Probabilities
If you know a little about probability theory, you might have realized that with some methods of casting the Alphabet Oracle the letters are not equally likely to occur. For example, with alphabet stones or leaves and with the coin and Three-Out-of-Four Methods, each letter has the same probability, but with the ancient astragalos and dice methods, some of the sums can occur in several different ways, and so the corresponding letters are more likely to occur by chance. Furthermore, due to the irregular shape of astragaloi, their four sides are not equally likely to occur (0.1 each for 1 and 6, 0.4 each for 3 and 4), 153 and many ancient dice were not perfectly “fair” (all six sides equally likely). This concerns some practitioners of the ancient divinatory arts, since it seems to imply that certain oracular responses are more likely than others. In this appendix, I will explain why there is no reason to be concerned.
I’ll discuss the issues by using a simple example. The laws of probability tell you what you can expect to happen if you repeat a “trial” (test) a large number of times. For example, if you toss a fair coin a large number of times (and if you toss it fairly!), you can expect about the same number of heads and tails. Probability theory says nothing about what will happen in an individual trial. If it is a fair trial, then (by definition) a head will be just as likely as a tail. Even if you have just tossed four heads in a row, on the next toss a head is just as likely as a tail. Many people find this surprising, but it is true. In fact, runs are more common than most people suspect, and when people try to act randomly (e.g., in playing games like Rock-Paper-Scissors), they tend to have too few runs. For example, you could expect to have one run of five heads out of every thirty-two tests of five tosses. Indeed, even a run of one hundred heads in a row does not violate the laws of probability, although it is very unlikely (and might lead you to suspect you have an unfair coin!). To state it plainly, no sequence of tosses violates the laws of probability, although sequences with approximately the same number of heads and tails are more likely (their probability fits a bell-shaped curve called the binomial distribution).
Now let’s bring this discussion back to cleromancy (divination by lots), and in particular to casting the Alphabet Oracle. You can see that the laws of probability do not limit in any way its ability to deliver a particular oracle to you. Even if the oracle has answered 
on your last four questions, there is nothing preventing it from answering again on your next question. If you kept track of the oracular responses over a lifetime of divination (perhaps tens of thousands of readings), I expect that each letter would turn up about the number of times you would expect by chance (e.g., 1/24 for drawing alphabet stones). All this means is that all twenty-four oracles are approximately equally useful; it does not in any way contradict the appropriateness of each individual oracular response.
This raises an obvious question: “Suppose I ask the same question a large number of times? Shouldn’t I get the same answer each time?” The answer is that we are talking about divination (contact with a divinity), not a game of chance or the repetition of a scientific experiment. In his collaborations with the Nobel Laureate quantum physicist Wolfgang Pauli, Carl Jung distinguished statistical laws from synchronistic laws.154 Statistics deals with causation in the material world, which is repeatable and therefore subject to statistics. Synchronicity (meaningful coincidence) connects material and mental phenomena by means of their shared meaning. Individual synchronistic events are unrepeatable and therefore statistics does not apply to them. Synchronistic laws do indeed describe regularities in experience, but different from the regularities described by statistical and physical laws. Divination uses the laws of synchronicity to set up a synchronistic event, which coordinates the physical and psychical realms and allows the psychical to manifest in the physical.
From a spiritual perspective, divination is the art of contacting a god or other spirit in order to gain knowledge or advice in a matter of some importance. How do you think a human sage would react if we came to them to ask a question, and having received their answer, came back ten minutes later and asked the same question, and then came back again, and again and again, until we had enough “samples” for statistical analysis? I expect that they would reward our arrogance and mistrust by not answering (i.e., “letting the chips fall where they may”), or perhaps teach us a lesson in humility in some other way. There is a long tradition in many cultures that the gods withdraw our prophetic powers if they are misused. Without the guiding hand of the god, you will get exactly what would be expected by chance: random readings.
“The master speaks but once.” This was Carl Jung’s comment about repeating a divination, which he wrote in his Forward to the I Ching,155 which is well worth reading. Does this mean that you should never ask the same question more than once? Not necessarily. There is nothing wrong with repeating a question to obtain clarification, although in this case you should be explicit about what is unclear, which means it’s really a different question. It is also appropriate to repeat a question if circumstances have changed since the first time you asked it. Again, that really makes it a different question, since its context has changed. If you just keep in mind that you are addressing a divinity to whom you owe respect, and that you are not playing a game (or running a scientific experiment), then you will not go wrong.
To come back to the original question, it does not matter that different ways of casting the oracle give different probabilities to the letters. Use whichever methods work best for you.
153. David, Games, Gods, and Gambling, 7.
154. Atmanspacher, “Dual-Aspect Monism à la Pauli and Jung,” Journal of Consciousness Studies 19, 9-10 (2012): 96–120.
155. The I Ching or Book of Changes: The Richard Wilhelm Translation rendered into English by Cary F. Baynes, Forward by C. G. Jung, 3rd ed. (Princeton: Princeton University Press, 1967), xxix.