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Designing Tournaments

Designing Tournaments. Colby Nadeau, Gus Johnson, and Taylor Gagne Mentor: Professor Dinitz. Types of Tournaments. Elimination Single Elimination Double Elimination Round Robin Consolation Ladder Tournaments. Elimination Trick.

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Designing Tournaments

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  1. Designing Tournaments Colby Nadeau, Gus Johnson, and Taylor Gagne Mentor: Professor Dinitz

  2. Types of Tournaments • Elimination • Single Elimination • Double Elimination • Round Robin • Consolation • Ladder Tournaments

  3. Elimination Trick • How many games are played in a single elimination tournament with 64 competitors? • 63 games • How many games are played in a single elimination tournament with 12 competitors? • 11 games • How many games are played in a single elimination tournament with 973 competitors? • 972 games

  4. Round Robin Tournament • A round robin tournament is a competition where every competitor plays against every other competitor one time. • Real World Examples: • FIFA World Cup Qualifier • World Chess Championships • Cricket World Cup

  5. Round Robin (2n) • Games Per Week = 2n/2 Weeks = 2n-1 • If 2n = 2 then there is only 1 game • 1 plays 2 shown as (12) • If 2n = 4 then there are 2 games a week for 3 weeks • Week #1 = (12) (34) • Week #2 = (13) (24) • Week #3 = (14) (23)

  6. 2n = 6 • There are 3 games a week for 5 weeks Week 1 = (12) (34) (56) Week 2 = (13) (25) (46) Week 3 = (14) (26) (35) Week 4 = (15) (24) (36) Week 5 = (16) (23) (45) • There is a much easier way to do this!

  7. Starter Construction • If 2n = 10 then there are 5 games a week for 9 weeks 0 8 1 ∞ 7 2 6 3 5 4

  8. Number of Variations vs. Players • There are different variations to how you could set up these tournaments depending on how many contestants there are. • Professor Dinitz helped discover that there are 526915620 different round robin tournament with 12 players.

  9. References/Thanks • References • Professor Dinitz • http://www.abitabout.com/Round-robin+tournament • http://culturekids.wordpress.com/2009/12/02/drawing-conclusions/ • We want to thank Professor Dinitz for helping us learn and prepare for our presentation.

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