Learning the Astragalomantic Oracular Verses

The way that astragalomancy works is pretty simple; Kostas Dervenis in his Oracle Bones Divination calls it the “Greek I Ching”, noting the similarity of the method.  Basically, what you do is you roll five knucklebones, or astragaloi, and you note the sides that come up.  The astragaloi act like four-sided dice, and each of the 56 different rolls you get (the order doesn’t matter) indicates a different outcome.  Each roll is associated with a particular godname and a matching oracular verse, not unlike grammatomancy (the methods are basically the same).  So, really, there’s little room for interpretation: roll the astragaloi, read the corresponding verse, and that’s your answer.  Expanding and meditating on the verse as it relates to the situation or the query is often necessary, but there’s little other inspiration to be had here, which is just as well.  I’m sure I can fit some more mystical aspects into it later, of course, but that’s later once I learn all the verses.

It’s learning the verses, however, that’s proving something of a struggle for me.  Each verse is four or five lines long, and there are 56 different verses.  Learning the one-line verses associated with the 24 letters of the Greek alphabet took a bit of time on its own, but that’s child’s play in comparison to this.  My memory may be good, but it’s not that good to just up and memorize a book’s worth of divination.  I want to be able, eventually, to pull out my astragaloi whenever needed and on the spot do a reading with them, which may mean that I won’t have a book of verses with me at any given moment, so I want to memorize them and know them by heart.  Getting there is hard, so I’m trying out different ways of learning them and comparing what I’ve done with other methods.

Geomancy, for instance, was easy because each set of meanings could be tied to a graphical form, the geomantic figure composed of four lines of one or two dots in each line.  Grammatomancy was easy because I had the 24 Greek letters as graphical forms to link their meanings and verses to, as well as the fact that the alphabet itself formed an index and acronym for the verses themselves (at least in Greek).  And, while I don’t know Tarot half as well as I probably should as a Hermetic magician, learning the symbolism could easily be done by association with the pretty pictures of the cards themselves (if I even bother to go that route, since the pictures lend themselves well to impromptu interpretation as they already are).    These all use some sort of graphical image as a symbol to which can be linked a referent, the verse or meaning; my mind plays well with these instead of just straight-up words or numbers.

Astragalomancy, however, is different; I’m just getting a set of numbers, a numeric ID, that gives me a particular verse and meaning.  It’s a different beast, and the lack of a distinct symbol bothers me.  The ID doesn’t register to my mind as a graphical image or a symbol in the same way a geomantic figure does, especially given the different forms it can take.  Consider the throw where you get two khion (1) throws, a hyption (3), a pranēs (4), and a kōon (6).  While I might write this down as 11346, there are 60 different permutations of this ID.  Add to it, the original sources don’t tend to list the numbers in a simple manner, so the actual ID of this is 43611 in the book!  While each verse begins with a description of the throw (in this case, “one four, one three, one six, and two ones: …”), that’s not helpful without me just up and memorizing all the verses by heart and running through them one by one until I get to the one I need, or until I get to the point where automatic recital of each verse is possible just from the start of each one (and, moreover, how each first line starts).  That takes time, and I’m trying to get up to speed as fast as possible with this.

Flashcards help, though, and I was able to link the sums of the throws to the Greek letters (one of the ways to do grammatomancy with astragaloi) in a day with this method.  For this, the online service Quizlet is amazing, and if you’re so interested, you can check out the sets of flashcards I’ve made for your own study.  Linking the throws to the letters involves summing up the sides of the astragaloi, however, and just observing the throws themselves isn’t a link I can make directly to the Greek letter just yet.  Over time, perhaps, as I regularly use the astragaloi it can happen, but I need that intermediate step first that detaches the throw to the Greek letter directly.  However, the way Quizlet works, you need to type in the answer to a given prompt more-or-less directly, and while it may be a useful activity for me to go through all the oracles themselves and make a one- or two-word summation of every verse, I haven’t gotten around to doing that just yet.  So, for me, the first step is to learn the throws of the astragaloi and how they associate with the different gods associated with each throw.

Still, that alone is difficult without some sort of pattern or method, and then I realized that I have a method for this.  Every software engineer is taught this method of “divide and conquer” (or, in Greek, διαίρει καὶ βασίλευε, diairei kai basileue), where you take a large problem and divide it up into smaller chunks that can more easily be solved, linking them all together in the end once they’re all good to go.  Looking at the astragalomantic throws, I realized that I can reorder the throws into a pattern that’s more numerically pleasing where there are 18 groups of 3 or 4 throws each, based partially on the Roman game of tali or knucklebones.  I group some of the smaller groups into larger ones based on the abstract number pattern linking them together:

  • Dogs and Vultures (all throws the same number, four possible throws)  e.g. 11111, 33333
  • Iacti Veneris + 1 (all four sides represented, four possible throws) e.g. 11346, 13446
  • 4X 1Y (four throws one side and last throw another, 12 possible throws with four groups of three based on X) e.g. 11113, 46666
  • 3X 2Y (three throws one side and two throws another, 12 possible throws with four groups of three based on X) e.g. 33444, 33666
  • 3X 1Y 1Z (three throws one side and two throws different, 12 possible throws with four groups of three based on X) e.g. 11134, 34446
  • 2X 2Y 1Z (two throws one side and two throws another and last throw another, 12 possible throws with four groups of three based on Z) e.g. 34466, 13344

Sure, it’s not exactly a traditional arrangement of the throws or a traditional way of enumerating them, but it works for me.  Every day I’ll study one or two more groups, learning what the pattern is and the throws of a similar pattern with different numbers, adding in the new rows to a Quizlet flashcard quiz and practicing it every hour or so until I build myself up enough to tackle the whole lot of 56 throws.  All in all, this isn’t a bad way to learn the basic associations of throws with the gods, and given my normal speed of memorization and learning, it’ll take about two or three weeks to learn all the associations of throws and gods comfortably enough that I can identify them at a glance.

Once I get the memorization of throws and gods down, and (if I deem it worthwhile) the memorization of the canonical order of the gods, then it’ll be time to link the association of throws and oracles down.  However, I plan on using the god-associations as a halfway point, so that I’ll actually be linking the oracle to the god and the god to the throw.  Thus, by recalling the god as a symbol, I can recall the oracle to which the symbol refers.  Learning each oracle will take more time than learning the god, since each verse also has to be memorized.  That said, I can speed up the process by learning the gist of each oracle first, then going back to learning the verses themselves, but we’ll see how I feel about that.  Given this, I expect it to take me two months or so of study and practice to memorize the verses, both by Quizlet and by constant use of the oracle to get me used to throwing the bones literally instead of just looking at flashcards.

How about you?  How do you learn a large block of information in a short period of time?  Are there any tips or tricks for memorization or recalling large amounts of information at once?

Fr. Rufus Opus, who is not me, made something awesome!

So, if you’re at all involved with the ceremonial magic blogosphere or Hermetic occulture online nowadays, you may have heard that there was a new book published this week: Seven Spheres by Frater Rufus Opus, from Nephilim Press.  This is Fr. Rufus Opus’ second time being in print (the first being a contribution to Holy Guardian Angel, ed. by Fr. Mike Cecchetelli), and his first time publishing a full book, which is a huge accomplishment for the man.

SONY DSC

From the Nephilim Press page:

Seven Spheres is more than a simple book of traditional Hermetic Magic. It is designed to be a series of rituals that function on many levels to take an average ordinary magician and turn them into a self-actualized powerhouse of proactive reality engineering. It’s entirely about attaining initiation and empowerment in the highest levels of un-manifest reality. These experiences and rites result in the release of a floodgate of power that pour down through the layers of progressive manifestation, building up awareness, understanding, and ultimately raw potential as you move from sphere to sphere through the rites, ultimately culminating in the anointing of the magician as Priest-King directing the forces that climax in your personal daily experience of the Joy of your life. This book isn’t about physical or spiritual mastery, it is entirely about understanding that you, personally, are beloved, honored, blessed, and highly favored of every intelligence, spirit, angel, and god of every sphere. This is about understanding who you are and what you can accomplish as a human being manifest upon the surface of the Earth. Spiritual enlightenment and material mastery will be yours, if you do the work described.

If you’re familiar with Fr. Rufus Opus’ stuff, you’ll know that he had a thing going on a while back called the Planetary Gates series of ebooks and rituals.  They formed the crux of his system of Hermetic theurgy: a series of conjurations calling upon the angels presiding over the planetary spheres.  He understood that a conjuration of one of these angels is a lot more than merely charging them to do such-and-such for you; rather, he realized that working with the angels can be a series of initiations into elevating oneself higher through the heavens to reach, essentially, godhood.  It’s a modern method of Renaissance Hermetic ritual with foundations in ancient Mediterranean and Near Eastern theurgy, and it’s awesome.

As some of my own readers are familiar, I’m a student of Fr. Rufus Opus himself and his Red Work series of classes.  It’s how I formally got started in being a ceremonial magician back in 2011, and I’ve been close to him since and have consulted with him on a number of topics.  The Planetary Gates texts he had online for quite some time was one of the pillars of his coursework, and I’ve used them extensively in my own work, culminating in my own conjuration of the angel of the fixed stars and an initiation into the Eighth Sphere.  I can’t suggest his approach enough to people who are new to the occult, since it affords so much and so fast to those who are willing to put the work in and do the rituals.

A while back, Fr. Rufus Opus took down the option to buy the Planetary Gates ebooks he had on his website, only recently acknowledging that he had done so to polish them up, add in more content and experiences, and refine it into a proper occult grimoire.  Now, after all that time, the fruits of his labors can be harvested!  The Planetary Gates texts were valuable for their content alone, sure, and how to go about performing Trithemian-style conjurations and how to plunge oneself into the heights and depths of the planets, getting everything one can over and over out of the heavens to benefit ourselves on Earth and in all other planes of existence.  Seven Spheres will have all that and more!  After all, as Fr. Rufus Opus says:

The point is to empower you to be the king and queen of your world. You are the center of your existence, and it is through your decisions and actions that you influence the experience of your manifest life. From money, to sex, to happiness, to fulfillment, all of your life experiences are the result of decisions you make based on your awareness of what’s going on at the time.

Even if you’re not into all that high and mighty theurgical henosis and apotheosis, chances are you’re into getting laid and getting paid.  From low and vulgar ends to the highest and most rarefied, Seven Spheres covers how you can do both at the same time.

So, the text was released this past Monday, November 17, and I noted almost immediately once the news hit Facebook that my blog hits started shooting up, with more than a few searches for “rufus opus” and “seven spheres”.  While it’s true that I do reference Fr. Rufus Opus’ work (I’m kinda indebted to him, after all, for essentially giving me a leg up in the occult world), I just want to make it clear: I am not the Hermeticist you are looking for.  I may be seen to approach his level of awesomeness and, on occasion, drunkenness, but let me tell you, the man you’re looking for is far more awesome and far more and far more often drunk than I could ever be.  To resolve this, I thought it might help if I mentioned that, no, I am not Fr. Rufus Opus, I’m just polyphanes, and I haven’t published anything except a few of my own ebooks yet (which, admittedly, I think you should also buy).  You want Fr. Rufus Opus’ new book, which you can buy from Nephilim Press for US$50.00, which is pretty much a steal for what is essentially a landmark work in modern Hermetic magic.

After all, I’ve already ordered my copy.  You really, really, really should, too.  Even if you have laminated copies of his Planetary Gates texts enshrined in a secure locked-down binder and kept in a safe place (because surely I can’t be the only one who does that), you should get a copy of Fr. Rufus Opus’ new book today while supplies last from Nephilim Press.  Add to it, Fr. Rufus Opus is planning on making this the primary textbook for his future style of Red Work courses, which means you should really get the book anyway especially if you’re considering learning from him.

Stop waiting.  Close this window, get out your PayPal login or credit card, and go to Nephilim Press right now to buy Fr. Rufus Opus’ Seven Spheres.  If you’re interested in doing some real Work, you can do much worse than opening the Gates and walking through them with this.

An Uncrossing Ritual to Free the Mouth

A while back at Crucible, on the eve of my giving my presentation, I had an interesting dream.  There was a new fad of piercing going around: three horizontal barbells going through each cheek, like it was a variation of corset piercings but for the sides of the face.  I decided to get a set for my own cheeks, and I was amused at how they looked, but they came with a drawback I hadn’t expected.  It was hard to open my mouth fully, and if I tried to open my mouth too wide then it would hurt too much, like having one’s wisdom teeth pulled.  Add to it, every time I tried to open my mouth, I would get these flaky bruises all down my neck and onto the left side of my chest; they would flake and brush off pretty easily, but more kept coming back.

The night before giving a presentation, I have a dream where it’s hard for me to open my mouth?  Yeah, I wasn’t going to chance it being “just a dream”, despite that I don’t often put stock into dreamwork or premonition dreams.  That said, I’m in the habit of going before Hermes every night and asking for true dreams to understand and to remember, so I wasn’t going to just shrug it off.  It may very well have been a stress dream, but some quick divination suggested it was a cross of some sorts, and I wasn’t going to have that going on the first time I gave a presentation to the occult community.  So, with my friends, I went to the local grocery store, got a few things, and cobbled together an on-the-spot uncrossing ritual with the aim to remove all blockages and bindings on one’s mouth.  This would be good for anyone leading a presentation, speech, or discussion, and isn’t too labor-intensive by any means; after all, if I can do this on the fly on a road trip, you can do this just as easily.

For the record, I would have completely forgotten about writing about this if it weren’t for the fact I’m also considering more follow-up ritual and investigation from some more recent dreams.  But hey, in case you were looking for a ritual to free one’s mouth from possible spellwork, here you go!

For this ritual, you’ll need:

  • Holy water
  • Four lemons
  • Whole cloves
  • Figs
  • Honey
  • Wine

Take the lemons and stick four whole cloves around the meridian of the lemon where it’s fattest.  When appropriate to do so, go to a 4-way crossroads of some sort (I used a bridge over a river), wash off with the holy water and fling the spiritual filth into the middle of the intersection.  Invoke Hermes and make an offering of a small mound of figs drizzled on top with honey and poured over with wine, saving some of each for yourself later.  Take each of the four lemons and roll them in an always downward direction from the top of your head, down your neck, down each of your arms, down your chest and back, down your legs, and down to under your feet, asking Hermes all the while to remove all crosses, curses, bindings, and restrictions placed upon you.   Spit on each of the lemons and pray that Hermes remove all crossings and bindings and have them affect the lemons, sour that they are that they close the mouth and tighten the voice, and that the lemons take all the hit placed upon you.

Take some of the leftover figs, honey, and wine for yourself.  Dip the figs in the honey, eating them while saluting Hermes and proclaiming that “truth is sweet and smooth”; drink some wine while saluting Hermes and proclaiming that “truth is swift and strong”.  Pray that Hermes especially watch over your mouth and tongue that you may speak fluidly and fluently, saying what must be said that it may be swift and convincing and that you may bear the messages of the gods and men to those who might hear them.

Carry two of the lemons in your pocket with you.  Take one of the lemons you spit upon and  throw it into the crossroads.  Leave the crossroads without looking back and taking a different course to your origin than you took to get there, and halfway through throw one of the lemons over your left shoulder.  During your presentation or speech, set one of the lemons out in a discrete place between you and the audience (on the podium, between your feet, etc.), then throw it away after the presentation.  Keep the last lemon with you until you return to a safe place at the end of the day, then throw it away outside your safe place where you most likely won’t pass by and is out of the way.

By the way, feel free to wash off with any kind of holy water, khernips, Florida water, or the like frequently during the time you do the ritual until the end of the day.  A bit of extra spiritual cleanliness definitely won’t hurt and it’ll help loosen up any curses or crosses sent upon you, making it easier for the lemons to take the hit.

On Astragalomantic Probabilities

Using the astragaloi, or knucklebones, for divination has really intrigued me lately, as if you couldn’t tell from my last two posts on the subject.  Something about them feels different from other divination tools I’ve used; it could be that they’re actual bones taken from a living creature once, or that they just feel more arcane and ancient than my divination dice or cards I’m known to use.  All the same, they’re quickly becoming my favorite divination tool (besides geomancy generally), and I’m struck by their power and potency in getting answers.  The method is overall simple: take five astragaloi, throw them, and find the oracular verse associated with the combination of the sides that come up.  It’s simple, but elegant and straightforward.

However, they’re also different from my other divination tools in that they have really weird statistical properties.  Consider a die: every side of the die has (approximately) an equal chance of coming up when thrown.  Thus, on a six-sided die, throwing a 1 comes up as often as throwing a 2, 3, 4, 5, or 6.  Knucklebones, however, are different: they’re not ideal Platonic solids, nor are they regularly shaped in any sense.  Their organic and geometrically awkward shape results in there being different probabilities in throwing an astragalos on any given side.  Of course, the probabilities will differ slightly based on the individual knucklebone used and how hard it’s thrown, but based on an analysis by Phil Winkelman, we can approximate throwing an astragalos onto a particular side as follows:

  • Khion (1): 10%
  • Hyption (3): 40%
  • Pranēs (4): 40%
  • Kōon (6): 10%

It struck me that, because of the statistical probabilities associated with each number, not all oracular verses associated with each throw of the astragaloi will come up equally.  Some verses might be relatively common, while others would be extraordinarily uncommon to obtain, whether for good or evil.  Having some free time on my hands, I decided to run a short statistical analysis on how common different throws of the astragaloi would come up and how that would affect divination using astragaloi as compared to my other divination methods or suggested ways to use the astragalomantic oracular verses.

For instance, consider the use of astragaloi for grammatomancy.  Grammatomancy is my expanded version of the Greek alphabet oracle, and traditionally you would use five astragaloi for obtaining a Greek letter by throwing the bones and summing up the sides of the astragaloi.  So, for instance, if you threw (1,1,6,4,3), the sum would be 1 + 1 + 6 + 4 + 3 = 15.  The minimum sum you can get is 5 (1,1,1,1,1) and the maximum is 30 (6,6,6,6,6); based on how the numbers add up, you could not obtain a sum of 6 which requires (1,1,1,1,2) nor a sum of 29 which requires (6,6,6,6,5).  Between the numbers 5 and 30 inclusive, excluding the numbers 6 and 29, there are 24 possible sums.  Thus, we can associate each sum with one of the 24 Greek letters, starting with 5 = Ω and 30 = Α.  However, because the probability of an astragalos rolling on a 1 or 6 is 0.1, and on a 3 or 4 is 0.4, we get different possibilities for rolling different combinations of astragaloi and, further, obtaining different sums.  Below is a table that maps each letter of the Greek alphabet with its corresponding astragaloi sum (presented both in Arabic numerals and Greek numerals) and the probability one will obtain that letter from rolling five astragaloi.  The more extreme (higher or lower) the sum, the more rare the throw.  Thus, it’s extraordinarily unlikely that one will obtain Α or Ω with astragaloi (0.001% of the time), but comparatively common to obtain Μ and Ν (15.48% of the time).

Letter Astragaloi Sum Probability
Numerical Greek
Α 30 Λʹ 0.00001
Β 28 ΚΗʹ 0.0002
Γ 27 ΚΖʹ 0.0002
Δ 26 ΚϜʹ 0.0016
Ε 25 ΚΕʹ 0.00325
Ζ 24 ΚΔʹ 0.008
Η 23 ΚΓʹ 0.02
Θ 22 ΚΒʹ 0.0328
Ι 21 ΚΑʹ 0.0624
Κ 20 Κʹ 0.09674
Λ 19 ΙΘʹ 0.12
Μ 18 ΙΗʹ 0.1548
Ν 17 ΙΖʹ 0.1548
Ξ 16 ΙϜʹ 0.12
Ο 15 ΙΕʹ 0.09674
Π 14 ΙΔʹ 0.0624
Ρ 13 ΙΓʹ 0.0328
Σ 12 ΙΒʹ 0.02
Τ 11 ΙΑʹ 0.008
Υ 10 Ιʹ 0.00325
Φ 9 Θʹ 0.0016
Χ 8 Ηʹ 0.0002
Ψ 7 Ζʹ 0.0002
Ω 5 Ε 0.00001

For me, being used to my divination dice, this is shocking.  I use a dodecahedron die (d12, 12-sided die) for grammatomancy, where I roll the die twice.  The first roll gives me an odd or even number, which refer to the first 12 or last 12 letters in the Greek alphabet, while the second roll gives me the letter within that set according to its rank.  So, if I roll a 5 and an 8, I end up with the Greek letter Theta (eighth letter of the first half of the alphabet).  Using a 12-sided die where every side has an equal chance of turning up (approximately 8.333% of the time), every letter of the Greek alphabet has an equal chance of occurring (4.1667% of the time).  The statistical difference between getting the same Greek letter with a 12-sided die used in this way compared to using five knucklebones is huge; we’d get Α on the die 4.1667% of the time, but on the astragaloi only 0.00001% of the time.  It’s not impossible, just far more unlikely.  Then again, another classical method of grammatomancy was the method of ψηφοι, psēphoi or “pebbles”, where one has a jar of stones each marked with a different letter.  By reaching into the jar and pulling out a random stone, you get approximately an equal chance of obtaining any single Greek letter, which gets us the same results as using a 12-sided die in my fashion of using one.  Whether the use of astragaloi or psēphoi was more common for grammatomancy isn’t clear to me, but both methods work.

So what about the actual throw for proper astragalomancy, where we’re looking at the combination that results instead of the sum that’s formed from the combination?  We know that:

  • There are four sides (1, 3, 4, 6) on each astragalos
  • There are five astragaloi
  • Order of the dice doesn’t matter

Thus, although there are 1024 possible combinations of astragaloi, we only end up with 56 possible throws of the astragaloi when we disregard the order and only consider unique combinations of the bones.  Below is a table that shows the probability for each possible throw of the astragaloi; remember that order doesn’t matter, so (1,1,3,4,6) is equivalent to (1,3,6,4,1) and (6,3,1,4,1).  Generally, the more 3s and 4s there are, the more likely a particular throw is.  Thus, we end up with a probability of 0.0001% for (1,1,1,1,1) and (6,6,6,6,6) as our most unlikely throws, and a probability of 10.24% for (3,3,3,4,4) and (3,3,4,4,4) as our most likely throws.

Throw Sum Probability
A B C D E
1 1 1 1 1 5 0.00001
1 1 1 1 3 7 0.0002
1 1 1 1 4 8 0.0002
1 1 1 1 6 10 0.00005
1 1 1 3 3 9 0.0016
1 1 1 3 4 11 0.0032
1 1 1 3 6 13 0.0008
1 1 1 4 4 11 0.0016
1 1 1 4 6 13 0.0008
1 1 1 6 6 15 0.0001
1 1 3 3 3 11 0.0064
1 1 3 3 4 12 0.0192
1 1 3 3 6 14 0.0048
1 1 3 4 4 13 0.0192
1 1 3 4 6 15 0.0096
1 1 3 6 6 17 0.0012
1 1 4 4 4 14 0.0064
1 1 4 4 6 16 0.0048
1 1 4 6 6 18 0.0012
1 1 6 6 6 20 0.0001
1 3 3 3 3 13 0.0128
1 3 3 3 4 14 0.0512
1 3 3 3 6 16 0.0128
1 3 3 4 4 15 0.0768
1 3 3 4 6 17 0.0384
1 3 3 6 6 19 0.0048
1 3 4 4 4 16 0.0512
1 3 4 4 6 18 0.0384
1 3 4 6 6 20 0.0096
1 3 6 6 6 22 0.0008
1 4 4 4 4 17 0.0128
1 4 4 4 6 19 0.0128
1 4 4 6 6 21 0.0048
1 4 6 6 6 23 0.0008
1 6 6 6 6 25 0.00005
3 3 3 3 3 15 0.01024
3 3 3 3 4 16 0.0512
3 3 3 3 6 18 0.0128
3 3 3 4 4 13 0.1024
3 3 3 4 6 15 0.0512
3 3 3 6 6 17 0.0064
3 3 4 4 4 18 0.1024
3 3 4 4 6 20 0.0768
3 3 4 6 6 22 0.0192
3 3 6 6 6 24 0.0016
3 4 4 4 4 19 0.0512
3 4 4 4 6 21 0.0512
3 4 4 6 6 23 0.0192
3 4 6 6 6 25 0.0032
3 6 6 6 6 27 0.0002
4 4 4 4 4 20 0.01024
4 4 4 4 6 22 0.0128
4 4 4 6 6 24 0.0064
4 4 6 6 6 26 0.0016
4 6 6 6 6 28 0.0002
6 6 6 6 6 30 0.00001

These probabilities are still different from the coin-toss method Kostas Dervenis gives in his Oracle Bones Divination.  Dervenis suggests one uses three coins flipped to obtain one of four results (T = tails, H = heads), each with the following probabilities:

  • Khion: HHH (12.5%)
  • Hyption: THH (37.5%)
  • Pranēs: TTH (37.5%)
  • Kōon: TTT (12.5%)

Thus, using coins as a substitute for astragaloi, we’d have a 0.0000305% chance of obtaining a (1,1,1,1,1) or (6,6,6,6,6) roll and a 7.41577% chance of obtaining a (3,3,4,4,4) or (3,3,3,4,4) roll.  These are pretty big changes in the probabilities of particular rolls, and all the other rolls would be affected similarly.  In either case, however, we have a situation where some results will come up far more regularly than others; then again, the oracle overall seems designed to have common outcomes assigned to the common fates, and extraordinary news to uncommon throws.  After all, it’s not every day you have the help of Zeus, King of the Gods and Men at your side, but far more common that you should wait a bit longer since your right time to act in the cosmos isn’t yet here.

So where does this leave us?  Should we forsake the use of dice and coins in favor of authentic knucklebones for astragalomancy since the probabilities of a given outcome are so different based on the tools used?  I don’t think so.  If we were playing a game of chance, then yes, the tools definitely matter, just as weighting a particular die to come up more on a given side would.  However, we’re not simply gambling with the gods here.  Divination is a sacred art and profession, and it helps the gods communicate with us so that we can ascertain their will as well as understand our own fates and our place in the divine order of creation.  Sure, it may be our hands that throw the bones, but it’s the hands of the gods that determine the outcome and how they land.  We’re not just rolling dice on our own, no more than things in the cosmos happen according to pure chance and nothing else.  This is why it’s important to invoke the gods of divination, like Hermes and Apollo, so that they’re involved in the throw of the astragaloi and can help guide them to fall on the proper sides so that we have a proper understanding of their wills and knowledge based on the result of the throw.  In that sense, using dice or bones or coins wouldn’t really matter, since it’s ultimately up to the gods to determine the outcome, and nothing is impossible for the gods.  Although they may have a preference for the system and tools used (hence the consecration and divination ritual from the previous post), they’re pretty handy when it comes to the myriads of tools used for divination.  So long as you’re letting the gods answer when you ask, the tools and their statistical qualities don’t matter in the long run.