I really enjoyed the league. Every league game, besides counting towards my rating, also counts towards the league score. I know that if I win enough games to get enough points to get promoted, I will get to play stronger opponents. Many players have developed ways to rule the league. I once developed a strategy allowing me to play against similar-strength players in higher divisions (I get more points for beating players in higher divisions) to help me advance divisions quickly and meet much stronger players.
Here are the rules for the GK leagues (quoted directly from the site):
1. Players in the same division can challenge each other to a league match consisting of two games (one playing as white and one as black) with time control set to 3 days per move by clicking on the "play" link next to the corresponding user name. League challenges cannot be declined and league games cannot be cancelled. Other players will not be able to challenge you to a game if the vacation flag is set for your account.
2. Each win is counted as +1 point towards the league rating, each draw is 0 points, and each loss is -1 points. League games affect chess rating as well, just like any other rated games.
3. In case the opponents end up in different divisions by the time the game is finished, the league score is calculated according to the following table: Difference Win Loss
winner 1-2 divisions higher +0.5 -0.5
winner 1-2 divisions lower +2 -2
winner 3+ divisions higher 0 0
winner 3+ divisions lower +5 -5
If the game ended in a draw, the player from the lower division will be awarded +0.5 points and -0.5 points will be given to the player from the higher division.
4. All players with 10 or more points will get promoted to the next higher division and players with -10 or less points will get relegated to the next lower division. If a division has more than 30 players, top 5 players will also get promoted and bottom 5 players will be relegated. In case a division has more than 60 players, 10 players will be promoted and 10 relegated. Only players with 3 or more completed games can be promoted/relegated.
5. All promotions and relegations are performed once a week -- Sunday morning GameKnot local time (PST).
6. If two players have the equal scores, the one who has been playing in the division longer will get promoted/relegated.
7. When joining the league initially, players with rating 1199 or less start in division D3, rating 1200 to 1499 -- division D2, rating 1500 to 1899 -- division D1, rating 1900 and higher -- division C3.
8. If you retire from the league, you can later on re-join the same division if you had positive/zero score, or one division below if you had negative score. Your score will be reset to zero when you re-join.
9. If you time out in three or more league games, you will be automatically disqualified from the league.