Double elimination
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The document describes the rules for determining the schedule of games in a round-robin tournament with a varying number of teams. It provides examples of tournaments with 3 to 16 teams and calculates the number of games, byes, and lines required based on the formula (N-1)^2, where N is the number of teams. The winner must defeat a specific opponent twice in order to become the champion in each example.
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Double elimination
- 1. Tadeo A. Rosalia 4-BPE-SPE 1 2 BYE G1 G2 3 W1L1 L1 G3 W2 L2 W3 W3 W2 vs. G4 3 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (3 – 1)2 = 4 – 3 = (2)2 = 1 Bye = 4 Games 3 Note: W3 must defeat W2 twice in order to become the champion. G - GAMES W - Winner Numbers - # of Teams
- 2. Tadeo A. Rosalia 4-BPE-SPE 1 2 3 4 G1 G2 G3 G4 G5 W1 W2 W3W4 W5 L1 L2 L3 Note: W5 must defeat W3 twice in order to become the champion. W5 W3 vs. G6 4 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (4 – 1)2 = 4 – 4 = (3)2 = no bye = 6 Games G - GAMES W - Winner Numbers - # of Teams
- 3. Tadeo A. Rosalia 4-BPE-SPE 1 2 BYE BYE BYE 3 4 5 G1 3 4 5 G2 G3 W1 W3 W2 L1 L1 L2 L3 L3 G4 G5 W5 W4 G6 W6 L5 G7 W7 W7 W5 G8 vs. Note: W7 must defeat W5 twice in order to become the champion. 5 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (5 – 1)2 = 8 – 5 = (4)2 = 3 Byes = 8 Games G - GAMES W - Winner Numbers - # of Teams
- 4. Tadeo A. Rosalia 4-BPE-SPE 1 2 3 4 5 6 BYE BYE G1 G2 G4 G3 3 4 W1 W3 W4 W2 L1 L3 L4 L1 L2 L2 G5 G6 W5 W6 G7 W7 L7 G8 G9 W8 W9 W9 W7 Vs. G10 Note: W9 must defeat W7 twice in order to become the champion. 6 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (6 – 1)2 = 8 – 6 = (5)2 = 2 Byes = 10 Games G - GAMES W - Winner Numbers - # of Teams
- 5. Tadeo A. Rosalia 4-BPE-SPE 1 2 3 4 5 6 7 BYE G1 G2 G3 G4 G5 W1 W4 W2 W3 W5 7 L1 L2 L3 L4 L5 L3 G6 G7 G8 W6 W8 W7 G9 G10 W9W10 L9 G11 W11 W11 W9 Vs. G12 Note: W11 must defeat W9 twice in order to become the champion. 7 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (7 – 1)2 = 8 – 7 = (6)2 = 1 Byes = 12 Games G - GAMES W - Winner Numbers - # of Teams
- 6. Tadeo A. Rosalia 4-BPE-SPE 1 2 3 4 5 6 7 8 G1 G2 G3G3 G4 G5 G6 W1 W2 W3 W4 W5 W6 L1 L2 L6 L5 La3 L4 G7 G8 W7 W8 G9 G10 G11 W11 L11 G12 W9 W10 G13 W12 W13 W13 W11 Vs. G14 Note: W13 must defeat W11 twice in order to become the champion. 8 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (8 – 1)2 = 8 – 8 = (7)2 = 0 Byes = 14 Games G - GAMES W - Winner Numbers - # of Teams
- 7. Tadeo A. Rosalia 4-BPE-SPE 1 2 BYE BYE BYE BYE BYE BYE BYE 3 4 5 6 7 8 9 G1 3 4 5 6 7 8 9 G2 G3 G4 G5 W1 W2 W3 W4 L1 L2 L5 L3 aL4 L1 L4 L3 G6 L5 W6 G7 W7 G8 W9 W5 G9 G10 L10 L9 G11 G12 W12 W11 G13 W13 La13 G14 W14 G15 Wa15 W15 Wa13 Vs. G16 Note: W15 must defeat W13 twice in order to become the champion. W9 W10 9 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (9 – 1)2 = 16 – 9 = (8)2 = 7 Byes = 16 Games G - GAMES W - Winner Numbers - # of Teams
- 8. Tadeo A. Rosalia 4-BPE-SPE BYE BYE BYE BYE BYE BYE 1 2 3 4 5 6 77 8 9 10 G1 G2 3 4 5 6 7 8 G3 G4 G5 G6 W1 W5 W3 W4 W6 W2 L1 L3 L5 L6 L4 L1 L2 L2 G7 G8 L5 L6 W8 W7 G9 G10 L10 L9 G11 G12 W9 W10 W11 W12 G13 G14 W13 W14 G15 W15 G16 L15 G17 W16 W17 W17 W15 vs. G18 Note: W17 must defeat W15 twice in order to become the champion. 10 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (10 – 1)2 = 16 – 10 = (9)2 = 6 Byes = 18 Games G - GAMES W - Winner Numbers - # of Teams
- 9. Tadeo A. Rosalia 4-BPE-SPE BYE BYE BYE BYE BYE 1 2 3 4 5 6 7 8 9 10 11 W1 G1 G2 G3 3 6 7 10 11 W2 W3 G4 W4 G5 W5 G6 G7 W6 W7 L1 L1 L6 L5 L2 L2 L3 L3 L4 L7 L7 G10 G9 G8 W10 W9 W8 G11 G12 W12 W11 L11 L12 G13 G14 W13 W14 G15 G16 W16 W15 G17 W17 L17 G18 W18 G19 W19 W19 W17 vs. G20 Note: W19 must defeat W17 twice in order to become the champion. 11 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (11 – 1)2 = 16 – 11 = (10)2 = 5 Byes = 20 Games G - GAMES W - Winner Numbers - # of Teams
- 10. Tadeo A. Rosalia 4-BPE-SPE BYE BYE BYE BYE 1 2 3 4 5 6 7 8 9 10 11 12 G1 G2 G3 G4 3 4 9 10 G5 G6 G7 G8 W1 W5 W6 W2 W3 W7 W8 L1 L1 L6 L5 L2 L2 L3 L3 L8 La7 L4 L4 G10 G9 G12 G11 G13 W10 W9 W12 W11 G14 L14 L13 G15 G16 W15 W16 G17 G18 W17 Wa18 G19 W19 L19 G20 G21 Wa20 W21 W21 W19 Vs. G22 Note: W21 must defeat W19 twice in order to become the champion. 12 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (12 – 1)2 = 16 – 12 = (11)2 = 4 Byes = 22 Games G - GAMES W - Winner Numbers - # of Teams
- 11. Tadeo A. Rosalia 4-BPE-SPE BYE BYE BYE 1 2 3 4 5 6 7 8 9 10 11 12 13 W1 G1 G2 G3 G4 G5 W2 W3 W4 7 8 13 G6 G7 G8 G9 W6 W7 W8 W9 L1 L2 L3 L3 L6 L7 L4 L4 L9 L8 L5 L5 G10 G11 G12 G13 G14 W10 W14 W11 W13 W12 G17 G15 G16 W15 W16 L15 L16 G18 G19 G20 W18 W20 W19 W17 G21 W21 L21 G22 G23 W22 W23 W23 W21 Vs. G24 Note: W23 must defeat W21 twice in order to become the champion. 13 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (13 – 1)2 = 16 – 13 = (12)2 = 3 Byes = 24 Games G - GAMES W - Winner Numbers - # of Teams
- 12. Tadeo A. Rosalia 4-BPE-SPE BYE BYE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 G1 G2 G3 G4 G5 G6 W1 W2 W3 W4 W5 W6 7 8 G7 G8 G9 G10 W7 W8 W9 W10 L1 L2 L3 L3 L7 L8 L4 L4 L10 L9 L5 L6 G11 G12 G13 G14 W11 W13 W14 W12 G15 G16 W16 W15 G17 G18 W18 W17 L17 L18 G19 G20 W19 W20 G21 G22 W21 W22 G23 W23 L23 G24 G25 W24 W25 W25 W23 Vs. G26 Note: W25 must defeat W23 twice in order to become the champion. 14 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (14 – 1)2 = 16 – 14 = (13)2 = 2 Byes = 26 Games G - GAMES W - Winner Numbers - # of Teams
- 13. Tadeo A. Rosalia 4-BPE-SPE BYE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 W1 G1 G2 G3 G4 G5 G6 G7 15 W2 W3 W4 W5 W6 W7 G8 G9 G10 G11 W11 W10 W9 W8 L1 L2 L3 L8 L9 L4 L5 L6 L7 L10 L11 L10 L7 G12 G13 G14 G15 G16 W12 W16 W13 W14 W15 G17 G18 W17 W18 G19 G20 L19 L20 W19 W20 G21G21 G22 G23 W21 G24 W23 W24 G25 G26 W25W26 G27 W27 W27 W25 Vs. G28 Note: W27 must defeat W25 twice in order to become the champion. 15 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (15 – 1)2 = 16 – 15 = (14)2 = 1 Bye = 28 Games G - GAMES W - Winner Numbers - # of Teams
- 14. Tadeo A. Rosalia 4-BPE-SPE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 G1 G2 G3 G4 G5 G6 G7 G8 G9 G10 G11 G12 W1 W2 W3 W4 W5 W6 W7 W8 W12 W11 W10 W9 L1 L2 L3 L4 L5 L6 L7 L8 G13 G14 G15 G16 L10 L9 W13 W14 W15 W16 L11 L12 G17 G18 G19 G20 W17 W18 W19 W20 G21 G22 W22 W21 G23 G24 W24 W23 L22 L21 G25 G26 W26 W25 G27 W27 L27 G28 W28 G29 W29 W29 W27 Vs. G30 Note: W29 must defeat W27 twice in order to become the champion. 16 TEAMS (N – 1)2 = # of games # of lines – N = # of bye(s) = (16 – 1)2 = 16 – 16 = (15)2 = 0 Bye = 30 Games G - GAMES W - Winner Numbers - # of Teams