{\displaystyle 14}
1340:
1320:
1300:
1283:{\displaystyle 13}
1280:
1260:
1240:
1220:
1197:
1177:
1157:
1140:{\displaystyle 14}
1137:
1117:
1097:
1077:
1057:
1028:
995:
972:
949:
884:
826:
771:
713:
688:
686:
655:rounds, each with
645:
625:
601:
599:
566:
534:
514:
497:
464:
446:in voting theory.
425:Four pairs in the
395:double elimination
140:CAF Cup of Nations
97:single-elimination
90:double round-robin
86:single round-robin
45:
18:Double round-robin
4673:978-2-915853-01-8
4352:Copeland's method
4272:{\displaystyle n}
4257:
4256:
4131:
4130:
3974:{\displaystyle x}
3959:
3958:
3729:or an odd number
3722:{\displaystyle n}
3646:
3645:
3642:
3641:
3017:
3016:
1966:{\displaystyle n}
1941:
1913:
1896:
1895:
1777:Schach-JahrbΓΌcher
1694:{\displaystyle k}
1671:{\displaystyle k}
1651:{\displaystyle k}
1605:{\displaystyle k}
1554:
1523:{\displaystyle 4}
1503:{\displaystyle 2}
1463:{\displaystyle 2}
1443:{\displaystyle 1}
1403:{\displaystyle 3}
1383:{\displaystyle 2}
1323:{\displaystyle 2}
1303:{\displaystyle 2}
1263:{\displaystyle 2}
1243:{\displaystyle 1}
1223:{\displaystyle 1}
1200:{\displaystyle 9}
1180:{\displaystyle 8}
1160:{\displaystyle 6}
1120:{\displaystyle 3}
1100:{\displaystyle 1}
1080:{\displaystyle 2}
1026:
998:{\displaystyle 1}
975:{\displaystyle 1}
952:{\displaystyle n}
937:
936:
879:
878:
824:
823:
766:
765:
682:
648:{\displaystyle n}
628:{\displaystyle n}
595:
537:{\displaystyle n}
493:
467:{\displaystyle n}
444:Condorcet paradox
388:Tournament length
339:
338:
331:
250:Copa Libertadores
235:American football
227:Cricket World Cup
170:tournaments. The
128:CONCACAF Gold Cup
29:Copeland's method
16:(Redirected from
4948:
4920:
4919:
4909:
4903:
4902:
4890:
4884:
4880:
4860:
4851:
4850:
4843:
4837:
4836:
4830:
4822:
4806:
4800:
4799:
4793:
4785:
4769:
4763:
4761:
4751:
4745:
4743:
4736:
4730:
4729:
4711:
4691:
4685:
4684:
4682:
4665:
4655:
4649:
4648:
4646:
4635:
4626:
4620:
4619:
4608:
4602:
4601:
4599:
4597:
4592:. August 1, 2012
4580:
4574:
4573:
4571:
4560:
4552:
4546:
4545:
4543:
4541:
4518:
4512:
4511:
4509:
4507:
4482:
4476:
4475:
4465:Billiard Monthly
4457:
4451:
4450:
4441:
4435:
4434:
4416:
4410:
4409:
4399:
4393:
4387:
4357:Condorcet method
4278:
4276:
4275:
4270:
4136:
4010:
4006:
4004:
4003:
3998:
3980:
3978:
3977:
3972:
3838:
3834:
3832:
3831:
3826:
3808:
3806:
3805:
3800:
3782:
3780:
3779:
3774:
3769:
3754:
3752:
3751:
3746:
3728:
3726:
3725:
3720:
3024:
2051:
2049:Diagonal Scheme
2044:
2036:
2034:
2033:
2028:
2005:, then subtract
2004:
2002:
2001:
1996:
1972:
1970:
1969:
1964:
1952:
1950:
1949:
1944:
1942:
1934:
1924:
1922:
1921:
1916:
1914:
1906:
1782:
1746:
1744:
1743:
1738:
1713:relatively prime
1700:
1698:
1697:
1692:
1677:
1675:
1674:
1669:
1657:
1655:
1654:
1649:
1637:
1635:
1634:
1629:
1611:
1609:
1608:
1603:
1591:
1589:
1588:
1583:
1565:
1563:
1562:
1557:
1555:
1547:
1529:
1527:
1526:
1521:
1509:
1507:
1506:
1501:
1489:
1487:
1486:
1481:
1469:
1467:
1466:
1461:
1449:
1447:
1446:
1441:
1429:
1427:
1426:
1421:
1409:
1407:
1406:
1401:
1389:
1387:
1386:
1381:
1369:
1367:
1366:
1361:
1349:
1347:
1346:
1341:
1329:
1327:
1326:
1321:
1309:
1307:
1306:
1301:
1289:
1287:
1286:
1281:
1269:
1267:
1266:
1261:
1249:
1247:
1246:
1241:
1229:
1227:
1226:
1221:
1206:
1204:
1203:
1198:
1186:
1184:
1183:
1178:
1166:
1164:
1163:
1158:
1146:
1144:
1143:
1138:
1126:
1124:
1123:
1118:
1106:
1104:
1103:
1098:
1086:
1084:
1083:
1078:
1066:
1064:
1063:
1058:
1037:
1035:
1034:
1029:
1027:
1019:
1004:
1002:
1001:
996:
981:
979:
978:
973:
958:
956:
955:
950:
887:
829:
774:
716:
697:
695:
694:
689:
687:
683:
678:
667:
654:
652:
651:
646:
634:
632:
631:
626:
615:tournament). If
610:
608:
607:
602:
600:
596:
588:
575:
573:
572:
567:
543:
541:
540:
535:
523:
521:
520:
515:
498:
494:
486:
473:
471:
470:
465:
334:
327:
323:
320:
314:
291:
283:
76:
21:
4956:
4955:
4951:
4950:
4949:
4947:
4946:
4945:
4926:
4925:
4924:
4923:
4911:
4910:
4906:
4892:
4891:
4887:
4862:
4861:
4854:
4848:
4846:Richard Schurig
4844:
4840:
4823:
4808:
4807:
4803:
4786:
4771:
4770:
4766:
4762:(contents page)
4753:
4752:
4748:
4741:
4739:Table de Berger
4737:
4733:
4693:
4692:
4688:
4680:
4674:
4663:
4657:
4656:
4652:
4644:
4633:
4628:
4627:
4623:
4610:
4609:
4605:
4595:
4593:
4582:
4581:
4577:
4569:
4558:
4554:
4553:
4549:
4539:
4537:
4535:
4520:
4519:
4515:
4505:
4503:
4501:
4484:
4483:
4479:
4459:
4458:
4454:
4443:
4442:
4438:
4431:
4418:
4417:
4413:
4401:
4400:
4396:
4388:
4381:
4376:
4330:McIntyre system
4288:
4261:
4260:
3983:
3982:
3963:
3962:
3811:
3810:
3785:
3784:
3757:
3756:
3731:
3730:
3711:
3710:
3707:
3699:
3693:
3687:
3681:
3669:LycΓ©e Condorcet
2007:
2006:
1975:
1974:
1955:
1954:
1928:
1927:
1900:
1899:
1765:
1717:
1716:
1683:
1682:
1660:
1659:
1640:
1639:
1614:
1613:
1594:
1593:
1568:
1567:
1535:
1534:
1512:
1511:
1492:
1491:
1472:
1471:
1452:
1451:
1432:
1431:
1412:
1411:
1392:
1391:
1372:
1371:
1352:
1351:
1332:
1331:
1312:
1311:
1292:
1291:
1272:
1271:
1252:
1251:
1232:
1231:
1212:
1211:
1189:
1188:
1169:
1168:
1149:
1148:
1129:
1128:
1109:
1108:
1089:
1088:
1069:
1068:
1043:
1042:
1007:
1006:
987:
986:
964:
963:
941:
940:
704:
685:
684:
668:
657:
656:
637:
636:
617:
616:
598:
597:
578:
577:
546:
545:
526:
525:
496:
495:
476:
475:
456:
455:
452:
435:
433:Circle of death
419:
417:Qualified teams
390:
375:
352:knockout system
344:
335:
324:
318:
315:
304:
292:
281:
108:
65:
35:
32:
23:
22:
15:
12:
11:
5:
4954:
4952:
4944:
4943:
4938:
4928:
4927:
4922:
4921:
4904:
4885:
4852:
4838:
4801:
4764:
4746:
4731:
4686:
4672:
4650:
4621:
4603:
4575:
4547:
4533:
4513:
4500:978-0550106254
4499:
4477:
4452:
4436:
4429:
4411:
4394:
4378:
4377:
4375:
4372:
4371:
4370:
4364:
4359:
4354:
4349:
4343:
4338:
4333:
4327:
4321:
4315:
4309:
4295:
4287:
4284:
4268:
4255:
4254:
4251:
4248:
4245:
4242:
4238:
4237:
4234:
4231:
4228:
4225:
4221:
4220:
4217:
4214:
4211:
4208:
4204:
4203:
4200:
4197:
4194:
4191:
4187:
4186:
4183:
4180:
4177:
4174:
4170:
4169:
4166:
4163:
4160:
4157:
4153:
4152:
4149:
4146:
4143:
4140:
4129:
4128:
4125:
4122:
4119:
4116:
4112:
4111:
4108:
4105:
4102:
4099:
4095:
4094:
4091:
4088:
4085:
4082:
4078:
4077:
4074:
4071:
4068:
4065:
4061:
4060:
4057:
4054:
4051:
4048:
4044:
4043:
4040:
4037:
4034:
4031:
4027:
4026:
4023:
4020:
4017:
4014:
3996:
3993:
3990:
3970:
3957:
3956:
3953:
3950:
3947:
3944:
3940:
3939:
3936:
3933:
3930:
3927:
3923:
3922:
3919:
3916:
3913:
3910:
3906:
3905:
3902:
3899:
3896:
3893:
3889:
3888:
3885:
3882:
3879:
3876:
3872:
3871:
3868:
3865:
3862:
3859:
3855:
3854:
3851:
3848:
3845:
3842:
3824:
3821:
3818:
3798:
3795:
3792:
3772:
3768:
3764:
3744:
3741:
3738:
3718:
3706:
3703:
3697:
3691:
3685:
3680:
3677:
3673:sliding puzzle
3644:
3643:
3640:
3639:
3636:
3633:
3630:
3627:
3624:
3621:
3618:
3615:
3612:
3609:
3606:
3603:
3600:
3596:
3595:
3592:
3589:
3586:
3583:
3580:
3577:
3574:
3571:
3568:
3565:
3562:
3559:
3556:
3552:
3551:
3548:
3545:
3542:
3539:
3536:
3533:
3530:
3527:
3524:
3521:
3518:
3515:
3512:
3508:
3507:
3504:
3501:
3498:
3495:
3492:
3489:
3486:
3483:
3480:
3477:
3474:
3471:
3468:
3464:
3463:
3460:
3457:
3454:
3451:
3448:
3445:
3442:
3439:
3436:
3433:
3430:
3427:
3424:
3420:
3419:
3416:
3413:
3410:
3407:
3404:
3401:
3398:
3395:
3392:
3389:
3386:
3383:
3380:
3376:
3375:
3372:
3369:
3366:
3363:
3360:
3357:
3354:
3351:
3348:
3345:
3342:
3339:
3336:
3332:
3331:
3328:
3325:
3322:
3319:
3316:
3313:
3310:
3307:
3304:
3301:
3298:
3295:
3292:
3288:
3287:
3284:
3281:
3278:
3275:
3272:
3269:
3266:
3263:
3260:
3257:
3254:
3251:
3248:
3244:
3243:
3240:
3237:
3234:
3231:
3228:
3225:
3222:
3219:
3216:
3213:
3210:
3207:
3204:
3200:
3199:
3196:
3193:
3190:
3187:
3184:
3181:
3178:
3175:
3172:
3169:
3166:
3163:
3160:
3156:
3155:
3152:
3149:
3146:
3143:
3140:
3137:
3134:
3131:
3128:
3125:
3122:
3119:
3116:
3112:
3111:
3108:
3105:
3102:
3099:
3096:
3093:
3090:
3087:
3084:
3081:
3078:
3075:
3072:
3068:
3067:
3064:
3061:
3058:
3055:
3052:
3049:
3046:
3043:
3040:
3037:
3034:
3031:
3028:
3018:
3015:
3014:
3012:
3010:
3008:
3006:
3004:
3002:
3000:
2998:
2996:
2994:
2992:
2990:
2987:
2984:
2981:
2978:
2975:
2972:
2969:
2966:
2963:
2960:
2957:
2954:
2951:
2947:
2946:
2944:
2942:
2940:
2938:
2936:
2934:
2932:
2930:
2928:
2926:
2924:
2921:
2918:
2915:
2912:
2909:
2906:
2903:
2900:
2897:
2894:
2891:
2888:
2885:
2883:
2879:
2878:
2876:
2874:
2872:
2870:
2868:
2866:
2864:
2862:
2860:
2858:
2855:
2852:
2849:
2846:
2843:
2840:
2837:
2834:
2831:
2828:
2825:
2822:
2819:
2817:
2815:
2811:
2810:
2808:
2806:
2804:
2802:
2800:
2798:
2796:
2794:
2792:
2789:
2786:
2783:
2780:
2777:
2774:
2771:
2768:
2765:
2762:
2759:
2756:
2753:
2751:
2749:
2747:
2743:
2742:
2740:
2738:
2736:
2734:
2732:
2730:
2728:
2726:
2723:
2720:
2717:
2714:
2711:
2708:
2705:
2702:
2699:
2696:
2693:
2690:
2687:
2685:
2683:
2681:
2679:
2675:
2674:
2672:
2670:
2668:
2666:
2664:
2662:
2660:
2657:
2654:
2651:
2648:
2645:
2642:
2639:
2636:
2633:
2630:
2627:
2624:
2621:
2619:
2617:
2615:
2613:
2611:
2607:
2606:
2604:
2602:
2600:
2598:
2596:
2594:
2591:
2588:
2585:
2582:
2579:
2576:
2573:
2570:
2567:
2564:
2561:
2558:
2555:
2553:
2551:
2549:
2547:
2545:
2543:
2539:
2538:
2536:
2534:
2532:
2530:
2528:
2525:
2522:
2519:
2516:
2513:
2510:
2507:
2504:
2501:
2498:
2495:
2492:
2489:
2487:
2485:
2483:
2481:
2479:
2477:
2475:
2471:
2470:
2468:
2466:
2464:
2462:
2459:
2456:
2453:
2450:
2447:
2444:
2441:
2438:
2435:
2432:
2429:
2426:
2423:
2421:
2419:
2417:
2415:
2413:
2411:
2409:
2407:
2403:
2402:
2400:
2398:
2396:
2393:
2390:
2387:
2384:
2381:
2378:
2375:
2372:
2369:
2366:
2363:
2360:
2357:
2355:
2353:
2351:
2349:
2347:
2345:
2343:
2341:
2339:
2335:
2334:
2332:
2330:
2327:
2324:
2321:
2318:
2315:
2312:
2309:
2306:
2303:
2300:
2297:
2294:
2291:
2289:
2287:
2285:
2283:
2281:
2279:
2277:
2275:
2273:
2271:
2267:
2266:
2264:
2261:
2258:
2255:
2252:
2249:
2246:
2243:
2240:
2237:
2234:
2231:
2228:
2225:
2223:
2221:
2219:
2217:
2215:
2213:
2211:
2209:
2207:
2205:
2203:
2199:
2198:
2195:
2192:
2189:
2186:
2183:
2180:
2177:
2174:
2171:
2168:
2165:
2162:
2159:
2157:
2155:
2153:
2151:
2149:
2147:
2145:
2143:
2141:
2139:
2137:
2135:
2131:
2130:
2127:
2124:
2121:
2118:
2115:
2112:
2109:
2106:
2103:
2100:
2097:
2094:
2091:
2088:
2085:
2082:
2079:
2076:
2073:
2070:
2067:
2064:
2061:
2058:
2055:
2037:from the sum.
2026:
2023:
2020:
2017:
2014:
1994:
1991:
1988:
1985:
1982:
1962:
1940:
1937:
1912:
1909:
1894:
1893:
1890:
1887:
1884:
1881:
1878:
1875:
1872:
1868:
1867:
1864:
1860:
1859:
1856:
1853:
1850:
1847:
1844:
1841:
1838:
1834:
1833:
1830:
1827:
1824:
1821:
1818:
1815:
1812:
1808:
1807:
1804:
1801:
1798:
1795:
1792:
1789:
1786:
1764:
1761:
1736:
1733:
1730:
1727:
1724:
1690:
1667:
1647:
1627:
1624:
1621:
1601:
1581:
1578:
1575:
1553:
1550:
1545:
1542:
1519:
1499:
1479:
1459:
1439:
1419:
1399:
1379:
1359:
1339:
1319:
1299:
1279:
1270:plays against
1259:
1239:
1219:
1196:
1176:
1156:
1136:
1116:
1096:
1076:
1056:
1053:
1050:
1025:
1022:
1017:
1014:
994:
971:
948:
935:
934:
931:
928:
925:
922:
919:
916:
912:
911:
908:
905:
902:
899:
896:
893:
877:
876:
873:
870:
867:
864:
861:
858:
854:
853:
850:
847:
844:
841:
838:
835:
822:
821:
818:
815:
812:
809:
806:
803:
799:
798:
795:
792:
789:
786:
783:
780:
764:
763:
760:
757:
754:
751:
748:
745:
741:
740:
737:
734:
731:
728:
725:
722:
703:
700:
681:
677:
674:
671:
665:
664:
644:
624:
594:
591:
586:
585:
565:
562:
559:
556:
553:
533:
513:
510:
507:
504:
501:
492:
489:
484:
483:
463:
451:
448:
434:
431:
418:
415:
389:
386:
374:
371:
343:
340:
337:
336:
295:
293:
286:
280:
277:
242:Conference USA
240:, such as the
203:FIFA World Cup
120:FIFA World Cup
107:
104:
64:
61:
33:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4953:
4942:
4939:
4937:
4934:
4933:
4931:
4917:
4916:
4908:
4905:
4900:
4896:
4889:
4886:
4883:
4878:
4874:
4870:
4867:(in German).
4866:
4859:
4857:
4853:
4847:
4842:
4839:
4834:
4828:
4820:
4816:
4812:
4805:
4802:
4797:
4791:
4783:
4779:
4775:
4768:
4765:
4759:
4758:
4757:FIDE Handbook
4750:
4747:
4740:
4735:
4732:
4727:
4723:
4719:
4715:
4710:
4705:
4702:(1): 96β100.
4701:
4697:
4690:
4687:
4679:
4675:
4669:
4662:
4661:
4654:
4651:
4643:
4639:
4632:
4625:
4622:
4617:
4613:
4607:
4604:
4591:
4590:
4585:
4579:
4576:
4568:
4564:
4557:
4551:
4548:
4536:
4534:9780679507499
4530:
4526:
4525:
4517:
4514:
4502:
4496:
4492:
4488:
4481:
4478:
4474:
4470:
4466:
4462:
4456:
4453:
4448:
4447:
4440:
4437:
4432:
4430:0-8031-1493-1
4426:
4422:
4415:
4412:
4407:
4406:
4398:
4395:
4391:
4386:
4384:
4380:
4373:
4368:
4365:
4363:
4360:
4358:
4355:
4353:
4350:
4347:
4344:
4342:
4339:
4337:
4334:
4331:
4328:
4325:
4322:
4319:
4316:
4313:
4310:
4307:
4303:
4299:
4296:
4293:
4290:
4289:
4285:
4283:
4280:
4266:
4252:
4249:
4246:
4243:
4239:
4235:
4232:
4229:
4226:
4222:
4218:
4215:
4212:
4209:
4205:
4201:
4198:
4195:
4192:
4188:
4184:
4181:
4178:
4175:
4171:
4167:
4164:
4161:
4158:
4154:
4137:
4134:
4126:
4123:
4120:
4117:
4113:
4109:
4106:
4103:
4100:
4096:
4092:
4089:
4086:
4083:
4079:
4075:
4072:
4069:
4066:
4062:
4058:
4055:
4052:
4049:
4045:
4041:
4038:
4035:
4032:
4028:
4011:
4008:
3994:
3991:
3988:
3968:
3954:
3951:
3948:
3945:
3941:
3937:
3934:
3931:
3928:
3924:
3920:
3917:
3914:
3911:
3907:
3903:
3900:
3897:
3894:
3890:
3886:
3883:
3880:
3877:
3873:
3869:
3866:
3863:
3860:
3856:
3839:
3836:
3822:
3819:
3816:
3796:
3793:
3790:
3770:
3766:
3762:
3742:
3739:
3736:
3716:
3704:
3702:
3696:
3690:
3684:
3678:
3676:
3674:
3670:
3666:
3662:
3661:Γdouard Lucas
3653:
3649:
3637:
3634:
3631:
3628:
3625:
3622:
3619:
3616:
3613:
3610:
3607:
3604:
3601:
3597:
3593:
3590:
3587:
3584:
3581:
3578:
3575:
3572:
3569:
3566:
3563:
3560:
3557:
3553:
3549:
3546:
3543:
3540:
3537:
3534:
3531:
3528:
3525:
3522:
3519:
3516:
3513:
3509:
3505:
3502:
3499:
3496:
3493:
3490:
3487:
3484:
3481:
3478:
3475:
3472:
3469:
3465:
3461:
3458:
3455:
3452:
3449:
3446:
3443:
3440:
3437:
3434:
3431:
3428:
3425:
3421:
3417:
3414:
3411:
3408:
3405:
3402:
3399:
3396:
3393:
3390:
3387:
3384:
3381:
3377:
3373:
3370:
3367:
3364:
3361:
3358:
3355:
3352:
3349:
3346:
3343:
3340:
3337:
3333:
3329:
3326:
3323:
3320:
3317:
3314:
3311:
3308:
3305:
3302:
3299:
3296:
3293:
3289:
3285:
3282:
3279:
3276:
3273:
3270:
3267:
3264:
3261:
3258:
3255:
3252:
3249:
3245:
3241:
3238:
3235:
3232:
3229:
3226:
3223:
3220:
3217:
3214:
3211:
3208:
3205:
3201:
3197:
3194:
3191:
3188:
3185:
3182:
3179:
3176:
3173:
3170:
3167:
3164:
3161:
3157:
3153:
3150:
3147:
3144:
3141:
3138:
3135:
3132:
3129:
3126:
3123:
3120:
3117:
3113:
3109:
3106:
3103:
3100:
3097:
3094:
3091:
3088:
3085:
3082:
3079:
3076:
3073:
3069:
3065:
3062:
3059:
3056:
3053:
3050:
3047:
3044:
3041:
3038:
3035:
3032:
3026:
3025:
3019:
3013:
3011:
3009:
3007:
3005:
3003:
3001:
2999:
2997:
2995:
2993:
2991:
2988:
2985:
2982:
2979:
2976:
2973:
2970:
2967:
2964:
2961:
2958:
2955:
2952:
2948:
2945:
2943:
2941:
2939:
2937:
2935:
2933:
2931:
2929:
2927:
2925:
2922:
2919:
2916:
2913:
2910:
2907:
2904:
2901:
2898:
2895:
2892:
2889:
2886:
2884:
2880:
2877:
2875:
2873:
2871:
2869:
2867:
2865:
2863:
2861:
2859:
2856:
2853:
2850:
2847:
2844:
2841:
2838:
2835:
2832:
2829:
2826:
2823:
2820:
2818:
2816:
2812:
2809:
2807:
2805:
2803:
2801:
2799:
2797:
2795:
2793:
2790:
2787:
2784:
2781:
2778:
2775:
2772:
2769:
2766:
2763:
2760:
2757:
2754:
2752:
2750:
2748:
2744:
2741:
2739:
2737:
2735:
2733:
2731:
2729:
2727:
2724:
2721:
2718:
2715:
2712:
2709:
2706:
2703:
2700:
2697:
2694:
2691:
2688:
2686:
2684:
2682:
2680:
2676:
2673:
2671:
2669:
2667:
2665:
2663:
2661:
2658:
2655:
2652:
2649:
2646:
2643:
2640:
2637:
2634:
2631:
2628:
2625:
2622:
2620:
2618:
2616:
2614:
2612:
2608:
2605:
2603:
2601:
2599:
2597:
2595:
2592:
2589:
2586:
2583:
2580:
2577:
2574:
2571:
2568:
2565:
2562:
2559:
2556:
2554:
2552:
2550:
2548:
2546:
2544:
2540:
2537:
2535:
2533:
2531:
2529:
2526:
2523:
2520:
2517:
2514:
2511:
2508:
2505:
2502:
2499:
2496:
2493:
2490:
2488:
2486:
2484:
2482:
2480:
2478:
2476:
2472:
2469:
2467:
2465:
2463:
2460:
2457:
2454:
2451:
2448:
2445:
2442:
2439:
2436:
2433:
2430:
2427:
2424:
2422:
2420:
2418:
2416:
2414:
2412:
2410:
2408:
2404:
2401:
2399:
2397:
2394:
2391:
2388:
2385:
2382:
2379:
2376:
2373:
2370:
2367:
2364:
2361:
2358:
2356:
2354:
2352:
2350:
2348:
2346:
2344:
2342:
2340:
2336:
2333:
2331:
2328:
2325:
2322:
2319:
2316:
2313:
2310:
2307:
2304:
2301:
2298:
2295:
2292:
2290:
2288:
2286:
2284:
2282:
2280:
2278:
2276:
2274:
2272:
2268:
2265:
2262:
2259:
2256:
2253:
2250:
2247:
2244:
2241:
2238:
2235:
2232:
2229:
2226:
2224:
2222:
2220:
2218:
2216:
2214:
2212:
2210:
2208:
2206:
2204:
2200:
2196:
2193:
2190:
2187:
2184:
2181:
2178:
2175:
2172:
2169:
2166:
2163:
2160:
2158:
2156:
2154:
2152:
2150:
2148:
2146:
2144:
2142:
2140:
2138:
2136:
2132:
2128:
2125:
2122:
2119:
2116:
2113:
2110:
2107:
2104:
2101:
2098:
2095:
2092:
2089:
2086:
2083:
2080:
2077:
2074:
2071:
2068:
2065:
2062:
2059:
2053:
2052:
2046:
2045:
2042:
2038:
2021:
2018:
2015:
1989:
1986:
1983:
1960:
1938:
1935:
1910:
1907:
1891:
1888:
1885:
1882:
1879:
1876:
1873:
1869:
1861:
1857:
1854:
1851:
1848:
1845:
1842:
1839:
1835:
1831:
1828:
1825:
1822:
1819:
1816:
1813:
1809:
1805:
1802:
1799:
1796:
1793:
1790:
1787:
1783:
1780:
1778:
1774:
1773:Johann Berger
1771:chess master
1770:
1763:Berger tables
1762:
1760:
1756:
1754:
1750:
1731:
1728:
1725:
1714:
1709:
1707:
1702:
1688:
1679:
1665:
1645:
1625:
1622:
1619:
1599:
1579:
1576:
1573:
1551:
1548:
1543:
1540:
1531:
1530:competitors.
1517:
1497:
1477:
1457:
1437:
1417:
1397:
1377:
1357:
1337:
1317:
1297:
1277:
1257:
1237:
1217:
1208:
1194:
1174:
1154:
1134:
1114:
1094:
1087:has distance
1074:
1054:
1051:
1048:
1039:
1023:
1020:
1015:
1012:
992:
983:
969:
960:
946:
932:
929:
926:
923:
920:
917:
914:
913:
909:
906:
903:
900:
897:
894:
892:
889:
888:
882:
874:
871:
868:
865:
862:
859:
856:
855:
851:
848:
845:
842:
839:
836:
834:
831:
830:
819:
816:
813:
810:
807:
804:
801:
800:
796:
793:
790:
787:
784:
781:
779:
776:
775:
769:
761:
758:
755:
752:
749:
746:
743:
742:
738:
735:
732:
729:
726:
723:
721:
718:
717:
711:
709:
702:Circle method
701:
699:
679:
675:
672:
669:
642:
622:
614:
592:
589:
560:
557:
554:
531:
508:
505:
502:
490:
487:
461:
449:
447:
445:
441:
432:
430:
428:
423:
416:
414:
412:
408:
402:
398:
396:
387:
385:
383:
379:
373:Disadvantages
372:
370:
367:
363:
360:
356:
353:
347:
341:
333:
330:
322:
312:
308:
302:
301:
296:This section
294:
290:
285:
284:
278:
276:
273:
271:
267:
263:
259:
255:
251:
247:
243:
239:
236:
232:
228:
224:
220:
216:
212:
208:
204:
200:
195:
193:
189:
186:
184:
180:
175:
173:
169:
165:
161:
157:
153:
149:
145:
141:
137:
133:
132:AFC Asian Cup
129:
125:
121:
117:
116:qualification
113:
105:
103:
100:
98:
93:
91:
87:
82:
80:
75:
70:
62:
60:
58:
54:
50:
41:
37:
30:
19:
4914:
4907:
4898:
4888:
4868:
4864:
4841:
4810:
4804:
4773:
4767:
4756:
4749:
4734:
4699:
4695:
4689:
4659:
4653:
4637:
4624:
4615:
4606:
4594:. Retrieved
4589:The Guardian
4587:
4578:
4562:
4550:
4538:. Retrieved
4523:
4516:
4504:. Retrieved
4490:
4480:
4472:
4469:the original
4464:
4455:
4444:
4439:
4420:
4414:
4404:
4397:
4389:
4305:
4301:
4281:
4258:
4132:
3960:
3708:
3700:
3694:
3688:
3682:
3664:
3658:
3647:
2039:
1897:
1776:
1766:
1757:
1710:
1703:
1680:
1612:. There are
1532:
1209:
1040:
984:
961:
938:
890:
880:
832:
777:
767:
719:
705:
453:
436:
424:
420:
403:
399:
391:
380:
376:
368:
364:
361:
357:
348:
345:
325:
316:
305:Please help
300:verification
297:
274:
222:
197:Frequently,
196:
190:
187:
176:
109:
106:Applications
101:
94:
89:
85:
83:
78:
68:
66:
52:
48:
46:
36:
4871:: 134β137.
4849:(in French)
4742:(in French)
1310:. In round
229:along with
219:rugby union
215:Super Rugby
69:round-robin
63:Terminology
4930:Categories
4709:1804.04504
4374:References
3695:and then,
1533:For every
524:games. If
342:Advantages
319:March 2022
279:Evaluation
258:EuroLeague
254:basketball
179:KBO League
160:ice hockey
4877:556959107
4827:cite book
4819:651254792
4790:cite book
4782:651254787
4596:August 1,
4540:August 1,
4506:August 1,
3820:−
3794:−
3740:−
2019:−
1987:−
1871:Round 13
1729:−
1623:−
1577:−
1490:in round
1430:in round
708:algorithm
673:−
558:−
506:−
272:seasons.
67:The term
4678:Archived
4642:Archived
4567:Archived
4485:Allied.
4286:See also
4241:Round 7
4224:Round 6
4207:Round 5
4190:Round 4
4173:Round 3
4156:Round 2
4139:Round 1
4115:Round 7
4098:Round 6
4081:Round 5
4064:Round 4
4047:Round 3
4030:Round 2
4013:Round 1
3943:Round 7
3926:Round 6
3909:Round 5
3892:Round 4
3875:Round 3
3858:Round 2
3841:Round 1
3679:Mnemonic
1837:Round 3
1811:Round 2
1785:Round 1
1769:Austrian
1753:Carousel
1470:against
1410:against
576:rounds,
211:UEFA Cup
183:baseball
168:Scrabble
152:draughts
4760:. FIDE.
4726:4931332
4304:(a BTD(
2977:9
2974:8
2971:7
2968:6
2965:5
2962:4
2959:3
2956:2
2953:1
2041:table.
1892:13 β 1
1187:and to
1127:and to
164:curling
4875:
4817:
4780:
4724:
4670:
4531:
4497:
4427:
4253:7 β 1
4236:3 β 4
4219:6 β 7
4202:2 β 3
4185:5 β 6
4168:1 β 2
4151:4 β 5
4148:3 β 6
4145:2 β 7
4142:1 β 1
1889:12 β 2
1886:11 β 3
1883:10 β 4
1874:7 β 14
1858:8 β 9
1855:7 β 10
1852:6 β 11
1849:5 β 12
1846:4 β 13
1840:2 β 14
1832:1 β 2
1829:13 β 3
1826:12 β 4
1823:11 β 5
1820:10 β 6
1814:14 β 8
1806:7 β 8
1800:5 β 10
1797:4 β 11
1794:3 β 12
1791:2 β 13
1788:1 β 14
613:tennis
409:match
209:, and
166:, and
144:bridge
4722:S2CID
4704:arXiv
4681:(PDF)
4664:(PDF)
4645:(PDF)
4634:(PDF)
4570:(PDF)
4559:(PDF)
4250:6 β 2
4247:5 β 3
4244:4 β 4
4233:2 β 5
4230:1 β 6
4227:7 β 7
4216:5 β 1
4213:4 β 2
4210:3 β 3
4199:1 β 4
4196:7 β 5
4193:6 β 6
4182:4 β 7
4179:3 β 1
4176:2 β 2
4165:7 β 3
4162:6 β 4
4159:5 β 5
1880:9 β 5
1877:8 β 6
1843:3 β 1
1817:9 β 7
1803:6 β 9
1749:chess
148:chess
84:In a
79:robin
74:ruban
4873:OCLC
4833:link
4815:OCLC
4796:link
4778:OCLC
4668:ISBN
4598:2012
4542:2012
4529:ISBN
4508:2012
4495:ISBN
4425:ISBN
4127:β 1
4110:β 4
4093:β 7
4076:β 3
4059:β 6
4042:β 2
4025:β 5
4022:β 6
4019:β 7
4016:β 1
1866:...
1863:...
1544:<
1350:and
1016:<
270:2010
268:and
266:2009
248:and
138:and
4714:doi
4124:β 2
4121:β 3
4118:β 4
4107:β 5
4104:β 6
4101:β 7
4090:β 1
4087:β 2
4084:β 3
4073:β 4
4070:β 5
4067:β 6
4056:β 7
4053:β 1
4050:β 2
4039:β 3
4036:β 4
4033:β 5
3638:12
3599:13
3594:11
3555:12
3550:10
3511:11
3467:10
3110:13
3066:13
2950:13
2882:12
2814:11
2746:10
2197:13
2129:13
1715:to
1706:bye
1167:to
1107:to
1067:),
930:10
927:11
924:12
921:13
918:14
863:10
860:11
857:12
840:14
837:13
811:10
808:11
805:12
802:13
782:14
756:10
753:11
750:12
747:13
744:14
454:If
309:by
223:not
181:in
51:or
4932::
4897:.
4869:41
4855:^
4829:}}
4825:{{
4792:}}
4788:{{
4720:.
4712:.
4700:44
4698:.
4676:.
4636:.
4614:.
4586:.
4561:.
4489:.
4463:.
4382:^
4308:))
3955:7
3938:3
3921:6
3904:2
3887:5
3870:1
3853:4
3850:3
3847:2
3844:1
3675:.
3635:11
3632:10
3602:13
3591:10
3561:13
3558:12
3520:13
3517:12
3514:11
3506:9
3479:13
3476:12
3473:11
3470:10
3462:8
3438:13
3435:12
3432:11
3429:10
3423:9
3418:7
3397:13
3394:12
3391:11
3388:10
3379:8
3374:6
3356:13
3353:12
3350:11
3347:10
3335:7
3330:5
3315:13
3312:12
3309:11
3306:10
3291:6
3286:4
3274:13
3271:12
3268:11
3265:10
3247:5
3242:3
3233:13
3230:12
3227:11
3224:10
3203:4
3198:2
3192:13
3189:12
3186:11
3183:10
3159:3
3154:1
3151:13
3148:12
3145:11
3142:10
3115:2
3107:12
3104:11
3101:10
3071:1
3063:12
3060:11
3057:10
3027:Γ
2989:13
2986:12
2983:11
2980:10
2923:13
2920:12
2917:11
2914:10
2857:13
2854:12
2851:11
2848:10
2791:13
2788:12
2785:11
2782:10
2725:13
2722:12
2719:11
2716:10
2678:9
2659:13
2656:12
2653:11
2650:10
2610:8
2593:13
2590:12
2587:11
2584:10
2542:7
2527:13
2524:12
2521:11
2518:10
2474:6
2461:13
2458:12
2455:11
2452:10
2406:5
2395:13
2392:12
2389:11
2386:10
2338:4
2329:13
2326:12
2323:11
2320:10
2270:3
2263:13
2260:12
2257:11
2254:10
2202:2
2194:12
2191:11
2188:10
2134:1
2126:12
2123:11
2120:10
2090:13
2087:12
2084:11
2081:10
2054:Γ
1478:11
1450:,
1418:12
1358:12
1338:14
1278:13
1207:.
1135:14
1055:14
933:9
915:2
910:8
907:7
904:6
901:5
898:4
895:3
875:6
872:7
869:8
866:9
852:5
849:4
846:3
843:2
820:7
817:8
814:9
797:6
794:5
791:4
788:3
785:2
762:8
759:9
739:7
736:6
733:5
730:4
727:3
724:2
413:.
205:,
162:,
158:,
156:go
154:,
150:,
146:,
134:,
130:,
126:,
81:.
47:A
4879:.
4835:)
4821:.
4798:)
4784:.
4728:.
4716::
4706::
4618:.
4600:.
4544:.
4510:.
4433:.
4306:n
4302:n
4267:n
3995:1
3992:+
3989:x
3969:x
3952:6
3949:5
3946:4
3935:2
3932:1
3929:7
3918:5
3915:4
3912:3
3901:1
3898:7
3895:6
3884:4
3881:3
3878:2
3867:7
3864:6
3861:5
3823:1
3817:n
3797:1
3791:n
3771:2
3767:/
3763:n
3743:1
3737:n
3717:n
3629:9
3626:8
3623:7
3620:6
3617:5
3614:4
3611:3
3608:2
3605:1
3588:9
3585:8
3582:7
3579:6
3576:5
3573:4
3570:3
3567:2
3564:1
3547:9
3544:8
3541:7
3538:6
3535:5
3532:4
3529:3
3526:2
3523:1
3503:8
3500:7
3497:6
3494:5
3491:4
3488:3
3485:2
3482:1
3459:7
3456:6
3453:5
3450:4
3447:3
3444:2
3441:1
3426:9
3415:6
3412:5
3409:4
3406:3
3403:2
3400:1
3385:9
3382:8
3371:5
3368:4
3365:3
3362:2
3359:1
3344:9
3341:8
3338:7
3327:4
3324:3
3321:2
3318:1
3303:9
3300:8
3297:7
3294:6
3283:3
3280:2
3277:1
3262:9
3259:8
3256:7
3253:6
3250:5
3239:2
3236:1
3221:9
3218:8
3215:7
3212:6
3209:5
3206:4
3195:1
3180:9
3177:8
3174:7
3171:6
3168:5
3165:4
3162:3
3139:9
3136:8
3133:7
3130:6
3127:5
3124:4
3121:3
3118:2
3098:9
3095:8
3092:7
3089:6
3086:5
3083:4
3080:3
3077:2
3074:1
3054:9
3051:8
3048:7
3045:6
3042:5
3039:4
3036:3
3033:2
3030:1
2911:9
2908:8
2905:7
2902:6
2899:5
2896:4
2893:3
2890:2
2887:1
2845:9
2842:8
2839:7
2836:6
2833:5
2830:4
2827:3
2824:2
2821:1
2779:9
2776:8
2773:7
2770:6
2767:5
2764:4
2761:3
2758:2
2755:1
2713:9
2710:8
2707:7
2704:6
2701:5
2698:4
2695:3
2692:2
2689:1
2647:9
2644:8
2641:7
2638:6
2635:5
2632:4
2629:3
2626:2
2623:1
2581:9
2578:8
2575:7
2572:6
2569:5
2566:4
2563:3
2560:2
2557:1
2515:9
2512:8
2509:7
2506:6
2503:5
2500:4
2497:3
2494:2
2491:1
2449:9
2446:8
2443:7
2440:6
2437:5
2434:4
2431:3
2428:2
2425:1
2383:9
2380:8
2377:7
2374:6
2371:5
2368:4
2365:3
2362:2
2359:1
2317:9
2314:8
2311:7
2308:6
2305:5
2302:4
2299:3
2296:2
2293:1
2251:9
2248:8
2245:7
2242:6
2239:5
2236:4
2233:3
2230:2
2227:1
2185:9
2182:8
2179:7
2176:6
2173:5
2170:4
2167:3
2164:2
2161:1
2117:9
2114:8
2111:7
2108:6
2105:5
2102:4
2099:3
2096:2
2093:1
2078:9
2075:8
2072:7
2069:6
2066:5
2063:4
2060:3
2057:2
2025:)
2022:1
2016:n
2013:(
1993:)
1990:1
1984:n
1981:(
1961:n
1939:2
1936:n
1911:2
1908:n
1735:)
1732:1
1726:n
1723:(
1689:k
1666:k
1646:k
1626:1
1620:n
1600:k
1580:1
1574:n
1552:2
1549:n
1541:k
1518:4
1498:2
1458:2
1438:1
1398:3
1378:2
1318:2
1298:2
1258:2
1238:1
1218:1
1195:9
1175:8
1155:6
1115:3
1095:1
1075:2
1052:=
1049:n
1024:2
1021:n
1013:k
993:1
970:1
947:n
891:1
833:1
778:1
720:1
680:2
676:1
670:n
643:n
623:n
593:2
590:n
564:)
561:1
555:n
552:(
532:n
512:)
509:1
503:n
500:(
491:2
488:n
462:n
332:)
326:(
321:)
317:(
303:.
217:(
31:.
20:)
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