New divination tools of Hermēs available up on my Etsy!

If you want something done, give it to a busy person.  And boy, between my usual stuff going on, a new shrine project that came together WAY too quickly for it to have been mere chance, and all the 2019 yearly forecast readings going on (have you gotten yours yet? special ends next Wednesday!), it’s a true blessing that I’ve been snowed in for the past few days and have had the time to actually do everything I need and get some sleep on top of that.

I’ve had it in my mind to make some divination tools for the public to have for a while now, based on some of the tools and methods I use.  I’ve written about a bunch on this blog from time to time over the year—granted, most of it is geomancy, which is pretty tool-independent when you get right down to it—and some of them require some specialized tools.  In general, most forms of divination, especially practiced in a modern way, don’t really require consecration or blessing, though it never hurts to do so.  Tarot readers can just pick up a pack of cards and get to work, but it can often help to cleanse them and spiritually prepare them for the work they’re doing.

However, not all the forms of divination I do are so free-wheeling or powered by my own spiritual sense, but are tied directly to the spirits and gods, a true divinization of divination as it were.  To that end, I like to have some of my tools properly prepared, blessed, consecrated, and linked up to the voices of those spirits and gods so that I can read what they say as much as I hear them.  For some time now, I’ve been working on how, exactly, to go about doing that for others, but I kept putting it on the back burner.  Well, no more of that; a bunch of supplies came in, and I promptly got myself read, got into the right headspace, made the right offerings, and got to Work with the Hellenic god of guides and guide of gods, men, spirits, souls, and heroes, Hermēs.

Long-time readers might remember two forms of divination I use with him:

Guess what?  You can now buy sets of four coins and sets of five astragaloi on my Etsy page, all consecrated, blessed, and ready to go.

Making these was a pleasure and an honor, and they’re specially made for those who work with Hermēs as the messenger of gods and men to communicate to them, and to any to approach them, the best advice in the time they need and the way they need, so that anyone who comes to the gods with sincerity, honor, and reverence may have the proper guidance to go where they must go, know what they must know, do what they must do, and become what they must be.  Not only are these tools for you, but they may be used through your service for any who come to you.  Just call on Hermēs, and he will answer.

I’ve prepared a bunch of these sets in a batch, which was easy enough for me, but supplies are still limited.  I may make more in the future, or I may make more only as special requests and commissions, I haven’t yet decided.  If you’re interested, head on over to my Etsy while supplies still last:

I include with the coin sets a short guide on how to use them along with a special prayer, but the bones contain no such guide due to the amount of information they can provide.  For that, I would strongly recommend getting one of the following texts:

Of course, there are other ways you can use the astragaloi, too; one such way is to use them for grammatomancy, the Greek alphabet oracle, which I just so happen to have written about and have a highly useful reference text on, too, also coincidentally available on my Etsy.  However, you might also consider getting John Opsopaus’ book, Oracles of Apollo (Llewellyn Publications, 2017), which has that and other divination methods included in it, as well.

So what are you waiting for?  Who can deny the blessings of the gods, and who would ignore their guidance?  Learn how to communicate with Hermēs and, through him, with the rest of the gods today; get in on these tools while they’re still there to get!

Compilation Paralysis

I’ve been on a compilation kick lately.  I mentioned in a recent post of mine about the Orphic Hymns that I’m compiling a personal temple text from a variety of sources because I don’t like having books in my temple room if I can avoid it; for instance, I have a copy of Dervenis’ Oracle Bones Divination that, up until quite recently, I’ve been using as my reference for astragalomancy, and have kept it with my shrines for the Greek gods.  This…makes me uncomfortable, so I transcribed all the necessary information from that into a personal ebook for me to keep a printout of instead.  Not only do I get to finally put the damn book back on the bookshelf after way too long, but I also get to reformat it, reorganize it, and include other information I want to reference, as well as tweak some of the translations for my own tastes.

Of course, one thing led to another.  I also included a few pages for grammatomancy, which also references a good chunk of my Mathesis correspondences to the letter, and because Opsopaus included the Delphic Maxims in his Oracles of Apollo book, I decided to include those, too.  Again, nothing too elaborate or in-depth; I have enough experience with these systems and the backgrounds and contexts in which they were written to not have to have all the extra information in a temple reference.  The final result is something I could be content with…except, of course, I wasn’t.  Given all the references to the other gods between grammatomantic correspondences to the zodiac signs and, by those, to the Greek gods (cf. Agrippa’s Orphic Scale of Twelve, book II chapter 14), I wanted to also have a section for the Orphic Hymns.  This is reasonable; after all, my personal vademecum-enchiridion-prayerbook has a number of them already transcribed, and while I won’t use all the Orphic Hymns in my practice, why not have a complete set for reference, just in case?  It wasn’t hard to find a copy of the Greek texts as well as the Taylor translations that I could simply copy, paste, and format for LaTeX’s customary needs.

But, of course, why stop there?  I also ended up adding Gemisthus Plethon’s hymns as well as those of Proclus, which I find useful for my Neoplatonic uses as well as my devotional ones.  And, if we’re going with devotions, I decided to also include a few prayers attributed to Hermes Trismegistus from the Corpus Hermeticum, the Asclepius, and so on, and because of those, I also wanted to bring in a few things from the PGM, which then became more than a few things from the PGM, and then I added in the planetary invocations from the Picatrix because those would be useful, too…

The ebook I was preparing ballooned from a simple reference for divination to a compendium of devotional and oracular texts.  Whoops.

But, yanno, I was hooked!  I wanted to bring in what I could, because it might be useful, whether in a devotion to the theoi or in divination or needing something to reference for meditation.  And, so, my penchant for completionism and perfectionism kicked in—hard—and I’ve been looking through my other references and books, trying to pick out useful prayers, invocations, rituals, and the like for my temple.  In effect, I was essentially making a typed-up version of my vademecum, with a different focus and with plenty more texts that I’m not accustomed to using.

This is all well and good, of course, assuming I could actually use the thing.  And in the form it was in, even in the form it had been in, it was quite plenty useful, and definitely satisfied my original needs of having a handy divination reference in my temple.  But since I brought in all these other things, I knew I wanted more, and because I wanted more, I also knew that it was incomplete.  And how would I tolerate having something be incomplete?  The idea is as distasteful as unnecessarily having books in my temple room.  Because it was incomplete, I didn’t want to print it out prematurely, especially with having to deal with page numbers or section enumeration, because if I wanted to add or fix something, I’d have to go back and reprint the damn thing for consistency, and even though I can get by by using the office printers once in a while for personal ends, I didn’t want to waste that much paper and ink.  Editing a text is one thing—I’m not opposed to using interim texts with scratched-in notes—but putting something on paper, especially printing something out, gives me a hard-to-achieve and yet so-satisfactory feeling of something being “fixed”, even if it is for my eyes only.  So, in order to make printing this thing meaningful, I wanted to make sure it was worthy and proper for printing.

It’s been over a month since I had the original problem of “I need a quick reference for divination”.  It’s also been over a month since I’ve had a workable, totally satisfactory solution for this problem, too, and yet I still haven’t fulfilled my needs.  Instead, I got caught up in a problem I call “compilation paralysis”: not wanting to proceed in some matter due to a fear of not having enough resources, options, or sources.

Some authors, especially those in academia or in teaching-types of writing, might know the feeling well, of not feeling like you have adequate source material to publish.  I have that same sensation, too, for my geomancy book-in-progress, knowing that there’s still so much more that might be included but…well, the benefits diminish after a certain point, and well before that, it’s probably better to cut out stuff that’s truly extraneous and unnecessary before adding anything more.  It does, in fact, help to start off with too much and cut down rather than having the opposite problem, and this is a habit I picked up in college for my research papers (getting down to the ten-page mark was a lot easier than trying to BSing and subtle-formatting my way up to it).  But, at the same time, consider the context: what these authors are dealing with is a single book on a single topic that is published for a single need.  Once that need is met, the book is (in theory, at least) publishable; further books can be written or new editions made with further appendices, but those aren’t strictly needed.  My problem, in this case, is dealing with something for me and me alone that needs to satisfy my sometimes-nebulous needs.

One of the reasons why I support people having a notebook or, perhaps even better from a utilitarian standpoint, a binder with written pages for their vademecum-enchiridion-prayerbooks or records of their prayers and rituals is because these are essentially living documents; as we grow in practice, they grow, too.  As we find new prayers, rituals, and correspondences, we add them in, organization be damned.  We can reevaluate the real use of these things we add, and reorganize what makes the cut, when we fill the first notebook and move onto the second one, as I did not too long ago.  These aren’t things that need to be polished, edited, or fixed in any way except what serves our needs in prayer and ritual, and as such, don’t need to be fancy, embellished, typeset, illumined, or otherwise made particularly fancy.  In fact, I have a personal fear of using those beautifully handcrafted, leatherbound, embossed, etc. journals I see floating across the internet and bookstores because I tremble at the thought of messing up such a beautiful work with errors or wasted paper; not only is my calligraphy not up to par to match the beauty of these books, but I find these things to be more appropriate to true works of devotion and love that are complete and refined unto themselves.  (I only speak for myself, of course.)

So, like, with my personal enchiridion, I don’t particularly care about making errors; there are scratchmarks, crossouts, and addenda all over the damn thing.  The important thing for me is not to waste space, so I try to be as efficient as possible cramming in as much information and references as possible into as few pages and lines as possible.  This is fine; after all, it’s my own personal thing, and nobody else needs to see or use it; besides, Moleskines can be expensive for such a notebook, even if they’re the perfect size to carry around (and fit in a Hyundai car manual leather case, I might add, which gives it extra padding and some extra utility, in case you wanted to try that out as a Moleskine bookcover).  The things I add to my enchiridion are a testimony to my growth and directions and shifts in focus I take in my practice, which I find is informative on its own.  The only important criterion I have for adding stuff to it, truly the only one, is whether something is going to be useful to me; if not, I’m not gonna waste the time writing it in or the ink to write it.

That’s what reminded me to get out of my compilation paralysis.  There’s no need to be scared or anxious about not having enough sources; if I need something later, I can just add it it.  It’s not like I didn’t already have these sources and there’s a threat of losing them; I’ve never needed a copy of the Homeric Hymns or the Nabataean prayers to the Sun or Saturn on hand when I didn’t already have my enchiridion or my copy of the Picatrix at hand, after all, so why should I be so worried about not having them in this temple reference?  I can always add new things into the overall document, print out the necessary pages, and just add them into the binder where appropriate.  It’s not that big a deal.  I know for a fact that I can always get this information should I need it, and if I haven’t needed it yet, there’s no harm to start off with that which I know I need right now and add stuff later.  I’ve got more than enough source material for what I need, anyway, and it’s more manageable to deal with two small binders than one massive one.

It’s a bitter pill for me to swallow, but even I have to admit it: none of us needs to know everything about our practices right out of the gate.  It might be nice, to be sure, but that’s also kind of the beauty of it, to let growth happen organically, especially if you’re in a practice that you’re developing on your own, as so many magicians and pagans are.  You don’t need full copies of the Homeric Hymns or Orphic Hymns in both Greek and English the moment you decide to build a shrine to one of the gods; you don’t need to know all the specific proportions of all the ingredients for the obscure incenses needed for all the planets from the Picatrix when you’re not even going to bother with a planet you’re going to interact with tonight once and probably not again for a few years more.  Part of the practice is just that: practice.  We do things, and then we do both more things and we do those same things more.  We learn, we accumulate, and we incorporate what we do into what eventually becomes our whole practice.  Part of that is necessarily finding more things to add and adding them at the proper time, as well as changing the things we do as we need to change them so as to keep doing them better or, at least, keep doing things better for our own sakes.  If we need to make emendations, do so at the proper time; you don’t know what would need them until you do or until they’re pointed out to you, and so much of that is based upon trial and error, experimentation and evaluation.  It’s not that big a deal.

There’s no need to worry, and there’s no cause for paralysis.  All you need to do is, simply, do.  Amend, fix, and add when you need to.  Don’t worry about trying to have everything ready for everything, especially when you don’t know what “everything” consists of.  Relax, then Work.

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?

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.