TCEC Swiss Tournament System
TCEC Swiss Tournament System is a variant of the Swiss tournament format. It is completely deterministic with a reasonably simple rule set, resembling the Monrad system. It can be played with any number of participants and any number of rounds. Rounds are either single or double rounds. It is designed to be played with 40-50 engines over 10-25 rounds. It is recommended to have an even number of engines.
There are P players and N rounds. The format is either single round or double round.
At the beginning of every round, the pairs are determined. See pairing below.
In the single round format, every pair plays once per round. Thus, there are ⌊P/2⌋ games (rounded down). In the double round format, every pair plays twice per round and the number of games is 2*⌊P/2⌋ per round. The second game is with reversed colors.
In case of an odd number of players, one player per round receives a BYE. The BYE games are scored as wins.
After all the rounds have been played, the tournament is complete. The final ranking of players is determined as per the following criteria: (priority order)
- Score (DESCending)
- Number of received BYEs (ASCending, less is better)
- Tiebreakers (e.g., number of black games DESC, SB, r-mobility score)
Every player is assigned a unique seeding number. This determines the player order in the first round and is used as a secondary ordering criterion in the following rounds.
- Equal distance seeding may be used to promote the expected top encounters to the later rounds of the tournament
Pairing starts by ranking the players by:
- Score (DESC; i.e., the top player has the highest score)
- Seed (ASC)
This ranking is called the pairing order.
- Every round (incl. the first round) uses the same pairing ordering scheme.
- The ranking for pairing is different to final ranking.
In case of an odd number of players, the player to receive the BYE is determined as follows. Order the players by:
- Number of received BYEs (DESC)
- Pairing order (ASC)
The bottom player receives the BYE.
That is, the worst-performing player that has not yet received a BYE receives one. If every player has already received a BYE, then the worst-performing player that has received a single BYE receives one. And so on.
Determine whether there exists a viable pairing for the round. That is, whether there exists any pairing in which no players meet the second time. If no viable pairings exist, remove the earliest round in the encounter history. Repeat this as necessary until a viable pairing exists. The removals are permanent, i.e., they carry over to the following rounds.
- The brute force method may be used to go through all possible pairings and determine whether any of them are viable. The worst-case performance is O(n⁴) steps (where n=#players), but computers are fast. In practice, such method is much faster when the previous encounters are removed from the iteration space. In such case, either a viable pairing is found quickly or the iteration space is reduced significantly due to previous encounters.
Perform pairing. The players are paired one by one in the pairing order as follows:
- Pick the first unpaired player by the pairing order. Mark the player as paired. This player is called the first-of-pair.
- Pick the highest-ranked player as the second-of-pair that maintains the following criteria:
- The pair has not met before (encounter history removal applies)
- The viability of the round pairing is maintained
Do this until every player has been paired. Add pairs in the encounter history for this round.
- The possible BYE player is not considered for pairing
Determine playing colors for each pair:
- Single rounds. Determine which player of the pair has the greater white game difference (i.e., games played as white - games played as black). The player with the greater white game difference gets the black pieces. In case the difference equals, then the player with the higher score gets the black pieces. If both players have the same score, then the following formula is used:
- First-of-pair receives the white pieces on rounds 2, 3, 6, 7, 10, 11, ... (first-of-pair has lower seed number)
- Second-of-pair receives the white pieces on rounds 1, 4, 5, 8, 9, 12, ...
- In other words, the following pattern is used to determine the white-game advantage between the first and the second of pair per rounds: 2112 2112 2112...
- The rationale for the 4-round pattern is that the white game difference is roughly even and uneven every second round. Thus, the pattern in flipped every second round with a total 4-round cycle.
- Double rounds. The first-of-pair always plays with the black pieces on the first encounter, and with the white pieces on the second encounter
Playing order within a round
- Single rounds. Pairs are ordered by the pairing order of the first-of-pair (DESC). That is, the worst-performing pair plays first.
- Double rounds. The single round schedule is executed twice. That is, the second encounter with reversed colors is after every pair has played once.