in the remainder pile will necessarily (if the procedure has been followed correctly) be 9 or 5, in the first count, and 8 or 4, in the second. 9 or 8 is assigned a value of 2; 5 or 4, a value of 3. The total of the three passes will be one of just four values: 6 (2+2+2), 7 (2+2+3), 8 (2+3+3), or 9 (3+3+3)—that value is the number of the first line. The forty-nine stalks are then gathered and the entire procedure repeated to generate each of the remaining five lines of the hexagram. The yarrow-stalk method produces unequal probabilities for obtaining each of the four totals, as shown in the table. Compared to the three-coin method discussed next, the probabilities of the lines produced by the yarrow-stalk method are significantly different. Note that the Yarrow algorithm is a particular algorithm for generating random numbers; while it is named after the yarrow-stalk method of consulting the I Ching, its details are unrelated to it. Coins Three-coin method The three-coin method came into use over a thousand years after the yarrow-stalk method. The quickest, easiest, and most popular method by far, it has largely supplanted yarrow stalks, but produces outcomes with different likelihoods. Three coins are tossed at once; each coin is given a value of 2 or 3, depending upon whether it is tails or heads, respectively. Six such tosses make the hexagram. Some fortune-tellers use an empty tortoise shell to shake the coins in before throwing them on a dish or plate. Modified Three-coin method The three-coin method can be modified to have the same probabilities as the yarrow-stalk method by having one of the coins be of a second coin type, or in some way be marked as special (i.e., be distinguishable from the other coins). All three coins are tossed at once. The results are counted just as in the original three-coin method, with two exceptions: one to make yin less likely to move, and one to make yang more likely to move. (The probability for 6/8/9/7 in the coin method is 2/6/2/6, but in the yarrow-stalk method is 1/7/3/5; hence, 6 has to occur less often, and 9 has to occur more often.) In the case where the special coin is tails and the other two are both tails—which would normally produce a 6—re-flip the marked coin: if it remains tails, then treat it