Single-Elim Byes Next Power of Two

Plan next-power-two single-elimination bracket with separate first-round byes/contests and total N−1 contests; no seeding or third-place match assumed.

Description

A single-elimination bracket can be padded to the next power of two.

A single-elimination bracket can be padded to the next power of two. Byes reduce contested first-round matches, while every elimination requires a loss.^[1]

Enter integer entrants 2–1000000. Return bracket slots, byes, contested first-round games and total games.

When to use Single-Elim Byes Next Power of Two

Use Single-Elim Byes Next Power of Two when you need to evaluate the supplied records under the calculation and evidence rules below. No seeding, third-place match or double-elimination bracket is supplied.

Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.

How to use Single-Elim Byes Next Power of Two and understand its results

Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.
Enter entrantCount using the field table and calculation rules, then run the tool.
Read bracketSlotCount, firstRoundByeCount, firstRoundContestedMatchCount, totalContestedMatches. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
entrantCount	Entrant count	number	Required

Enter integer entrants 2–1000000. Return bracket slots, byes, contested first-round games and total games.

slots=2^ceil(log2(N)); byes=slots−N; matches=N−1

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
bracketSlotCount	Bracket slot count	number
firstRoundByeCount	First round bye count	number
firstRoundContestedMatchCount	First round contested match count	number
totalContestedMatches	Total contested matches	number

json

{
  "input": {
    "entrantCount": 10
  },
  "output": {
    "bracketSlotCount": 16,
    "firstRoundByeCount": 6,
    "firstRoundContestedMatchCount": 2,
    "totalContestedMatches": 9
  }
}

Limitations and assumptions

No seeding, third-place match or double-elimination bracket is supplied.

Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Swiss Tournament Round Count log₂(n): A doubling-capacity estimate provides a simple Swiss-round planning heuristic. Actual pairing and tie resolution depend on tournament rules. For a complementary task, use Bridge HCP High Card Points: Bridge high-card points value honors in a 13-card hand. Suit shape is a separate useful description.

References

Single-Elim Byes Next Power of Two — tool.io

Similar or alternative tools

Swiss Tournament Round Count log₂(n)
A doubling-capacity estimate provides a simple Swiss-round planning heuristic. Actual pairing and tie resolution depend on tournament rules.
Bridge HCP High Card Points
Bridge high-card points value honors in a 13-card hand. Suit shape is a separate useful description.