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MadMonkey: Already people complain that some players get "too" much credit for winning a tournament when there are only 4 players in the tournament - having only 2 or 3..... I honestly don't think that is a good idea. 4 is a good minimum number.
But as for the elimination tournaments, you should ALWAYS have either 4, 8, 16, 32, 64, or 128 spaces for players
4 sign up - have 4 player elimination tournament, no byes
5 sign up - have 8 player tournament, with 3 players getting byes
6 sign up - have 8 player tournament, with 2 players getting byes
7 sign up - have 8 player tournament, with 1 player getting bye
8 sign up - have 8 player tournament
9 sign up - have 16 player tournament, with 7 players getting byes
10 sign up - have 16 player tournament, with 6 players getting byes
11 sign up - have 16 player tournament, with 5 players getting byes
... and so on. At first when I looked at your tournament examples you posted below, at quick glance I first thought... Oh, those look OK - but then noticed they were a 12 section tournament with 8 players, and a 14 section tournament with 9 players... which of course would be interesting to see what the system does in later rounds when there is an odd amount of sections to match people up against.