I studied Latin in high school (here in Italy is pretty common), but not Greek, so any advice is a precious help.
So, if I insist on using greek words for the abilities (I am not sure about this, but for now I’d like to keep them), then should I use kratos, tekhne and thumos? They are philologically more correct?
Thank you to all of you for precious advices and insights, they are much appreciated!
I would not say that those three words are philologically more correct. They are just words… But they are a close match for STR, DEX, and WIL with the setting you are trying to evoke and the vocabulary of Homeric or epic Greek. Of the three, tekhne is the most dubious fit (for DEX), but personally I like that it implies “skill” and the ability to craft solutions to problems (not merely athletic agility). There’s really not a single obvious term for agility in Homeric or even classical Greek that resonates with the needs of your game.
Then again, a more exact match for DEX strictly as agility would be δεξιότης (dexiotes) although that can also imply cleverness. It has the advantage of beginning with the syllable DEX, but it’s not a common word in ancient Greek.
Continuing on the developing theme of offering alternate Greek words for your terms… 
I’d honestly suggest you just call the Game Master a “Game Master” - however, if you do want to give them a Greek title, you might consider instead the modern “hegemon”, from Greek ἡγεμών, “one who leads”, parallel to Latin dux, with further senses of “guide” or “commander, chief.” It’s a bit better analogy for “Game Master” and has the significant benefit that the word “hegemon” already exists in modern English.
Cheers!
Oh, yeah, the possibilities are fun!
You could have paediagogue (not paedogogue) from παιδιά (play), or, to go with Latin, magister ludi for another unwanted set of connotations. Or why not scholarch, relying on the old sense of σχολή? 
Frankly, I think guide ὁδηγός is pretty good. ἡγεμών makes me think of the Macedonian takeover, even though it is an English word…
Seriously though, Gundobad, I’m with you. Gamemaster (or Referee) are best!
I really don’t like the concept behind “Game Master”. For me there is a pivotal difference between Referee and Game Master and I prefer the former. I proposed diaititís (διαιτητής), but @yochaigal pointed me towards ὁδηγός that I found really fitting
I’d really love to visit Knossos! Also: I just ran my Stonetop game in Iron Age Greece today. My head is definitely in this space (although a little later in history :- ). I’m glad to see everything move forward.
I really feel bored with Pseudo-names for gods, and I’m so surprised when I see it in newer games.
So glad this game isn’t going that route.
It’s pretty surreal. Apparently the British “historians” reconstructed the site by configuring rooms and sculptures according to their beliefs about how the ancients lived. They glued stuff together, broke floors and walls and rearranged objects how they saw fit. I think it would make modern archeologists cry.
It was still very cool though.
Here is a picture of a “throne room” in Knossos. I took it! Very cool animal painting on the wall. They loved dolphins or something.
The guy who dynamited the site of Troy has to go in the Hall of Fame for old-school archaeologists, fantastic commitment to the bit. The Bomberman school of excavation.
I drafted the first version of Theourgía (one of two kinds of magic in Thálassa).
I would be happy to know what you think about this:
Theourgía
Theourgía is the highest form of magic. It consists of a set of magical practices performed to evoke Gods in order to see them or know them or in order to influence them or ask them a blessing. It is a power higher than all human wisdom embracing the blessings of divination, the purifying powers of initiation and all the operations of divine possession.
The practitioner evokes the God competent for a specific domain on which he wants to have effect:
- Apollo: divination and healing.
- Ares: might in battle.
- Artemis: protection in the night and charms in the hunt.
- Aphrodite: love charms and potions.
- Athena: insights and strategy.
- Hermes: thievery and trickery.
- Hephaestus: blessing weapons and armors.
- Hera: blessing marital unions.
- Persephone: calling upon the souls of the dead.
- Poseidon: control over sea and weather
A time of recollection and concentration is required to appeal to the deity, equal to 1d6 turns. Then roll 1d20: if the result is 16+, the deity hears and grants the request. In any case the practice will consume THU like any other magic.
edit: I have reworded the second paragraph better and added an evocation time in the last one
Does it matter to you that theourgia is a late ancient Greek word, from the Roman imperial period, fostered by Neoplatonists? That is, it’s not a Homeric term or concept. I understand that “realism” is not the goal (ha!) but capturing the spirit of Epic seemed to be one of the goals.
Prayer, in Homeric Greek, was λιτή or εὐχή (the latter being more along the lines of what you have). Again, I don’t assume you are trying to make it “authentic,” and there is no need to do so, but you did express the wish to capture a certain flavor linked to a historical period.
“Magic” didn’t exist yet by that term. Ancient Greeks described the rituals of the magi (Zoroastrian priests from the Persian Empire, a post-Homeric empire) as “magic” (related to those priests). From there, any hocus pocus could be described as “magic.”
You know that I greatly appreciate your advice about terminology!
I isolated theourgia and goïteia as “divine” and “arcane” magic (knowing that “magic” was a linguistic cast from Persian).
So I definitely rename theourgia with eukhḗ
What about goïteia? Any suggestion?
eukhḗ is really just “prayer,” but prayer was, I think, deemed to be effective and not something done routinely by time of day as a modern Christian or Muslim might do.
For the other kind of magic, I might look into the words used in the episode of the Odyssey where Calypso occurs. There may be no word for “magic” in Homeric Greek.
You might also like to look at a book like Walter Burkert’s Greek Religion: Archaic and Classical, which breaks down ritual procedures part by part with reference to ancient Greek terms.
I’ll think more about “magic” in this context and if I get a chance I’ll find my Greek Odyssey and look to find a likely term.
Thank you for the reference, I’ll look for it
it would be great! I don’t know how to thank you (apart from putting you in the game credits 
)
I research a bit Book X of the Odyssey, when Circe is encountered
There is a reference of her enchanting beasts:
τοὺς αὐτὴ κατέθελξεν, ἐπεὶ κακὰ φάρμακ᾽ ἔδωκεν, X, 213
I think the word is κατέθελξεν → katéthelxen
but I can’t find any further reference to this word
it seems an archaic form of καταθέλγω (katathélgō) → subdue by spells
That’s good! I recommend using φάρμακα (neuter plural) for arcane magic: drugs, potions, spells, enchantments.
I explored the Greek Magical Papyri (a late text, influenced by Egyptian culture), that thematically may be a little off-axis, but I thought better than adapt a spell list from another game (even from the Knave/Cairn d100 spell list).
So, I isolated 30 spells (recursions removed).
My concern is that 30 is an odd number, even it you can roll it combining a d10 and a d3 
Just gotta say, I love this project. I always wanted to play something ancient greek’ish after playing Assassin’s Creed Odyssey.
Hello! It’s a great list of spells from Roman antiquity.
I would not remark on this if you had not specified your interest in the fantasy of the Epic Age, but the “Greek Magical Papyri” are actually half Egyptian. That is, while classical scholars extract the Greek texts out of context and treat it as “Greek magic,” much of the contents are omitted, because they are in Egyptian. It is possible to get at the Egyptian material, which is similar. You can read about these papyri here (if you have access to this site), but let it suffice to quote the author, a world expert on these texts. He regards these papyri
as manifestations of Greco-Egyptian private ritual, a highly eclectic form of ritual and scribal practice that emerged first in the cosmopolitan cities of late Ptolemaic Egypt. Whoever composed, copied, and used these ritual texts, they coined a new verbal and visual idiom of ritual power by adapting freely from Egyptian, Greek, and Jewish rituals, texts, and authoritative traditions.
At the same time, there are (scanty) examples of similar spells from throughout the Roman Empire. (The Egyptian climate kept these papyri intact, unlike other regions.) Basically, though, these papyri are more about Egyptian private religion of the late Ptolemaic period than “ancient Greek magic.”
But nothing need be lost. I see two constructive responses to this, so that people shouldn’t tell you not to use it.
One is just to shrug and say that it’s fun and cool and you aren’t really aiming at a specific age of ancient Greek fantasy. That is perfectly acceptable, because it’s your world and your game.
Another is to embrace the Egyptian heritage of these rituals. What if this kind of magic came from Egypt, in your fantasy setting? The fantasy of pharaonic Egypt evokes imaginative responses just as does the mythos of Homer, and the two could exist in the same world. A hero can have sojourned in Egypt, or be of Egyptian origin, in order to have acquired this magic.