the sequence of numbers from 1 up to . Here is an example table for 7 or 8 competitors: Then to get the opponents a second table is constructed. Every horizontal row is populated with the same numbers as row 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). By merging above tables we arrive at: Then the first column is updated: if the number of competitors is even, player number is alternatingly substituted for the first and second positions, whereas if the number of competitors is odd a bye is used instead. 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. For more historical details, see Ahrens. See also Group tournament ranking system, including details of tie-breaking systems Combinatorial design, a balanced tournament design of order n (a BTD(n)) Tournament (graph theory), mathematical model of a round-robin tournament Other tournament systems: Swiss system tournament McMahon system tournament, a variation of the Swiss system that incorporates pre-tournament rankings to prevent early lopsided pairings Single-elimination tournament Shaughnessy playoff system, a type of single-elimination tournament featuring four teams Double-elimination tournament McIntyre system, a series of tournament formats that combine features of single- and double-elimination tournaments Bridge: Duplicate bridge movements Chess: List of round-robin chess tournaments Scheveningen system, where each member of one team plays each member of the other Voting: Condorcet method Condorcet criterion References External links Round Robin Tournament Scheduling link to schedules (balanced,cyclic,first-fit,whist). Round Robin System Tables (Scoring - Programme) Free Printable Round Robin Brackets Tournament systems Chess tournament systems