Calculating Swiss Record Required to Reach Elimination Rounds

Here’s some Python that calculates how many players will reach each record in a Swiss tournament with a Top 8 or similar cut.

from typing import Sequence

# Math from https://www.mtgsalvation.com/forums/magic-fundamentals/magic-general/325775-making-the-cut-in-swiss-tournaments
def swisscalc(num_players: int, num_rounds: int, num_elimination_rounds: int) -> Sequence[int]:
    num_players_in_elimination_rounds = 2 ** num_elimination_rounds
    base = num_players / (2 ** num_rounds)
    num_players_by_losses = [0] * (num_rounds + 1)
    multiplier = 1.0
    total_so_far = 0
    record_required = None
    for losses in range(0, num_rounds + 1):
        wins = num_rounds - losses
        numerator = wins + 1
        denominator = losses
        if denominator > 0:
            multiplier *= (numerator / denominator)
        num_players_by_losses[losses] = base * multiplier
        if not record_required and num_players_in_elimination_rounds:
            total_so_far += num_players_by_losses[losses]
    return num_players_by_losses

Example usage:

$ python3
>>> rounds = 4
>>> r = swisscalc(24, rounds, 3)
>>> for losses in range(len(r)):
...     print(f'{r[losses]} players at {rounds - losses}–{losses}')
... 
1.5 players at 4–0
6.0 players at 3–1
9.0 players at 2–2
6.0 players at 1–3
1.5 players at 0–4

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