On Astragalomancy

My birthday was last month, and I was fortunate enough to spend it with my mother and sister, with whom I haven’t spent a birthday in something like eight years.  I was in town to watch over my mother after a hip surgery of hers, and it coincided with my birthday (a few days after Crucible, no less!), and besides coming down with a minor cold for a day or two, it was overall a fantastic trip and a good way to spend my birthday.  My mother is the type to always spoil people on their birthday; she lives for gift-giving, and most of her house is filled with Christmas, Hanukkah, and birthday supplies year-round.  One of the rooms in her house (my old room, no less) is filled with nothing but tchotchkes and trinkets that she’s accumulated over the years of working at Lillian Vernon and shopping at antique stores and QVC that she doles out regularly, always somehow replenishing her wares of knick-knacks and the like.  I tend to dislike her taste of gifts, personally.  It’s only occasionally that I find something I like in her house that I’d like to have for myself, and I’d rather her save her money for herself.  She insists otherwise, however, so I just redirect her to my Amazon wish list and she’s content with that, and I’m more than content with her buying me stuff I actually know I want.  She’s really too kind to indulge me at all at this age.

This year, like many years, she’s gotten me books on magic and divination; of the more-than-200 items on my wish list, a vast majority of them are books, so this isn’t surprising.  However, this year she got me a book I’ve had my eye on for a while: Oracle Bones Divination by Kostas Dervenis. The author calls it a “Greek I Ching”, and although I don’t quite agree with that, I can see where he’s coming from.  The book is short and to-the-point, focusing on a form of divination used in ancient and classical Greece where one uses a set of five dice to obtain a particular oracle.  It’s not unlike the use of Greek letter divination or grammatomancy in that light, but there are some major differences; no letters are required here, and while grammatomancy has only 24 results, this form of divination has 56, and the literature explicitly links each result not only to an oracular answer but also to a particular deity or divinity.  However, there’s no one single body of oracular verses for this; many different sites had their own variations, although they generally coincided for the most part.  Fritz Graf’s article “Rolling the Dice for an Answer”  (published in “Mantikê: Studies in Ancient Divination” as part of the series “Religions in the Graeco-Roman World”, vol. 155, Brill, 2005) contains one such list, based mainly on the inscriptions found at Kremma in Pisidia and Perge in Pamphylia, both in Anatolian colonies of the Greeks, while Dervenis’ work is based on other locations from ancient Anatolia; they’re mostly the same, with about 40% of the divine names different and 25% of the oracular verses different.  No one complete list of names and verses survives, though it’s hypothesized that there’s one specific originating text from which derive all the others.

In a word, this book describes Greek astragalomancy, or divination with astragaloi.  Astragaloi (singular astragalos, or Latinized astragalus) are the knucklebones (actually the anklebones) of sheep, goats, or rams, and were used as a type of die by primitive people and are still used in some cultures, especially nomadic, shepherding, or rural communities like those in mountainous areas of Greece or by Mongolian people in traditional games.  Given the way an astragalos is shaped, a person can throw an astragalos like a die and can come up with one of four results, each with a numeric value associated with it:

  • Khion (χιον, “of the island of Chios”), narrow concave side, with a value of 1
  • Hyption (υπτιον, “lying on the back”), broad concave side, with a value of 3
  • Pranēs (πρανης, “lying on the front”), broad convex side, with a value of 4
  • Kōon (κωον, “of the island of Cos”), narrow convex side, with a value of 6


Just a note: classically, the astragaloi were tallied such that they counted the side that was face down.  Us modern people are used to throwing dice to read the side facing up.  It could be that different regions had or have different ways of traditionally throwing dice and counting things up.  I prefer the modern way, although Dervenis doesn’t specify which method to use.

While the names of the four sides are fixed, and the values associated with each name is well known, I found some confusion in figuring out which of the narrow sides was Khion and which was Kōon.  Dervenis gives Khion (1) to the narrow convex side and Kōon (6) to the narrow concave side, while most other sources I’ve found reverse the two, such that Khion is concave and Kōon convex.  I use the latter method since I find it more plausible.  Like any die, the opposite sides add up to 7 (3 + 4 and 1 + 6), and it makes sense that the convex (bulging) side is given to the larger number of a given pair, while the concave (hollow) side is given to the smaller number.  Thus, I give the narrow convex side to 6 and the narrow concave side to 1, even though Dervenis switches them.  It’s really a matter of style, I suppose, since it only affects how I read the bones; the actual oracles themselves don’t change, though my selection of them differs from Dervenis’ method.

The astragalos has a shape approximating that of a rectangular prism, so there are technically six sides to the thing, but the two short sides are too round and narrow for the astragalos to land on them.  Thus, although it’d make sense for an astragalos to have six sides with a value for each (1, 2, 3, 4, 5, and 6), there are really only four results (1, 3, 4, and 6).  A modern tabletop RPG four-sided die can be used instead of an astragalos, substituting 2 with 3, 3 with 4, and 4 with 6.  Alternatively, Dervenis suggests the use of three coins flipped so that three heads is equal to 1, two heads with 3, two tails with 4, and three tails with 6.  Astragaloi can be a little difficult to obtain, but you can find them in some Mongolian traditional supply stores from time to time.  Dervenis suggests one uses three coins flipped to obtain one of four results (T = tails, H = heads):

  • Khion: HHH
  • Hyption: THH
  • Pranēs: TTH
  • Kōon: TTT

The problem with this is that one gets slightly different probabilities using coins than when one rolls actual knucklebones.  In order to get one of four results with three coins, we ignore the order in which we flip the coins.  However, each combination has a 1/8 chance, or 12.5% chance.  There’s only one combination that has all heads or all tails, so Khion and Kōon come up approximately 12.5% of the time each.  Hyption and Pranēs, however, are split with the rest; thus, if Khion and Kōon have 1/8 each, then we have 6/8 leftover, meaning that obtaining a Hyption or Pranēs with coins has a 3/8 chance each, or a 37.5% chance.  Knucklebones, however, have different probabilities due to their odd shapes; rolling a Hyption or Pranēs has about a 40% chance each, but rolling a Khion or Kōon has about a 10% chance each.   Thus, the likelihood of certain outcomes when using coins or when using astragaloi are going to differ.  It reminds me of a similar debate in i ching divination, where the traditional yarrow stalk method yields a different probability than the coin-based method, leading some people to favor one method over the other or claim that coin-based methods are false and misleading.  Still, the difference in outcome probabilities with coins versus knucklebones is much smaller than it is with coins versus yarrow stalks, so perhaps Dervenis is alright in suggesting the use of coins.

In Greek astragalomancy, five astragaloi are thrown and their combination inspected without regard for order.  Thus, a throw of 1-1-1-3-6 is equivalent to one of 6-1-1-3-1, and both are associated with the same oracular verse.  As mentioned before, there are 56 different combinations of throws, but we can view each throw of the astragaloi as a sum of the value of each astragalos.  Thus, 1-1-1-3-6 yields the sum 12.  This sort of summation was used in the ancient game of pleistobolinda, which is basically Greek dice gambling where the highest throw wins (though there are more complex rules to make scoring more fun).  In pleistobolinda with five astragaloi, we can get 24 different results ranging from 5 to 30, with the values 6 and 29 impossible to obtain given the numeric values available to us.  This means we link astragalomancy with grammatomancy, using give astragaloi to obtain one of 24 numbers and link that number to one of the 24 letters of the Greek alphabet.  Happily, Apollonius Sophistes on his page about the Greek alphabet oracle already gives us such a correspondence between the sums of five astragaloi to the 24 letters of the Greek alphabet.  Following the rule of pleistobolinda where the greatest sum wins the round, we give the highest throw of five astragaloi (30) to Alpha, the best oracle in grammatomancy, and the lowest throw (5) to Omega, the worst oracle.  The rest of the letters get assigned their respective values accordingly from high to low based on their position in the Greek alphabet.

Thus, with five astragaloi, we can pick and choose which set of oracles we want to use: if we’re only going to use the sum of the throw, we’d use the Greek alphabet oracle, but if we inspect the combination of individual astragaloi, then we’d use the astragalomantic oracle.  With the same set of tools we can pick and choose how we can get an answer, but it’s not clear to me how to link the two together, if we should at all.  For instance, consider the throw 1-1-1-1-1.  The sum of this throw is 5, associated with Omega with the oracle “you will have a difficult harvest, not a useful one”, which is the worst oracle you can get in grammatomancy.  However, in astragalomancy, the corresponding oracle for this says “Zeus the Savior will inspire you; he will give you happiness and all that you wish for, but sing the praises of Aphrodite and Hermes”.  This is actually quite a nice oracle to get, so long as you pay your respects to the good gods; plus, Dervenis links this throw of the astragaloi to the god Zeus Olympiou, Zeus of Olympos, while grammatomancy would link its corresponding oracle to the planet Saturn and, thus, the titan Kronos.  I see other issues with other results in trying to link Dervenis’ astragalomancy with grammatomancy, so although I can use the same set of tools for both, it may not be great to link the two together unless I find that grammatomancy and astragalomancy serve different ends.  Like, it’d be cool if grammatomancy could suggest a method of action while astragalomancy what will overall happen, but both seem to answer in terms of both advice on action and what will happen.  It’s unclear, although there is some connection between the two; one of the throws has in its oracular verse the verse associated with the letter Kappa (“fighting with waves is difficult; endure, friend”), though whether astragalomancy came before grammatomancy or vice versa isn’t clear.

Happily, the order in which the astragaloi are thrown don’t matter for astragalomancy; while one can simply throw a single astragalos five times, it’s implied that one throws five astragaloi at once.  However, although it’s never said in any text, it’s never mentioned about whether the manner in which the astragaloi themselves fall is interpreted, not just on which side but how far apart they end up, whether they bounce, the overall shape of the astragaloi placement, and the like.  There’re no rules for this, as far as I can tell, but where the astragaloi fall can often be as important as how they fall.  It’s similar to the cowrie shell divination I use; if they tend to fall in a straight line, it indicates motion to or some involvement with a particular entity, especially if all the shells fall in a line leading to a particular shrine or statue.  One flying off in a bizarre direction can indicate a wild hare up something’s ass.  This is far more free-form and is more ominous than oracular, so it all depends on the circumstances of the query, but it’s something to keep in mind.

All the same, astragalomancy is definitely a divination system I plan to be using and studying in tandem with grammatomancy.  After all, the use of dice has always been important for divination (sorcery and sortilege come from the same word, Latin sors meaning “lots” or selection by chance), and are excellent symbols of Hermes, to whom astragaloi and dice generally have always been linked.  Still, the use of knucklebones for divination has a different feel to it, a different charm and aesthetic that feels…well, older, classier, and more classical, and happily the set of knucklebones I bought on Ebay came in a set of 10, so I can keep one on Hermes’ altar and one in a satchel I keep of divination and magical tools on the go.  I’m getting to the point where I prefer to use them over my divination dice (a standard set of tabletop RPG dice from Chessex), but since I went ahead and consecrated my plastic divination dice, I figured why not undergo a consecration ritual for my astragaloi, too? Or, hell, turn astragalomancy from something casually done into something with a bit more flair?

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