Swiss system tournaments, a type of group tournament common in chess and other board games, and in card games such as bridge, use various criteria to break ties between players who have the same total number of points after the last round.
In chess, where results are simply win/loss or draw, strength of schedule is the idea behind the methods based on the games already played: that the player that played the harder competition to achieve the same number of points should be ranked higher.
[5] A practical benefit of the cumulative system is that it is simple to track with pen and paper when running a large tournament.
Of course in the age of computers and smart phones, instead of accumulating points scored against weak players, we could just calculate who had the toughest schedule as with the Solkoff and median systems.
An alternative explanation for the popularity of the cumulative system is that it is easier for coaches, players and the audience to follow the potential scores and prizes, as the point totals don't vary and only need to be added to from round to round.
[10] The system was named after William Sonneborn and Johann Berger, but it was invented by Oscar Gelbfuhs.
What we call the Sonneborn-Berger system was not invented by Sonneborn or Berger, and it was not originally designed for tie-breaking.
In 1886 Sonneborn criticized the system and suggested an improvement that would give a better-weighted score.
[citation needed] When the system is used to break ties between equally scoring players, adding in the square of the player's raw score does no good, so the Sonneborn improvement is omitted.
[14] The Brightwell Quotient used in the World Othello Championship uses a formula based on strength of schedule and margin of victory within games; it also allows for byes.
FIDE rules provide for a single fast decisive game, known as Armageddon.
As a last resort, ties are broken by a random process such as a coin flip.
[16] Harry Golombek points out deficiencies in most of the tie-break systems and recommends a playoff if there is time.