from the Swiss pairing system. Final scores and tie-breaking There is a fixed number of rounds. After the last round, players are ranked by their score. If players remain tied, a tie-break score is used, such as the sum of all opponents' scores (Buchholz chess rating). Analysis, advantages, and disadvantages Assuming no drawn games, determining a clear winner (and, incidentally, a clear loser) would require the same number of rounds as that of a knockout tournament, which is the binary logarithm of the number of players rounded up. Thus three rounds can handle up to eight players, four rounds can handle up to sixteen players, ten rounds can handle up to one thousand and twenty-four players, and so on. If fewer than this minimum number of rounds are played, two or more players could finish the tournament with a perfect score, having won all their games but never having faced each other. Due to the fact that players should meet each other at most once and pairings are chosen dependent on the results, there is a natural upper bound on the number of rounds of a Swiss-system tournament, which is equal to half of the number of players rounded up. Should more than this number of rounds be played, the tournament might run into the situation that there is either no feasible round, or some players have to play each other a second time. Compared to a knockout tournament, a Swiss system has the advantage of not eliminating anyone; a player who enters the tournament knows that they can play in all the rounds, regardless of results. The only exception is that one player is left over when there is an odd number of players. The player left over receives a bye: they do not play that round but are usually awarded the same number of points as for winning a game (e.g. one point for a chess tournament). The player is reintroduced in the next round and will not receive another bye. Another advantage compared to knockout tournaments is that the final ranking gives some indication of the relative strengths of all contestants, not just of the tournament winner. By contrast, in a knockout tournament the second-best contestant is not necessarily the losing finalist, but could be any of the contestants defeated by the eventual tournament winner in earlier rounds. In a Swiss-system tournament, sometimes a player has such