ScheduleRoundRobinMatches.cs

int numberOfTeams = 9;
Console.WriteLine("Matches:");
(int, int)[] matches = Statics.ScheduleRoundRobinMatches(numberOfTeams);
for (int i = 0; i < matches.Length; i++)
{
    Console.WriteLine($"{i + 1}. #{matches[i].Item1} vs #{matches[i].Item2}");
}

public static class Statics
{
    /// <summary>
    /// Schedules matches between a set number of teams where each team plays each other
    /// team once ordered to maximize resting time between each team's matches.
    /// </summary>
    /// <param name="numberOfTeams">The number of teams to schedule matches for.</param>
    /// <returns>
    /// All the matches necessary for each team to play each other team once ordered
    /// to maximize resting time between each team's matches.
    /// </returns>
    public static (int, int)[] ScheduleRoundRobinMatches(int numberOfTeams)
    {
        int size = numberOfTeams;
        int matchCount = (size - 1) * size / 2;
        (int, int)[] matches = new (int, int)[matchCount];
        for (int i = 1, k = 0; i <= size; i++)
        {
            for (int j = i + 1; j <= size; j++, k++)
            {
                matches[k] = (i, j);
            }
        }
        int[] counts = new int[size];
        int[] bias = new int[size];
        (int, int)[] scheduled = new (int, int)[matchCount];
        for (int i = 0; i < matchCount; i++)
        {
            int index = -1;
            int priority = int.MaxValue;
            for (int j = 0; j < matchCount - i; j++)
            {
                int currentPriority =
                    bias[matches[j].Item1 - 1] + counts[matches[j].Item1 - 1] +
                    bias[matches[j].Item2 - 1] + counts[matches[j].Item2 - 1];
                if (currentPriority < priority)
                {
                    index = j;
                    priority = currentPriority;
                }
            }
            scheduled[i] = matches[index];
            for (int j = index; j < matchCount - i - 1; j++)
            {
                (matches[j], matches[j + 1]) = (matches[j + 1], matches[j]);
            }
            for (int j = 0; j < size; j++)
            {
                bias[j]--;
            }
            bias[scheduled[i].Item1 - 1] = 0;
            bias[scheduled[i].Item2 - 1] = 0;
            counts[scheduled[i].Item1 - 1]++;
            counts[scheduled[i].Item2 - 1]++;
        }
        return scheduled;
    }
}