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#King of the Tournament

In graph theory, a tournament is a set of N vertices, where each each vertex is connected to each other vertex with a directed edge.

In layman terms, its a round-robin tournament, where every team plays every other team.

At the beginning of each round, each player will receive N*5 points, and randomly ordered from 1 to N.

Then, there will be N-1 turns, where a given player, P, will face the (P+T)%Nth player on the Tth turn (T goes from 1 to N).

On a turn, the two players will both use X points against the other (these points are non-refundable). The winner will be the player that committed the most points. The tiebreakers will be (in the following order):

1. The player with the least points
2. The player with an ordering closest to the current turn number (wraps around, 1 is closer than 3 in a 6 person game)
3. The player who won last between the two
4. The player who is after the current turn number (wraps around)

After each player plays each other player, the kings of the tournament are determined, and the next round will commence, where only the kings will play.

A king is a player that either defeated every other player, or, for each player P that it did not beat, there exists at least one other player that the king beat that beat P. (Aka, if I were playing you, I wouldn't necessarily have to beat you, I would just have to beat a player that beats you)

If a round ends with the same amount of players as the last, the player(s) with the least amount of wins in the round will be eliminated. If all players have the same amount of wins in the last round, then the player(s) with the least amount of total wins will be eliminated. In the case of a tie, all remaining players will be declared the winners.