Designing Tournaments

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Presentation transcript:

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

Types of Tournaments Elimination Round Robin Consolation Single Elimination Double Elimination Round Robin Consolation Ladder Tournaments

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

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

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)

2n = 6 There are 3 games a week for 5 weeks There is a much easier way to do this!

Starter Construction If 2n = 10 then there are 5 games a week for 9 weeks 8 5 7 6 4 2 3 1 ∞ Week 0 0∞ 45 81 36 72 Week 1 1∞ 56 02 47 83 Week 2 2∞ 67 13 58 04 Week 3 3∞ 78 24 60 15 Week 4 4∞ 80 35 71 26 Week 5 5∞ 01 46 82 37 Week 6 6∞ 12 57 03 48 Week 7 7∞ 23 68 14 50 Week 8 8∞ 34 70 25 61

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. Number of Players 2 4 6 8 10 12 Number of Variations 1 396 526915620

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.