DRAFT IN PROGRESS

# King-of-the-Hill Considered Inadequate

King-of-the-Hill (KOTH) pairings match the top-ranked player in a tournament with the second-ranked, #3 vs. #4, and so on all the way down. KOTH is used widely in North America to pair the last round of Scrabble tournaments, and in Asia to pair entire tournaments.

There is an appealing yet simplistic fairness to KOTH. Players seek to optimise their final rankings by playing opponents ranked as high as possible, because if they win, they not only get credit for the win but inflict a loss on a significant rival. Sometimes, the only way that a player can finish first is to play the top-ranked player and beat them. Since more than one player may be in this position at the same time, awarding the right to play the leader to the closest-ranked rival justly rewards that rival for their performance so far. The same argument can be repeated down to the bottom of the rankings.

And yet it is widely recognized that the #1-#2 pairing is sometimes exceedingly unfair to the player ranked #3. It can happen that the top two players have played each other already, possibly even more than once, while #3 has not played #1. It is preferable that the eventual winner of a tournament have played as many as possible of the other top finishers; tournaments which are decided by comparing how many times top players were able to beat significantly weaker players are uninteresting for all concerned.

When this problem is addressed, the standard solution is called "KOTH without repeats" or "KOTH without three-peats". #1 is paired with the highest-ranked player that he has not already played (or in the case of three-peats, played twice), and so on down the rankings.