Normalize the score to be between -1 and 1 using an alpha that
    approximates the max expected value

def normalize(score, alpha=15):
    """
    Normalize the score to be between -1 and 1 using an alpha that
    approximates the max expected value
    """
    norm_score = score / math.sqrt((score * score) + alpha)
    if norm_score < -1.0:
        return -1.0
    elif norm_score > 1.0:
        return 1.0
    else:
        return norm_score