def normalised_scores(scores, turns):
    """
    The per-turn normalised scores matrix

    Parameters
    ----------
    scores : list
        A scores matrix (S) of the form returned by the scores function.
    turns : integer
        The number of turns in each round robin.

    Returns
    -------
    list
        A normalised scores matrix (N) such that:

            N = S / t

        where t is the total number of turns played per repetition for a given
        player excluding self-interactions.
    """
    nplayers = len(scores)
    normalisation = turns * (nplayers - 1)
    return [
        [1.0 * s / normalisation for s in r] for r in scores]