Thinking about different things associated with the Wuxing [Five Phases] for the Five Powers Jam had me look deeper into the Bagua and the I Ching [Yijing; the Book of Changes]. Seeing has I have also been working on a new space generator to help me populate the universe for URCAT, I have also been looking a lot at rolls and probabilities and the I Ching is also an interesting source for that as well!
Background of Bagua
For those of you who are unaware, the Bagua are a set of eight cosmological principles that are often used to represent a wide distribution of interrelated concepts. These are often represented by trigrams, symbols made from 3 lines in set patterns. Each of these lines are either solid or broken, representing the mixture of Yang and Yin in each of the symbols’ makeup. Bagua are used in the I Ching, but they are also used in certain elements of Oriental Medicine, acupuncture, Feng Shui, and several Martial Arts. You can find some of these in the Flag of South Korea [Taegeukgi] where bagua are called palgwae. I might talk more about what they all represent later, so watch this space if you are interested in that.
But what is the I Ching?
The I Ching, also know as the Yijing, originally was a divination manual from early Chinese history. It combines the eight trigrams into 64 possible hexagrams. Each of these are attached to advice on a particular course of action derived from the elemental descriptions and the cultural implications behind their placements. Today while some still use it for divination or meditative contemplation, it also became a source of social commentary for Taoist and Confucian scholars interpreting it in the millennia since its first compiling.
Why am I discussing this now? Well, I have had several ideas come to me on possible Five Powers Jam entries that could potentially incorporate the Bagua. However, the main topic I wanted to discuss here is how diviners generate the hexagrams.
Generating Random Numbers in Divination
Today, there are two traditional ways that are still used to generate the hexagrams, either a complicated counting system manipulating a set of yarrow stalks or using three coin flips. The former is a process that referenced in early history back when the use of heating turtle shells and ox scapula were still a common practice. The Three Coins system was developed much later as a means of making the process simpler and faster.
Each process is designed to create a number between 6 and 9. This is because the lines can either remain Yin or Yang or shift between the two, creating two hexagrams that work together to divine the present and future or the short-term and long-term outcomes depending on what question is being asked.
What is important for this article is that the results probabilities are actually different between the yarrow-stalk method and the three coin method. While both have an 50/50 chance of creating a yang or yin line, they differ in the likelihood of creating a shifting line. This difference in statistical chances actually is perceptible for people who have used both sources for an extended period of time, at least according to anecdotal sources I have found.
Can We Create Bagua in Other Ways?
These probabilities can also be replicated with dice. As you could see in the 6 to 9 assignment table above, even numbers are associated with Yin and odd numbers with Yang, so we will use these for our results. The three coin method can be easily replicated with a single 8-sided dice with 1 & 8 being shifting lines. The Yarrow method would be more complicated. We could use 2d8 with with the first or last two Yins (2+4 or 14+16) being shifting lines and the first or last three Yangs (3+5+7 or 11+13+15) being shifting lines.
Of course, if you don’t want to go to the effort of worrying about shifting lines and the like, you could just assign each trigram a numerical value and use the an 8-sided dice to select the top and then bottom trigrams. However, I find this rushed method to be contrary to the original intentions behind the I Ching.
Lessons?
What could a game designer draw from this look at random number generators? The first thing I bring away from this is to be careful about making adjustments. Even a small change can result in noticeable shifts in results. Sometimes this is intentional, but it may also be a side effect of simplifying a process. Probability calculation tools like https://anydice.com/ can be extremely useful in this regard.
That said, it is also important to make sure that you don’t make your system too complicated. The Yarrow Stalk system was displaced by many in favor of the Three Coin system because it was a laborious process that required manual dexterity and interfered with the contemplative aspects of divination. Excessive rolling, math, and other complications can turn a user off from using a particular system or tool.
I think this is one reason why I am not a big fan of some of the specialized dice systems despite some of their advantages. For example, the “plus, neutral, minus” of FATE is great for people who would like to minimize math and it is great for creating resolution in the middle of the spread. However, it adds another step in the process interpreting the number to a “yes/neutral/no” since most of us don’t have Fate dice laying around. The combination of Fate Core and Modiphius’s early problems with book design are why Mindjammer has never worked for me despite enjoying my early examination of the setting.
Finally, as a user of the I Ching myself as a method of contemplation, examining the probability differences between the Yarrow Stalk and Three-Coin methods has led me to reconsider some elements of my own practice. It does not leave me to reconsider my use of the I Ching since I do not actually use it for divination purposes. However it is interesting to think about how the different methods of generating random results has changed the expected results just as much as the actual use of the manual has evolved in both it’s home culture and around the world.