FIDE Play-Off and Tie-Break Regulations

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1. Scope These regulations shall apply to all FIDE-rated competitions. Note: See article 4.1.

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10. Ratings-based Tie-Breaks for Individuals These tie-breaks must be dropped from the tournament tie-break list when unrated players are present, unless detailed rules on the handling of unrated players are included in the tournament regulations or established and published by the Chief Arbiter before the start of the tournament. Note: These tie-breaks are not recommended when a player can get more than one rating during the tournament (e.g. due to multiple rating reports). If they are nevertheless chosen, the rating used to calculate them is the first one, unless the specific regulations of the tournament state otherwise. 10.1 Average Rating of Opponents (ARO) The average of the ratings of the opponents played over the board, rounded to the nearest whole number (0.5 rounded up). 10.2 Tournament Performance Rating (TPR) Calculated adding to ARO a number (called rating difference (RD) - which may be negative) resulting from the conversion of the fractional score (number of points achieved in games played over the board divided by the number of games) into RD (see the corresponding conversion table in the FIDE Rating Regulations). 10.3 Perfect Tournament Performance (PTP) This is a whole number corresponding to the lowest rating that a player should have for their expected score to be greater than or equal to their tournament score. For a zero score, this number is set 800 points lower than the rating of the lowest rated opponent. The expected score is the sum of the scoring probabilities which are defined in the FIDE Rating Regulations by the conversion table of rating differences into scoring probabilities. Each rating difference is calculated by using the aforementioned lowest rating and the rating of each opponent faced by the player during the tournament. The full rating scale is used in this conversion (i.e. no ±400 cut). 10.4 Average [Tournament] Performance Rating of Opponents (APRO) The average of the performances (TPR) of the opponents played over the board, rounded to the nearest whole number (0.5 rounded up). 10.5 Average Perfect [Tournament] Performance of Opponents (APPO) The average of the perfect performances (PTP) of the opponents played over the board, rounded to the nearest whole number (0.5 rounded up). 10.6 Rating (RTNG) Players are sorted according to their rating, from highest to lowest. Alternatively, they can be sorted in reverse order (i.e. from lowest to highest).

Referencing norms: AllOpponentsRated, AroValue, AverageRatingOfOpponents, GameRoundOverTheBoard, OpponentOverTheBoard, OpponentRatingInRound, RatedParticipant

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11. Team Tie-Breaks 11.1 In team tournaments each match between two teams may report two types of scores: 11.1.1 Match Points (MP) Points assigned to a team-win, team-draw, and team-loss. 11.1.2 Game Points (GP) Sum of the individual points that each player of the team scores.

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12. Tie-Breaks Specific for Team Knockouts Even though these tie-breaks may be used in team competitions (see Article 13), and are described as such, they are specific for team knockouts when both teams have the same number of match points and game points. For these tie-breaks: individual forfeit wins or losses are considered as standard wins or losses if the team received a pairing-allocated bye, the game points considered for each board are the same as those assigned to a standard win. 12.1 Board Count (BC) For each team and each board, multiply the board number (e.g. one for first board, two for second board) by the number of game points achieved on that board in all games played by the team in the tournament, regardless of who was playing on it. The lower the sum of these products, the higher the ranking of the team. It can only be used when all tied teams have (scored) the same number of game points. 12.2 Top Board Results (TBR) This is the number of game points achieved on the first board in all games played by the team in the tournament, regardless of who was playing on that board. If the results on the top board are not decisive, reapply this tie-break to the top-most board not yet counted. Continue reapplying this tie-break in the same way until the tie is broken. 12.3 Bottom Board Elimination (BBE) This is the number of game points achieved on all boards except for the bottom board in all games played by the team in the tournament, regardless of who was playing on those boards. If excluding the bottom board is not decisive, reapply this tie-break to the bottom-most board not yet excluded. Continue reapplying this tie-break in the same way until the tie is broken.

en · official · sha256:545678253f1bfe3df050d0e440c313b158dce754096e9778fc14ce43154d7470

13. Tie-Breaks Specific for Team Competitions All tie-breaks described in Articles 6-10, or some variation of them, may be also applied for teams, using teams MP or GP as the reference score for the team – the primary score being the default, if the reference score is not explicitly indicated. 13.1 Match Points or Game Points (MPvGP) Match Points in team competitions that are decided by Game Points or Game Points in team competitions that are decided by Match Points. 13.2 Extended Sonneborn Berger (ESB) for Teams Combining MP and GP, four combinations of Sonneborn-Berger tie­breaks are available. Any of them or any combinations of them can be used. Each (Extended) Sonneborn-Berger tie-break is calculated adding for each opponent a value given by the product of two elements: the total number of MP or GP achieved by the opponent at the end of the tournament; the number of MP or GP scored against that opponent. The four possibilities are: 13.2.1 EMMSB Total MP opponent × MP scored 13.2.2 EMGSB Total MP opponent × GP scored 13.2.3 EGMSB Total GP opponent × MP scored 13.2.4 EGGSB Total GP opponent × GP scored See Article 16 for Unplayed Rounds Management. 13.3 Extended Direct Encounter for Teams (EDE) 13.3.1 Apply the Direct Encounter rule (Article 6), first using the primary score (MP or GP), then, if no ties were broken in accordance with this rule, using the secondary score. 13.3.2 If exactly two teams are still tied in both MP and GP, the rules of a competition must specify whether the Tie-Breaks specific for Team Knockouts apply (Article 12), and, if so, which ones and in what order. The four reasonable possibilities are: EDEBT => EDE + BC + TBR EDEBB => EDE + BC + BBE EDET => EDE + TBR EDEB => EDE + BBE 13.3.3 Any time a new subset of tied teams is determined, restart with the new subset from 13.3.1. 13.4 Scores and Schedule Strength Combination (SSSC) This tie-break adds together two elements: 13.4.1 the secondary score of a team (GP if the primary score is given by MP, or vice versa); 13.4.2 a value that represents the strength of its oppsition (called Schedule Strength). This value is the result of a division between: [dividend] Buchholz of the team, based on the primary score (note: if the tie-break value must be known before playing, use Fore Buchholz); [divisor] a normalising factor, given by the highest achievable primary score in the tournament divided by the highest secondary score achievable in a single match, rounded to the nearest integer towards zero, or by a different value if stated by the rules of the competition

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14. Modifiers Each tie-break based on a sum of values (that can come from either results, ratings or any value calculated using them) can be redefined by applying a modifier, which is a way to vary the elements that are part of the calculation, usually excluding some of these elements or, more rarely, adding some: 14.1 Cut-1: Cut the Least Significant Value 14.1.1 It is the most used modifier, applicable in many tie-breaks. The most commonly used are: Buchholz Cut-1 (BH-C1, exclude the opponent's lowest score) ARO Cut-1 (ARO-C1, exclude the opponent's lowest rating) Progressive Score Cut-1 (PS-C1, exclude the score achieved after the first round) Sonneborn-Berger Cut-1 (SB-C1, exclude the contribution (product) associated with the opponent with the lowest score - if there is more than one such opponent, exclude the lowest contribution associated with them). 14.1.2 In team competition, all the Extended Sonneborn-Berger tie-breaks for teams (see Article 13.2) are calculated excluding the contribution (product) associated with the opponent with the lowest MP score (for EMMSB and EMGSB) or GP score (for EGMSB and EGGSB) - if there is more than one such opponent, exclude the lowest contribution associated with them. 14.2 Cut-2: Cut the two Least Significant Values Most commonly used is Buchholz Cut-2 (BH-C2). 14.3 Median­1: Cut the Least and the Most Significant Values (in that order) Most commonly used is Buchholz Median-1 (BH-M1). 14.4 Median­2: Cut the two Least and the two Most Significant Values (in that order) Most commonly used is Buchholz Median-2 (BH-M2). 14.5 Limit: Change a Limit The most common modification is in Koya: the limit of 50% of the maximum possible tournament score can be either increased or decreased by half point at a time to let respectively fewer or more opponents contribute to the evaluation of the tie-break. All modifiers are subject to Unplayed Rounds Management (see Article 16).

Referencing norms: AroCut1Value, AverageRatingOfOpponentsCut1, BuchholzCut1Value, BuchholzCut1WithoutVur, SbLeastSignificantValue, SbLowestOpponentScore, SonnebornBergerCut1Value, SonnebornBergerCut1WithoutVur

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15. Unplayed Rounds 15.1 An unplayed round is any round in which a participant, paired or not, did not play a game in an individual tournament, or a match in a team tournament 15.2 In tournaments with pre-determined pairings, forfeit wins or losses (the only possible unplayed rounds) are treated as regular games or matches, except that all forfeits in ratings-based tie-breaks (see Article 10) and forfeit losses in Type B tie-breaks (see Article 7) remain unplayed rounds. 15.3 For Swiss tournaments, apply Article 16.

Referencing norms: RoundRobinSbEntryOfForfeit

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16. Unplayed Rounds Management in Swiss Tournaments In Individual or Team Swiss tournaments, the tie-breaks Buchholz (see Article 8.1), Sonneborn-Berger (see Articles 9.1 and 13.2) and their variants (Fore Buchholz, see Article 8.3; and "Cut" Modifiers, see Articles 14.1 to 14.4), which are directly or indirectly based on opponents' results, are affected by the presence of unplayed rounds in the record of participants. 16.1 The following definitions are used in this section: 16.1.1 requested bye: a half-point-bye or a zero-point-bye (note: any round after a participant withdraws is a zero-point-bye) 16.1.2 voluntary unplayed round ("VUR"): a round in which a participant was not available to play, i.e. a requested bye or a forfeit loss 16.2 Unplayed rounds can be divided into the following categories: 16.2.1 Pairing-allocated byes or full-point byes 16.2.2 Forfeit wins 16.2.3 Requested byes that are followed by at least one round that is not a VUR 16.2.4 Forfeit losses 16.2.5 Requested byes that are either followed only by VURs or in the last round of a tournament 16.3 When a participant has unplayed rounds, for the sole purpose of calculating the tie-break of their opponents, the participant's score is adjusted in the following way: 16.3.1 Unplayed rounds of categories 16.2.1, 16.2.2, 16.2.3 and 16.2.4 are evaluated with the result (win, draw, loss) corresponding to the awarded number of points or, for teams, match points and game points. 16.3.2 Unplayed rounds of category 16.2.5 are evaluated as draws. 16.4 To calculate the participant's own tie-break, each of their unplayed rounds is evaluated as if the participant had played against a dummy, with the result (win, draw, loss) corresponding to the points awarded. The dummy’s score for the tie-break calculation is the participant’s own score. However, it shall not exceed: 16.4.1 the scheduled opponent's adjusted score (see Article 16.3), for unplayed rounds of categories 16.2.2 and 16.2.4 (forfeits); 16.4.2 the points awarded for a draw multiplied by the number of rounds in the tournament, for all other unplayed rounds (categories 16.2.1, 16.2.3 and 16.2.5). Note: For team competitions, "points" means "match points and game points". 16.5 Cut-1 Exception 16.5.1 When a modifier calls for cutting the least significant value (see Articles 14.1 to 14.4) of a participant with one or more VURs, the lowest contribution coming from such rounds shall be cut, as long as such contribution is not lower than the least significant value. This means: For Buchholz, cut the lowest contribution coming from a VUR. For Sonneborn-Berger, after determining: the lowest contribution coming from a VUR the least significant value (see 14.1.1.d and 14.1.2) cut the higher of these two values (note: they are the same element if the least significant value comes from a VUR). 16.5.2 Rule 16.5.1 applies again to the remaining elements when the modifier requires more cuts (see Articles 14.2 and 14.4). 16.6 The rules of the competition may specify in advance alternative provisions to Articles 16.3, 16.4 or 16.5.

Referencing norms: AdjustedPointsOfByeBeforePlay, AdjustedPointsOfForfeitLoss, AdjustedPointsOfNonVoluntaryUnplayed, AdjustedPointsOfPlayedGame, AdjustedPointsOfTrailingBye, AdjustedScore, BuchholzContributionOfUnplayedRound, BuchholzCut1WithVur, DummyScoreForForfeit, DummyScoreForPairingBye, DummyScoreForRequestedBye, ForfeitLossIsVur, ForfeitWinIsNotVoluntary, HalfPointByeIsVur, PairingByeIsNotVoluntary, PlayedRoundIsNotVoluntary, RequestedByeFollowedByNonVur, RequestedByeFollowedOnlyByVurs, RequestedByeIsVur, SonnebornBergerCut1WithVur, SwissSbEntryOfUnplayedRound, VurCount, ZeroPointByeIsVur

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2. Ranking of Tied Participants (Players or Teams) 2.1 The regulations of the tournament should specify whether tied participants will share the same place in the standings or, if not, a method for ranking them. If neither is done, choose 2.2.2 as the ranking method and apply 4.1.1. 2.2 The available methods of ranking tied participants are: 2.2.1 Over-the-Board play-offs (see Article 3) 2.2.2 Off-the-Board tie-breaks (see Article 4 onwards)

Referencing norms: HigherScoreRankedAbove

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3. Play-offs 3.1 If play-offs are required, the following parameters shall be set out in the specific tournament regulations, as needed: 3.1.1 Whether play-offs are for all tied positions, or specific tied positions (e.g. 1st place only) 3.1.2 Whether qualification for play-offs applies after application of none, some or all of the tie-breaks selected in Article 4.1. 3.1.3 The format (e.g. Round Robin or Knockout) 3.1.4 The method by which pairing numbers are allocated 3.1.5 The method by which colours are allocated 3.1.6 The time limit(s) for all of the games 3.1.7 The schedule for the games, or the break between each game

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4. Tie-Breaks 4.1 They shall take the form of an ordered list of tie-breaks chosen by the Chief Organiser either among those listed in Article 5, or self-defined in the specific regulations of the tournament. 4.1.1 If necessary, the Chief Arbiter shall complete the list by choosing additional tie-breaks from those listed in Article 5, and publish the list before the start of the tournament. 4.2 For the final tournament standings, participants shall be ranked in the order specified by the respective tie-break, starting from the first specified tie-break and moving to the next in the list for each subgroup of participants still tied. When the tie-break list is exhausted, any remaining tie should be broken by drawing of lots, unless the rules of the tournament specify that such ties will not be broken. 4.3 These tie-breaks calculate an evaluation which may be based on: Type A a subset of the games by the tied participants. Tie-Breaks of this type may appear multiple times in the tie-break list. Type B participants' own results or data, so their value can be calculated or predicted by the involved participants before or during their own games Type C opponents' (final) results, so they can be calculated only at the end of the tournament. Type D opponents' prior known data (e.g. ratings, but also results of previous rounds), so their values can be calculated after the pairings are published (i.e. before the games are played) or some combination of all the above. 4.4 If two participants play each other more than once, each game or match will be treated as a separate encounter (except as provided in Article 6.1.2). Consequently, the data of the opponents (e.g. ratings, scores) will be used in sums and averages as many times as the two participants played each other.

Referencing norms: EqualAtPosition, FirstDifferingTiebreakRanksAbove, StandingsContradictTiebreaks, TiebreakPosition

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5. Tie-Breaks List and Description Name (in alphabetical order) | Type | Section | Acronym | Cut-1 Average of Opponents' Buchholz | CC | 8.2 | AOB | Average Perfect [Tournament] Performance of Opponents | DC | 10.5 | APPO | Average [Tournament] Performance Rating of Opponents | DC | 10.4 | APRO | Average Rating of Opponents | D | 10.1 | ARO | ● Buchholz | C | 8.1 | BH | ● Direct Encounter | A | 6 | DE | Fore Buchholz | D | 8.3 | FB | ● Rounds one Elected to Play in | B | 7.6 | REP | Koya System for Round Robin | BC | 9.2 | KS | Number of Games Played with Black | B | 7.3 | BPG | Number of Games Won | B | 7.2 | WON | Number of Games Won with Black | B | 7.4 | BWG | Number of Wins | B | 7.1 | WIN | Perfect Tournament Performance | DB | 10.3 | PTP | Rating | B | 10.6 | RTNG | Sonneborn-Berger | BC | 9.1 | SB | ● Standard Points | B | 7.7 | STD | (Sum of) Progressive Scores | B | 7.5 | PS | ● Tournament Pairing Number | B | 7.8 | TPN | Tournament Performance Rating | DB | 10.2 | TPR | Tie-Breaks specific for Team Knock-Outs Board Count | B | 12.1 | BC | Bottom Board Elimination | B | 12.3 | BBE | Top Board Results | B | 12.2 | TBR | Tie-Breaks specific for Team Competitions Extended Sonneborn-Berger for teams | BC | 13.2 | ESB | ● Extended Direct Encounter for teams | A | 13.3 | EDE | Match Points or Game Points | B | 13.1 | MPvGP | Scores and Schedule Strength Combination | BC/BD | 13.4 | SSSC |

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6. Direct Encounter (DE) (Type A, i.e. multi-listable) 6.1 If some or all the tied participants have met each other, the sum of the scores from these encounters is used to produce separate standings (for use in 6.2 and 6.3), with the following caveats: 6.1.1 forfeit wins or losses not covered by Article 15.2 are excluded unless the specific regulations of the tournament state otherwise - when included, forfeit wins or losses are equivalent to games played 6.1.2 contrary to the provisions of Article 4.4, if two participants have met more than once, the addend to be used by them in the aforementioned sum is the average score of these games. 6.2 If all the tied participants have met each other, the separate standings determine all rankings among them, except for any further ties among any subset of them, for which Article 6 shall be reapplied until no further ties can be resolved. 6.3 In Swiss tournaments, if the tied participants have not played all the games against each other, but one of them will be alone at the top of the separate standings whatever the outcome of the missing games, that participant is ranked first among the tied participants – the same applies to the second rank when the first is assigned this way; and so on. Article 6 shall then be reapplied to all remaining unranked participants of this set.

Referencing norms: DirectEncounterDecidesAll, DirectEncounterScoreWithGames, DirectEncounterScoreWithoutGames, MembersMet, SameMember

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7. Type B Tie-Breaks (based on Participant's own Record) 7.1 Number of Wins (WIN) The number of rounds where a participant obtains, with or without playing, as many points as awarded for a win. 7.2 Number of Games Won (WON) The number of games won over the board. 7.3 Number of Games Played with Black (BPG) The number of games played over the board with the black pieces. 7.4 Number of Games won with Black (BWG) The number of games won over the board with the black pieces. 7.5 (Sum of) Progressive Scores (PS) After each round a participant has a certain tournament score. This tie-break is calculated adding the score of the participant at the end of each round. 7.6 Rounds one Elected to Play (REP) The number of rounds reduced by the number of half-point-byes, zero-point-byes or forfeit losses that a participant had in the tournament. 7.7 Standard Points (STD) The number of rounds in which a participant scores more points than their scheduled opponent, or obtains, without playing, more points than those awarded for a draw, plus half the number of rounds in which the participant scores the same number of points as their scheduled opponent, or obtains, without playing, the same number of points as awarded for a draw. 7.8 Tournament Pairing Number (TPN) Players are sorted according to their (final) tournament pairing number in ascending order. Alternatively, they can be sorted in reverse order (i.e. in descending order).

Referencing norms: GamesPlayedWithBlack, GamesWithBlackValue, GamesWon, GamesWonValue, GamesWonWithBlack, NumberOfWins, NumberOfWinsValue, PlayedGameRoundPoints, ProgressiveScores, ProgressiveScoresValue, RoundInRecord, RoundsElectedToPlay, RoundsElectedValue, ScoreAfterRound, TournamentScore, UnplayedRoundPoints, WinsWithBlackValue

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8. Buchholz and other Tie-Breaks related to Buchholz Note: These tie-breaks must not be used in round-robins. 8.1 Buchholz (BH) The sum of the scores of each of the opponents of a participant. 8.2 Average of Opponents' Buchholz (AOB) The average of the Buchholz (or Fore Buchholz) score of the opponents played over the board. 8.3 Fore Buchholz (FB) Buchholz score calculated as if all paired games for the final round had ended in draws. See Article 16 for Unplayed Rounds Management.

Referencing norms: Buchholz, BuchholzContributionOfGame, BuchholzValue

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9. Tie-Breaks based on both participant's and opponents' results 9.1 Sonneborn-Berger (SB) It is calculated by adding, for each round, a value given by multiplying the final score of the opponents by the points scored against them. See Article 16 for Unplayed Rounds Management. 9.2 Koya System (for Round Robin) (KS) The number of points achieved against all participants who have scored at least 50% of the maximum possible tournament score.

Referencing norms: RoundRobinSbEntryOfGame, SonnebornBerger, SonnebornBergerValue, SwissSbEntryOfGame