A complete guide to understanding tournament rankings when players finish with equal points. 28 tiebreak systems explained with practical examples.
In chess tournaments, it's common for multiple players to finish with the same score. Tie breaks determine the final ranking without needing extra games.
Imagine a tournament where 3 players all finish with 5 points out of 7. Who gets first place? That's where tie breaks come in. They use mathematical criteria based on the games already played to establish a fair ranking.
ChessPairings.org supports 28 tiebreak systems, all calculated according to the official FIDE Handbook C.07 (effective 2026). You can configure them in any order to match your tournament regulations.
Click on each tiebreak to see examples and technical details. Organized by category as in the software.
Based on the sum of your opponents' scores. The most commonly used tie breaks.
Like standard Buchholz, but excludes the lowest opponent's score from the sum. This compensates for an unfortunate first-round pairing against a weak player who drops out.
Why Cut-1 first? FIDE recommends Buchholz Cut-1 as the primary tiebreak because it's more fair — it removes the impact of your worst opponent.
Player A's opponents scored: 5, 4.5, 4, 3.5, 3, 2, 1 (cut)
Buchholz Cut-1 = 22 (excluding the 1)
When cutting, Voluntary Unplayed Rounds (half-bye, zero-bye, forfeit loss) are cut first, even if they don't have the lowest score.
Buchholz adds up the final scores of all your opponents. If you played against strong opponents (who scored many points), your Buchholz will be higher.
The logic: Scoring 5 points against opponents who each scored 4-5 points is harder than scoring 5 points against opponents who only scored 1-2 points.
Player A and Player B both have 5 points after 7 rounds.
Result: Player A ranks higher because they faced stronger opposition.
Article 16.3 - Adjusted Scores: When an opponent has unplayed rounds, their score is adjusted:
Article 16.4 - Dummy Opponent: For your own unplayed rounds, a virtual opponent is used with your final score.
Excludes the two lowest opponent scores. Useful for longer tournaments (9+ rounds) where a player might face two weak opponents.
Player A's opponents scored: 5, 4.5, 4, 3.5, 3, 2, 1 (both cut)
Buchholz Cut-2 = 20
Excludes both the highest and lowest opponent scores. This removes extreme values from both ends, giving a more "average" strength of opposition.
Player A's opponents scored: 5, 4.5, 4, 3.5, 3, 2, 1
Median Buchholz = 17 (4.5 + 4 + 3.5 + 3 + 2)
Excludes the two highest and two lowest opponent scores. Even more aggressive trimming for very long tournaments.
9-round tournament. Opponents scored: 6, 5, 4.5, 4, 3.5, 3, 2, 1.5, 1
Median-2 = 17 (4.5 + 4 + 3.5 + 3 + 2)
Weighs opponent strength by your result against them. Beating strong players matters more.
Multiplies each opponent's score by the result you achieved against them. Win = full score, Draw = half score, Loss = 0.
The logic: Rewards beating strong opponents more than beating weak ones.
Player A has 4 points from 5 games:
Total SB = 10
Formula: SB = Σ (Opponent's Adjusted Score × Result)
Uses adjusted scores (Art. 16.3) for played rounds and dummy opponent (Art. 16.4) for unplayed rounds.
Like standard SB, but excludes the lowest contribution. The VUR rule applies: voluntary unplayed rounds are cut first.
From the SB example above (contributions: 4, 3, 1.75, 1.25, 0):
Cut the 0 → SB Cut-1 = 10
But if the 0 was from a played loss and player had a half-bye contributing 0.5, the half-bye would be cut instead (VUR rule).
Like standard Sonneborn-Berger, but excludes the two lowest contributions. In longer tournaments (7+ rounds), multiple "unlucky" results can occur — for example, two losses against weak opponents. Cut-2 removes both anomalies, giving a more accurate picture of the quality of your wins.
Your SB contributions across 7 rounds: 4, 3.5, 3, 1.5, 1, 0.5, 0
SB Cut-2 excludes the two lowest (0.5 and 0):
SB Cut-2 = 13 (4 + 3.5 + 3 + 1.5 + 1)
Based on wins and direct results. Rewards decisive play.
The simplest tiebreak: if two tied players played each other, whoever won that game ranks higher.
For more than 2 players: A mini-tournament is calculated among all tied players, using only their games against each other.
Players A, B, and C all have 5 points. Their games against each other:
Mini-standings: A=1.5, B=1, C=0.5
Final ranking: A, B, C
Works like the standard direct encounter, but forfeit wins and losses count as regular games. In the classic version, forfeits may be treated differently; with this variant, a forfeit win counts exactly like an over-the-board win.
Player A and Player B both have 5 points. Player A beat Player B by forfeit in round 3 (Player B didn't show up).
With standard direct encounter, the forfeit might not count.
With this variant, Player A ranks higher.
Counts all rounds where the player scored a full point, including forfeit wins, PAB, and byes.
The logic: A player with 4 wins and 2 losses played more decisively than one with 2 wins and 4 draws, even if both have 4 points.
Both players have 4 points after 6 rounds:
Result: Player A ranks higher.
"The number of rounds where a participant obtains, with or without playing, as many points as awarded for a win."
Includes: played wins, forfeit wins, PAB, full-point byes.
Counts only games actually played and won at the board. Excludes forfeit wins, byes, and PAB.
Same WIN, but Player B ranks higher on WON.
"The number of games won over the board."
Counts games won while playing with the Black pieces (OTB only).
The logic: Winning with Black is statistically harder since White moves first.
Both players have 4 wins:
Player B ranks higher.
"The number of games won over the board with the black pieces."
Based on cumulative round-by-round scores. Rewards early wins.
Adds up the cumulative score after each round. Early wins count more because they contribute to every subsequent total.
Two players with 3.5 points after 5 rounds:
| Round | A | Cum. | B | Cum. |
|---|---|---|---|---|
| 1 | 1 | 1 | 0 | 0 |
| 2 | 1 | 2 | 0.5 | 0.5 |
| 3 | 0.5 | 2.5 | 1 | 1.5 |
| 4 | 0 | 2.5 | 1 | 2.5 |
| 5 | 1 | 3.5 | 1 | 3.5 |
A: 1+2+2.5+2.5+3.5 = 11.5
B: 0+0.5+1.5+2.5+3.5 = 8
Player A ranks higher despite same final score.
Like Progressive, but excludes the lowest cumulative value. This compensates for an unlucky first-round loss.
From previous example:
A: 2+2.5+2.5+3.5 = 10.5 (cut the 1)
B: 0.5+1.5+2.5+3.5 = 8 (cut the 0)
Like standard Progressive, but excludes the two lowest cumulative values. Useful in tournaments with many rounds where early rounds can create anomalous situations.
After 6 rounds your cumulative scores are: 0, 1, 2, 3, 4, 5
Progressive Cut-2 = 14 (2 + 3 + 4 + 5)
Excludes both the highest and lowest cumulative values, keeping only the middle values. Removes anomalies in both directions: neither a disastrous start nor a brilliant finish excessively influences the result.
After 5 rounds your cumulative scores are: 0, 1, 2, 3, 4
Progressive Median = 6 (1 + 2 + 3)
More extreme version of Progressive Median: excludes the 2 highest and 2 lowest cumulative values. Recommended only for very long tournaments (9+ rounds) where very "clean" data is needed to discriminate between tied players.
9-round tournament. Cumulative scores: 0, 1, 1.5, 2.5, 3, 4, 4.5, 5.5, 6.5
Progressive Median-2 = 15.5 (1.5 + 2.5 + 3 + 4 + 4.5)
Based on opponent ratings and tournament performance.
Calculates the average Elo rating of all opponents faced (excluding byes).
Both players have 5 points after 6 games:
Player A ranks higher.
Like ARO, but excludes the lowest-rated opponent from the average. Recommended by FIDE for tournaments with consistent ratings.
A's opponents: 2100, 1950, 2050, 1900, 2000, 1850
AROC = 2000 (average of remaining 5)
Like standard ARO, but excludes the two lowest-rated opponents. If you faced two players with very low ratings (beginners, unrated players), these won't drag down your average. Useful in open tournaments with wide rating disparities.
Opponents' ratings: 2100, 1950, 1800, 1400, 1200
Standard ARO = (2100+1950+1800+1400+1200)/5 = 1690
ARO Cut-2 = (2100+1950+1800)/3 = 1950
Excludes both the highest-rated and lowest-rated opponent, calculating the average from the middle values only. Removes both the "I played a Grandmaster" and the "I played a beginner" effects.
Opponents' ratings: 2300, 1900, 1800, 1750, 1200
ARO Median = 1817 ((1900+1800+1750)/3)
More extreme version of ARO Median: excludes the 2 highest-rated and 2 lowest-rated opponents. Recommended for very long open tournaments with wide rating variability.
9-round tournament. Opponents' ratings: 2350, 2200, 2000, 1950, 1900, 1850, 1800, 1500, 1300
ARO Median-2 = 1900 ((2000+1950+1900+1850+1800)/5)
TPR indicates at what Elo level you played in the tournament. It's calculated from the average Elo of your opponents plus a bonus from the FIDE lookup table based on your scoring percentage. The more points you score against strong opponents, the higher your performance. This is the same method used by FIDE for title norm calculations (IM, GM).
Formula: TPR = Average Opponent Elo + FIDE Table Bonus
You played opponents with average Elo 1800 and scored 4/5 (80%).
The FIDE table gives a bonus of +240 for 80%.
TPR = 1800 + 240 = 2040 — you played like a 2040-rated player!
A more precise version of TPR. Instead of using the FIDE lookup table with rounded values, it finds the exact rating at which your expected score equals your actual score, using a binary search algorithm with decimal precision. The differences from standard TPR are small but can be decisive in tournaments with many tied players.
Additional tie breaks based on color balance and participation.
Counts how many games the player had with the Black pieces.
The logic: Playing more games with Black is a disadvantage, so achieving the same score with more Black games shows stronger performance.
Both players have 4 points after 7 rounds:
Counts the number of rounds in which the player chose to play, excluding voluntarily skipped rounds (requested byes, withdrawals). This replaces the old GE (Games Played) system and was introduced in the FIDE 2024 rules. The idea is to reward players who showed up: between two players with the same score, the one who actually played more games ranks higher.
In a 7-round tournament:
All else being equal, Player A ranks higher.
REP replaces the former "Games Played" (GE) criterion. Only rounds where the player elected to participate count — PAB counts as elected, but requested byes and withdrawal rounds do not.
Counts only points scored against opponents who achieved at least 50% of the maximum possible score. Common in Round Robin tournaments.
10-player Round Robin (max 9 points), 50% threshold = 4.5 points.
Player A's results against opponents with ≥4.5 points:
Koya = 1.5
How FIDE rules handle unplayed rounds in tiebreak calculations.
Odd number of players — one gets a PAB (1 point).
Opponent no-show or disqualification.
Player requests time off.
Player leaves mid-tournament.
VUR (Voluntary Unplayed Round) = rounds the player chose not to play: half-byes, zero-byes, forfeit losses. In Buchholz Cut variants, VUR contributions are cut first — even if they don't have the lowest value.
FIDE recommends different combinations depending on your tournament.
Players have unreliable or missing ratings.
All players have reliable FIDE/national ratings.
Every player plays every other player.
Common questions about tie breaks in chess tournaments.
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