as a 6 (moving yin); otherwise, it remains an 8 (static yin). As a 6 can become a 6 or an 8, it reduces the probability of the moving 6. In other words, it makes the old yin less likely to change (or move). In the case where the special coin is heads and the other two are both tails—which would normally produce an 7—re-flip the marked coin: if it remains heads, then it remains as a 7 (static yang); otherwise, it becomes a 9 (moving yang). As a 7 can become a 7 or an 9, it reduces the probability of the static 7. In other words, it makes the young yang less likely and hence more yangs change as a result. This method retains the 50% chance of yin:yang, but changes the ratio of moving yin to static yin from 1:3 to 1:7; likewise, it changes the ratio of moving yang to static yang from 1:3 to 3:5, which is the same probabilities as the yarrow-stalk method. Two-coin method Some purists contend that there is a problem with the three-coin method because its probabilities differ from the more ancient, yarrow-stalk, method. In fact, over the centuries there have even been other methods used for consulting the oracle. The two-coin method involves tossing one pair of coins twice: on the first toss, two heads give a value of 2, and anything else is 3; on the second toss, each coin is valued separately, to give a sum from 6 to 9, as above. This results in the same distribution of probabilities as for the yarrow-stalk method. Simplified two-coin method A modified version of the two-coin method improves on the original on several aspects. First, while maintaining the probabilities of the traditional yarrow-stalk method, it simplifies outcomes such that they become intuitive at first sight, without need of further calculations. Second, it reduces the average number of coin throws per hexagram by 25%, from 12 to 9. It does so by requiring to throw the coins a second time only if both coins land on the same face (either both heads, or both tails), thus only in 50% of instances. Third, it is easy to memorize, as it clearly identifies heads with yang, and tails with yin, and a greater share of heads/tails with old (aka mature, moving, changing) yang/yin. The modified two-coin method involves tossing one pair of coins