3 Tournaments Other uses 3 Tournaments Other uses rank adjustment - - PDF document

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1

§3 Tournaments §3 Tournaments

• rank adjustment (or challege) tournament

rank adjustment (or challege) tournament

• each match is a challenge for a rank exchange

each match is a challenge for a rank exchange

• types: ladder, hill climbing, pyramid, king of the hill

types: ladder, hill climbing, pyramid, king of the hill

• elimination tournament (or cup)

elimination tournament (or cup)

• each match eliminates the loser from the tournament

each match eliminates the loser from the tournament

• types: random selection, random pairing, single elimination

types: random selection, random pairing, single elimination

• scoring tournament

scoring tournament

• each match rewards the winner

each match rewards the winner

• types: round robin

types: round robin

• hybridizations

hybridizations

Other uses Other uses

• game balancing

game balancing

• duelling synthetic players

duelling synthetic players

• adjusting point rewarding schemes

adjusting point rewarding schemes

• heuristic search

heuristic search

• selecting suboptimal candidates for a genetic algorithm

selecting suboptimal candidates for a genetic algorithm

• group behaviour

group behaviour

• modelling pecking order

modelling pecking order

• learning player characteristics

learning player characteristics

• managing history knowledge

managing history knowledge

Example: Hill climbing tournament Example: Hill climbing tournament

Juhani Juhani Tuomas Tuomas Aapo Aapo Simeoni Simeoni Timo Timo Lauri Lauri Eero Eero m m0 m m3

3

m m1

1

m m4

4

m m2

2

m m5

5

Example: Elimination tournament Example: Elimination tournament

Juhani Juhani Tuomas Tuomas Aapo Aapo Simeoni Simeoni Timo Timo Lauri Lauri Eero Eero m m0 m m1

1

m m2

2

m m3

3

m m4

4

m m5

5

Example: Scoring tournament Example: Scoring tournament

m m5

5

Lauri Lauri m m10

10

m m4

4

Timo Timo m m14

14

m m9

9

m m3

3

Simeoni Simeoni m m17

17

m m13

13

m m8

8

m m2

2

Aapo Aapo m m19

19

m m16

16

m m12

12

m m7

7

m m1

1

Tuomas Tuomas m m20

20

m m18

18

m m15

15

m m11

11

m m6

6

m m0 Juhani Juhani Eero Eero Lauri Lauri Timo Timo Simeoni Simeoni Aapo Aapo Tuomas Tuomas

Terms Terms

• players:

players: p p0

0…

…p pn

n − 1 − 1

• match between

match between p pi

i and

and p pj

j:

: match match( (i i, , j j) )

• utcome:
• utcome: WIN

WIN,

, LOSE

LOSE,

, TIE

TIE

• rank of

rank of p pi

i:

: rank rank( (i i) )

• players with the rank

players with the rank r r: : rankeds rankeds( (r r) )

• round: a set of (possibly) concurrent matches

round: a set of (possibly) concurrent matches

• bracket: diagram of match pairings and rounds

bracket: diagram of match pairings and rounds

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Rank adjustment tournaments Rank adjustment tournaments

• a set of already ranked players

a set of already ranked players

• matches

matches

• independent from one another

independent from one another

• utcome affects only the participating players
• utcome affects only the participating players
• suits on

suits on-

• going tournaments

going tournaments

• example: boxing

example: boxing

• matches can be limited by the rank difference

matches can be limited by the rank difference

Ladder and pyramid tournaments Ladder and pyramid tournaments

p pi

i:

: rank rank( (i i) = 0 ) = 0 p pj

j:

: rank rank( (j j) = 1 ) = 1 p pk

k:

: rank rank( (k k) = 2 ) = 2 p pm

m:

: rank rank( (m m) = 3 ) = 3 p pn

n:

: rank rank( (n n) = 4 ) = 4 p pi

i:

: rank rank( (i i) = 0 ) = 0 p pj

j:

: rank rank( (j j) = 1 ) = 1 p pk

k:

: rank rank( (k k) = 2 ) = 2 p pm

m:

: rank rank( (m m) = 2 ) = 2 p pn

n:

: rank rank( (n n) = 2 ) = 2 rankeds rankeds(2) = { (2) = { k k, , m m, , n n } }

Elimination tournaments Elimination tournaments

• loser of a match is eliminated from the

loser of a match is eliminated from the tournament tournament

• no ties! → tiebreak competition

no ties! → tiebreak competition

• winner of a match continues to the next round

winner of a match continues to the next round

• how to assign pairings for the first round?

how to assign pairings for the first round?

• seeding

seeding

• examples

examples

• football cups, snooker tournaments

football cups, snooker tournaments

Random selection and random Random selection and random pairing pairing

p pi

i

p pj

j

p pk

k

p pm

m

p pn

n

p pi

i

p pj

j

p pk

k

p pm

m

p pn

n

Single elimination Single elimination

p pi

i

p pj

j

p pk

k

p pm

m

p pn

n

p pq

q

p pr

r

p ps

s

Bye Bye

bye bye p pi

i

p pj

j

p pk

k

p pm

m

p pn

n

p pq

q

p pr

r

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Seeding Seeding

• some match pairing will not occur in a single

some match pairing will not occur in a single elimination tournament elimination tournament

• pairings for the first round (i.e., seeding) affects

pairings for the first round (i.e., seeding) affects the future pairings the future pairings

• seeding can be based on existing ranking

seeding can be based on existing ranking

• favour the top

favour the top-

• ranked players

ranked players

• reachability: give the best players an equal

reachability: give the best players an equal

• pportunity to proceed the final rounds
• pportunity to proceed the final rounds

Seeding methods Seeding methods

• random

random

• does not favour any player

does not favour any player

• does not fulfil reachability criterion

does not fulfil reachability criterion

• standard and ordered standard

standard and ordered standard

• favours the top

favours the top-

• ranked players

ranked players

• rdered standard: matches are listed in increasing order
• rdered standard: matches are listed in increasing order
• equitable

equitable

• in the first round, the rank difference between the players is

in the first round, the rank difference between the players is the same for each match the same for each match