For indivisible prizes, such as trophies, championship titles, free entries, etc., the following Tiebreak systems are used to break ties among players with the same final score.


          What if several players are tied at the end with the same score?  The tiebreak systems used are:


           The computer adds up the scores of each tied player's opponents (a half‑point is counted for any rounds that the opponent did not play), and disregards the least-significant (usually the lowest scoring) opponent (the Modified Median System).  The player with the highest total has played opponents with the best scores in the tournament‑‑ in theory, the hardest opponents. 


            If the players are still  tied, the low scoring opponents’ scores are counted as well (Solkoff Tiebreaks). 


            If the players are still  tied, the computer then adds each player's score to his/her score from the previous round (the Cumulative System).  Thus, if a player won his first game, lost his second, won his third, won his fourth, and drew his last game, his score in the tournament would be 1 point after round 1, still 1 point after round 2 (he lost), 2 points after round 3, 3 points after round 4,  and 3 ˝ points after round 4.  His Cumulative Tiebreaks would be 1 + 1 + 2 + 3  + 3˝ = 10˝.


            To break ties among players who are still  tied with the same Cumulative Tiebreaks, the computer then repeats this process, but it adds all the Cumulative Tiebreaks of the opponents of each tied player (the Cumulative Tiebreakers of the Cumulative Tiebreakers, or CTBCTB system).  This almost  always breaks the tie.  The Cumulative System rewards players who win earlier when the opponents are easier, then face tougher opponents.