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For a conventional single-elimination bracket, round the number of entrants up to the next power of two. Subtract the actual entrant count from that bracket size to find the first-round byes. A bye lets an entrant advance without playing that round.

Calculate the bracket size and byes

Let N be the number of entrants. Choose the smallest power of two that is at least N; call that bracket size B. Then calculate:

  • Bracket size: the smallest power of two greater than or equal to N.
  • First-round byes: B − N.

This fills out a conventional knockout draw so that later rounds halve cleanly. For example, a bracket with 8 slots has three rounds, while one with 16 slots has four. The round count is log₂(B), including the opening round even when some entrants receive byes. Poolism’s bracket generator illustrates the power-of-two bracket approach.

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Example: make a bracket for 13 entrants

The next power of two at least 13 is 16, so use a 16-slot draw. It needs 3 byes, because 16 − 13 = 3. The remaining 10 entrants play five opening matches.

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  1. Start with 13 entrants and 16 bracket slots.
  2. Assign 3 entrants a first-round bye.
  3. Pair the other 10 entrants in 5 matches.
  4. Advance those 5 match winners and the 3 bye recipients into an eight-entrant round.
  5. Continue through the 8-, 4-, and 2-entrant rounds to determine the champion.

The event has four rounds from the opening round through the final. It requires 12 played matches in total: each match eliminates one entrant, and 12 eliminations leave one champion. The same match-count rule applies to any completed single-elimination event with at least two entrants: N − 1 matches. Byes affect when entrants play, not how many matches are needed to produce one winner. SimpleMoney Sports Game Tools’ bracket calculator provides the 13-entrant example and related calculations.

Decide who receives each bye

Bye allocation depends on the event’s draw and seeding rules. In a seeded draw, a common convention is to give byes to the highest seeds and arrange leading seeds so they are separated in early rounds. That is a convention, not a universal rule; check the applicable organizer or governing authority’s current rules before finalizing a sanctioned bracket. Poolism’s generator demonstrates a top-seed approach.

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If entrants are not reliably ranked, or the event does not prescribe a seeding method, tell participants how the draw will be decided—for example, by random draw—before they rely on the bracket. There is no universal tie-break or randomization procedure established for every tournament.

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Lay out and check the bracket

Use a paper draw sheet, electronic bracket, or reusable display board to show who plays in the opening round, who has a bye, and where each winner advances. A historical ERIC tournament-draw guide illustrates marking byes and advancement on a draw sheet; it is a layout reference, not a current governing rule.

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  • Confirm that the bracket has the next power-of-two number of slots.
  • Check that the number of byes equals bracket slots minus entrants.
  • Make sure first-round matches plus bye recipients fill exactly half the bracket for the next round.
  • Verify that the draw follows the event’s rules for seeds, byes, and participant placement.

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