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Why some participants go straight to round #2

In single and double elimination brackets, you'll often find that some participants skip the first round (they receive byes). This cannot be avoided unless the number of participants is a power of two (2, 4, 8, 16, 32, ...) — a number that can be repeatedly halved until only 1 person remains.

Imagine you paired everyone in round #1 of a 6 player bracket: 1v6, 2v5, 3v4. Three players would advance, leaving you with a bad situation. See top portion of the image below.

To avoid this, byes should be awarded in round #1 to two players. Following this rule, round #1 (sometimes referred to as the qualifying round in this scenario) would have 3v6 and 4v5. The two winners, or qualifiers, would advance to join players 1 and 2 in the next round. The bracket at this point becomes balanced with 4 participants, a power of 2. See bottom portion of the image below.

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