Imagine beating a player in your game, scoring better than him against the strongest opponent in the group — and still finishing behind him in the final standings.
It sounds impossible.
Yet under certain circumstances this is exactly what can happen when the FIDE Direct Encounter (DE) tie-break is applied repeatedly.
This article explains why.
Why Tie-Breaks Exist
In chess tournaments tie-break systems exist for a simple reason:
many players finish with the same number of points, and we need a way to order them.
A good tie-break should use as much information as possible from the tournament.
Criteria such as Buchholz or Sonneborn-Berger look at all opponents and all results.
They aggregate many observations and therefore reduce randomness — or at least they attempt to.
The Direct Encounter (DE) tie-break works very differently.
When two players are tied, it looks only at the game they played against each other.
At first sight this seems natural:
if A beat B, then A should be ranked ahead of B.
Unfortunately tournaments are more complicated than that.
The Problem the New Rule Tried to Solve
The 2024 revision of the FIDE regulations tried to address a real limitation of the classical Direct Encounter (all play all). Consider three players tied on points:
- A beat B
- A beat C
- B and C never played each other
Under the old rules Direct Encounter could not be applied, because the “mini-tournament” among the tied players was incomplete. Yet the situation is obvious:
A defeated both of the other players and is clearly the strongest within that group.
The new formulation correctly fixes this problem by allowing arbiters to determine that A must be ranked first even if B and C did not meet.
So far, this is a sensible improvement. But the regulation goes further. After determining the winner of the group, it allows the arbiter to remove that player and repeat the procedure on the remaining players.
And this is where problems start to appear.
One Game — or Just a Few
Before looking at the example, it is useful to remember something simple. In chess tournaments the scoring scale is
- win = 1
- draw = ½
- loss = 0
This scale is not a natural law.
It is simply a historical convention. We could just as well have used 3–1–0, 5-2–0, ... and the tournament would still work.
Moreover, a single chess game is a very noisy observation. It can depend on
- preparation
- fatigue
- a single tactical mistake
- simple luck
That is why tournaments consist of many rounds.
Yet Direct Encounter bases the final ordering on one game — or sometimes just a few games. From a statistical point of view, this is already fragile.
An Old Lesson from Voting Theory
Long before chess tournaments existed, people had already noticed similar paradoxes.
Pliny the Younger recounts an episode from the Roman Senate. Three different decisions were under consideration. The option supported by the largest number of senators was not adopted because, once one of the other proposals was withdrawn, the order of preferences shifted and a completely different outcome emerged (Handbook of Computational Social Choice, 2016, p. 3).
In other words, removing one alternative changed the relative ranking of the others. This phenomenon later became a classic topic in the theory of voting systems. And something very similar can happen with Direct Encounter.
A Concrete Example
Consider a tied group of seven players with the following Direct Encounter scores within the group.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | Pts | max | |
|---|---|---|---|---|---|---|---|---|---|
| 1 | ■ | 0.5 | 1.0 | 1.0 | 0.5 | 0.0 | 1.0 | 4.0 | 4.0 |
| 2 | 0.5 | ■ | 1.0 | 1.0 | 0.5 | 0.5 | 1.0 | 4.5 | 4.5 |
| 3 | 0.0 | 0.0 | ■ | 1.0 | 1.0 | 1.0 | 1.0 | 4.0 | 4.0 |
| 4 | 0.0 | 0.0 | 0.0 | ■ | 1.0 | 1.0 | 0.5 | 2.5 | 2.5 |
| 5 | 0.5 | 0.5 | 0.0 | 0.0 | ■ | -- | 1.0 | 2.0 | 3.0 |
| 6 | 1.0 | 0.5 | 0.0 | 0.0 | -- | ■ | 1.0 | 2.5 | 3.5 |
| 7 | 0.0 | 0.0 | 0.0 | 0.5 | 0.0 | 0.0 | ■ | 0.5 | 0.5 |
Player 2 has 4.5 points and cannot be caught by anyone else.
So the first step is perfectly clear:
Player 2 is ranked first.
According to the current procedure, we now remove Player 2 and all his results, and apply Direct Encounter again to the remaining players. This is where something surprising happens.
Consider Players 1 and 3:
- Player 1 drew with Player 2
- Player 3 lost to Player 2
- Player 1 defeated Player 3
At first sight the situation is obvious. Player 1 beat Player 3 and also performed better against the strongest player in the group. Yet after removing Player 2 and recalculating Direct Encounter among the remaining players, Player 3 may end up ranked ahead of Player 1.
No new games have been played.
No new information has appeared.
The system has simply deleted the results against the subgroup winner.
And by deleting those results it penalised the player who had actually performed better against him.
Why This Happens
The mechanism is simple. When the winner of the group is removed:
- players who scored well against him lose points
- players who scored poorly against him lose little or nothing
So the recalculation may reverse the relative order of the remaining players.
This is not an accident. It is a structural effect of the procedure.
Why This Is Especially Risky in Swiss Tournaments
In round-robin tournaments every player meets every other player. In Swiss tournaments this is rarely the case. Players inside a tie-break group often have not played each other at all. This makes Direct Encounter particularly fragile. Instead of using the information produced by the entire tournament, the system may end up relying on one game — or a very small number of games.
A Surprising Regulatory Choice
The recursive application of Direct Encounter effectively acts as a cut on the best results. When the subgroup winner is removed, players lose one of their strongest comparative results — often a draw or even a win against the strongest opponent in the group.
This is strikingly inconsistent with the philosophy of other FIDE tie-break systems, where cuts are applied to the worst results (for example in Buchholz or Sonneborn-Berger), precisely in order to reduce noise and accidental pairings. Direct Encounter therefore removes information in the opposite direction: instead of discarding the weakest results, it may eliminate the strongest ones.
Despite these limitations, the FIDE regulations allow Direct Encounter to appear more than once in the list of tie-breaks.
This means the final ranking of a tournament may depend repeatedly on a criterion based on one game or a few games. When that happens, the final classification may start to resemble a lottery rather than a measurement of tournament performance.
Final Remark
The intuition behind Direct Encounter is understandable. If one player clearly dominated the others in a tied group, that information should be used. But once the winner has been identified, it is much safer to continue with criteria that use all the information produced by the tournament. Repeating Direct Encounter multiple times risks introducing exactly the instability that tie-break systems are supposed to eliminate.
Tie-break systems should reduce randomness, not amplify it.
When a ranking method depends on one game or a few games, and when removing a third player can reverse the order of the others, caution is advisable. These issues deserve careful consideration if we want tournament rankings to reflect the real structure of the competition rather than the accidental outcome of a single encounter.
My personal recommendation would therefore be to remove Direct Encounter entirely from tie-break systems and to rely instead on criteria that make use of as many games as possible. Any global method that aggregates information from the tournament as a whole will generally be far more stable than a rule based on a single encounter.
For a broader discussion on common misunderstandings about tournament systems see also: Misconception.