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

§3 Tournaments Other uses §3 Tournaments Other uses � rank adjustment (or challege) tournament rank adjustment (or challege) tournament � game balancing game balancing � � � each match is a challenge for a rank exchange each match is a challenge for a rank exchange � duelling synthetic players duelling synthetic players � � � types: ladder, hill climbing, pyramid, king of the hill types: ladder, hill climbing, pyramid, king of the hill � � adjusting point rewarding schemes adjusting point rewarding schemes � � elimination tournament (or cup) elimination tournament (or cup) � � heuristic search heuristic search � � each match eliminates the loser from the tournament each match eliminates the loser from the tournament � � selecting suboptimal candidates for a genetic algorithm selecting suboptimal candidates for a genetic algorithm � � types: random selection, random pairing, single elimination types: random selection, random pairing, single elimination � � group behaviour group behaviour � � scoring tournament scoring tournament � � modelling pecking order modelling pecking order � � each match rewards the winner each match rewards the winner � � learning player characteristics learning player characteristics � types: round robin types: round robin � � � hybridizations hybridizations � managing history knowledge managing history knowledge � � Example: Hill climbing tournament Example: Elimination tournament Example: Hill climbing tournament Example: Elimination tournament Juhani Juhani Juhani Juhani m m 0 m 0 m 0 0 Tuomas Tuomas Tuomas Tuomas m m 1 m m 3 1 3 Aapo Aapo Aapo Aapo m 2 m m 1 m 2 1 Simeoni Simeoni Simeoni Simeoni m 5 m m 3 5 m 3 Timo Timo Timo Timo m 4 m 2 m m 4 2 Lauri Lauri Lauri Lauri m m 4 4 m 5 m 5 Eero Eero Eero Eero Example: Scoring tournament Example: Scoring tournament Terms Terms Tuomas Tuomas Aapo Aapo Simeoni Simeoni Timo Timo Lauri Lauri Eero Eero � players: players: p p 0 0 … … p p n � n − 1 − 1 � match between match between p p i and p p j : match match ( ( i i , , j j ) ) i and j : Juhani Juhani m 0 m m m 6 m 11 m m m 15 m 18 m m m 20 � 0 6 11 15 18 20 � outcome: outcome: WIN , LOSE , TIE WIN , LOSE , Tuomas m 1 m 7 m 12 m 16 m 19 � Tuomas m m m m m TIE 1 7 12 16 19 � rank of rank of p p i i : : rank rank ( ( i i ) ) � Aapo Aapo m 2 m m m 8 m 13 m m 17 m 2 8 13 17 � players with the rank players with the rank r r : : rankeds rankeds ( ( r r ) ) � Simeoni Simeoni m m 3 m 9 m m m 14 3 9 14 � round: a set of (possibly) concurrent matches round: a set of (possibly) concurrent matches � Timo m 4 m 10 Timo m m 4 10 � bracket: diagram of match pairings and rounds bracket: diagram of match pairings and rounds � Lauri Lauri m 5 m 5 1

Rank adjustment tournaments Ladder and pyramid tournaments Rank adjustment tournaments Ladder and pyramid tournaments � a set of already ranked players a set of already ranked players � p i p i : : rank rank ( ( i i ) = 0 ) = 0 p i p i : : rank rank ( ( i i ) = 0 ) = 0 � matches matches � � independent from one another independent from one another � p j : rank rank ( ( j j ) = 1 ) = 1 p j : rank rank ( ( j j ) = 1 ) = 1 p j : p j : � outcome affects only the participating players outcome affects only the participating players � � suits on suits on- -going tournaments going tournaments � p p k k : : rank rank ( ( k k ) = 2 ) = 2 p k p k : : rank rank ( ( k k ) = 2 ) = 2 � example: boxing example: boxing � p m : rank rank ( ( m m ) = 2 ) = 2 p m : � matches can be limited by the rank difference matches can be limited by the rank difference p m p m : : rank rank ( ( m m ) = 3 ) = 3 � p n p n : : rank rank ( ( n n ) = 2 ) = 2 p n : rank rank ( ( n n ) = 4 ) = 4 p n : rankeds (2) = { (2) = { k k , , m m , , n n } } rankeds Random selection and random Random selection and random Elimination tournaments Elimination tournaments pairing pairing � loser of a match is eliminated from the loser of a match is eliminated from the � p i p p p i i i tournament tournament � no ties! → tiebreak competition no ties! → tiebreak competition � p j p j p p j j � 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? p k p k � p p k k � seeding seeding � � examples examples p p m p m p � m m � football cups, snooker tournaments football cups, snooker tournaments � p n p p n p n n Single elimination Single elimination Bye Bye p i p i p p i i p j p j p p j j p k p k p p k k p m p p p m m m p n p p p n n n p q p p p q q q p r p r p p r r p s bye p bye s 2

Seeding Seeding methods Seeding Seeding methods � random random � some match pairing will not occur in a single some match pairing will not occur in a single � � elimination tournament � does not favour any player does not favour any player elimination tournament � � does not fulfil reachability criterion does not fulfil reachability criterion � � pairings for the first round (i.e., seeding) affects pairings for the first round (i.e., seeding) affects � � standard and ordered standard standard and ordered standard � the future pairings the future pairings � favours the top favours the top- -ranked players ranked players � � seeding can be based on existing ranking seeding can be based on existing ranking � � ordered standard: matches are listed in increasing order ordered standard: matches are listed in increasing order � � favour the top favour the top- -ranked players ranked players � � equitable equitable � � reachability: give the best players an equal reachability: give the best players an equal � in the first round, the rank difference between the players is in the first round, the rank difference between the players is � � opportunity to proceed the final rounds the same for each match the same for each match opportunity to proceed the final rounds 3