will be 1, 1, 2, 2½, 2½. The sum of these numbers is 9. Additionally, one point is subtracted from the sum for each unplayed win, and ½ point is subtracted for each unplayed draw. In the previous example, if the fourth-round draw was instead a ½ point bye, then ½ point would be subtracted and the final sum would be 8½. This system places more weight on games won in the early rounds and the least weight on games won in the final rounds. The rationale for this system is that a player who scored well early in the tournament has most likely faced tougher opponents in later rounds and should therefore be favored over a player who scored poorly in the start before subsequently scoring points against weaker opponents . 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. Cumulative opponent's score This sums the cumulative scores of the player's opponents . Result between tied players If the tied players played each other, if one of them won then that player finishes higher on tie-break . Most games with the black pieces The player that had the black pieces the most times finishes highest on tie-breaks . Most wins (Baumbach) The player with the most wins finishes highest on tie-breaks. This is used as the first tie-break rule for individual tournaments in ICCF. Kashdan Invented by Isaac Kashdan, this system awards four points for a win, two points for a draw, one point for a loss, and none for an unplayed game. As a result, if players with no unplayed games tie, the one with fewer draws finishes higher on the tie-break (i.e. a win and a loss is better than two draws) . Sonneborn–Berger score Add the scores of every opponent the player beats and half of the score of every opponent the player