A complete guide to understanding tournament rankings when players finish with equal points. 17 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 17 tiebreak systems, all calculated according to the official FIDE Handbook C.07 (effective August 2024). 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).
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
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."
Additional tie breaks based on progressive scores, ratings, and color balance.
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 first round's contribution. 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)
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:
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)
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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