private double bowl_SD() {
        // use the scores of bowls we have seen 
        // to estimate the SD of the scores of remaining bowls
        double ret = 0;
        double avg = 0;
        double x = 0;
        for (int i = 0; i < accumulated_bowl_number ; i++) {
            avg += (double)(accumulated_bowl_score[i]);
        }
        avg /= (double)(accumulated_bowl_number);
        for (int i = 0; i < accumulated_bowl_number ; i++) {
            x = (double)(accumulated_bowl_number) - avg;
            ret += x * x;
        }
        ret /= (double)(accumulated_bowl_score.length - 1);
        ret = Math.sqrt(ret);
        return ret;
    }