The method of dealing with ties depends on the kind of tournament.
Swiss Tournaments
For Swiss tournaments, Chess.com uses eight tie breaking methods to ensure that ties are broken in the fairest way possible. The following list of tie-breaking methods is used, from top to bottom, moving down the list only if there is still a tie after using the previous method. For example the Sonneborn-Berger method is only used if the result is still a tie after trying the Buchholz Cut 1 and Buchholz methods.
Tie breaking methods:
Buchholz cut 1 - Your Buchholz score is calculated by adding together the tournament scores of each player you played against, except the one with the lowest score (this is the 'cut 1.') The final number is your Buchholz tie-break score.
Buchholz - The same as above, except the lowest score is not dropped, and is included in the calculation.
Sonneborn-Berger - This is calculated by adding up the tournament score of each opponent you defeated, and half the tournament score of each drawn opponent.
Direct encounter - If any players are still tied at this point, and all tied players have played against each other in the tournament, then the player with the most points out of those games is the winner. If the tied players have not all played each other, or there is a tie for points within those games, then it is still a tie.
Number of wins - The player with the highest total number of wins breaks the tie.
Number of wins with black - The player with the highest number of wins with the black pieces breaks the tie.
AROC 1 - This stands for Average Rating of Opponents Cut 1. This means the rating of all your opponents (excluding the lowest rated opponent) is averaged, and the player with the highest average opponent rating is the winner. Opponent rating is based on rating at the start of each round.
Rating - If it is still a tie at this point, then the player with the highest rating wins. This is based on rating at the start of the last round.
Round Robin tournaments
Round Robin tournaments (such as Daily tournaments) use the Sonneborn-Berger tie break method. If you don’t want to use tie breaks in your tournament, you can disable it in the advanced options when creating your tournament.
If you do disable tie breaks, both tied players will advance to the next round. See here for more info on creating tournaments.
However, most tournament directors do use tie breaks. The Sonneborn-Berger method will give the win to the player who has defeated the players with the most tournament points.
Below is an example of a group in a daily tournament where this tie break is used. You can see the top two players have the same score: 8.5. The tie break points are based on the score of players they have defeated and drawn against.
In the below image, the first place player has more tie break points, so they have advanced. Without the tie break, both players 1 and 2 would have advanced since they have the same score.
If two players have the same score and the same tie break score, both will advance. Unlike with Swiss tournaments, Round Robin tournaments do not have secondary tie-break methods. If it is still a tie after the Sonneborn-Berger method, the tie will remain unbroken.
Here is an example from the same tournament; both players 1 and 2 had the same score and the same tie break; both advanced to the next round:
Below is a simplified example of how the Sonneborn-Berger score method works:
Group # -- | Bob | Mary | John | Score | Tie Break |
1. Bob | X | 0 1 | 1 1 | 3 | 4.5 |
2. Mary | 0 1 | X | 0 0.5 | 1.5 | 3.75 |
3. John | 0 0 | 0.5 1 | X | 1.5 | 2.25 |
A player's Sonneborn-Berger score is calculated by adding together the score points of the players they have defeated and half of the score points of players they have drawn against.
In the table above, Bob won one game against Mary and two games against John. So Bob gets 1x1.5 points from Mary and 2 x 1.5 points from John, which sums up to 4.5 tie break points.
Mary won one game against Bob and drew one game against John. So Mary gets 1x3.0 points from Bob and 0.5x1.5 points from John, which sums up to 3.75 tie break points.
John won one game and drew one game against Mary. So John gets 1.5x1.5 points from Mary, which sums up to 2.25 tie break points.