King Of The Court is a type of tournament in which players rotate partners until, ideally, everyone has played with everyone else. At the end you see which individual player won the most, and that player is anointed King. It's a way to make an individual contest out of a doubles event.
Below is a format that satisfies our basic requirements: each player must play on a team with each other player once, and must face each other player twice. Additionally, it attempts to even out play on the two courts. A lot of math and number-crunching went into this. Various solutions were arrived at in different ways by John Greensage, John Kirkland, and Conrad Damon. We'll spare you the math. The solution below and court assignments are from Kirkland.
To begin, players draw numbers 1-8 out of a hat. The chart below shows the teams and which courts they play on. Player 1 spends the day on Court A, while the others split their games between the two courts.
| Court A | Court B |
|---|---|
| 1 / 2 vs 3 / 4 | 5 / 6 vs 7 / 8 |
| 1 / 3 vs 6 / 8 | 2 / 4 vs 5 / 7 |
| 1 / 8 vs 2 / 7 | 3 / 6 vs 4 / 5 |
| 1 / 7 vs 3 / 5 | 2 / 8 vs 4 / 6 |
| 1 / 5 vs 4 / 8 | 2 / 6 vs 3 / 7 |
| 1 / 4 vs 6 / 7 | 2 / 3 vs 5 / 8 |
| 1 / 6 vs 2 / 5 | 4 / 7 vs 3 / 8 |
Score sheet for 8 players
Cade Loving has come up with an alternative format, where players are seeded and more attention is paid to matchups. His description is below. See also this document (Word doc) which is a more comprehensive treatise on formats.
Essentially, I have chosen my pairings based on an idealized last game of the
day whereby players are as evenly matched in ability as possible, and the
progression of games allows both better and weaker players to "warm up" in the
match ups with the most probable outcomes. One way of determining these
outcomes is to look at the pairings' total rank. For example, 1 & 8 versus
2 & 7 is a great matchup because each pairing's total rank is 9.
What makes this work is seeding the 8 players to help mitigate random factors
that come out in hat-draw style. So, after deciding seeds, the games flow as
follows:
Court A Court B
1&3 -v- 6&8 (4 -v- 14) 2&4 -v- 5&7 (6 -v- 12)
1&6 4&7 (7 v 11) 3&8 2&5 (11 v 7)
1&2 7&8 (3 v 15) 3&4 5&6 (7 v 11)
1&5 2&6 (6 v 8) 4&8 3&7 (12 v 10)
1&8 4&5 (9 v 9) 2&7 3&6 (9 V 9)
1&7 3&5 (8 V 8) 4&6 2&5 (10 V 10)
*6&7 5&8 *1&4 2&3 (13 V 13 and 5 v 5)
*Before the Last round, if desired, player tabulation can be taken to
determine which of the last two matchups is the "finals" and the games can be
played in succeession.
Another design feature is that the 3rd round mitigates 1&2's power by matching
them agains 7&8.
Here is an anaysis of each player's likely outcomes in order of matchups.
W="certain" win, L="certain" loss, PW=probable win, PL=probable loss, ?=even
possibilities.
1: W, PW, W, ?,?,?,?
2: W. PW, W, ?,?,?,?
3: W, PL, PW, ?,?,?,?
4: W, PL, PW, ?,?,?,?
5: L, PW, PL, ?,?,?,?
6: L, PW, PL, ?,?,?,?
7: L, PL, L, ?,?,?,?
8: L, PL, L, ?,?,?,?
It's actually not too far-fetched to imagine 8 coming out with a better record
than 1 when you look at the possibilities!
In the name of fairness, I also have the tournament drawn up so that number 1
does not stay on the same court all day, but I realize it may not matter to
some, and I wanted to present it as close to the way you did for easy
comparison.