Fraenkel's note concerned lines 32 and 33:
Fraenkel says that this refers to a Greek game where movement of the pieces is determined by a throw of the dice, with 3 sixes being an especially lucky throw. Though Fraenkel does not say so, this must be a game in the Five Lines family, likely the 11 line variant. (Fraenkel actually mentions Petteia, which cannot be the game as it did not involve dice. But Petteia used the same capture technique as Hnefatafl, which did have a Welsh variant that may have used dice in approximately the manner that Fraenkel discusses.)τὰ δεσποτῶν γὰρ εὖ πεσόντα θήσομαι
τρὶς ἓξ βαλούσης τῆσδέ μοι φρυκτωρίας.
The above gaming table may represent what Aeschylus is talking about. This has been interpreted as a game in the winning position, with a die showing six missing in the center, which would therefore be a winning throw of three sixes. Ulrich Schädler disagrees with this interpretation, suggesting that the nine lines are probably an artistic representation of what would have been 11 lines on a real board, and the 18 positions = 3 x 6 showing on the dice is a coincidence. He feels that it is impossible that it is in winning position because there are no pieces on the "sacred line." Finally, he suggests that some sort of figurine in the center is more likely than a third die, as in other miniatures, but he does not appear to be aware of the Agamemnon reference. Regardless, his argument about the sacred line is probably conclusive.
Here is Pollux on Five Lines and the Sacred Line:
Apparently this proverb meant to do something risky as a last resort (but that might win the game).Pollux (9.97): ἐπειδὴ δὲ ψῆφοι μέν εἰσιν οἱ πεττοί, πέντε δ᾽ ἑκάτερος τῶν παιζόντων εἶχεν ἐπὶ πέντε γραμμῶν, εἰκότως εἴρηται Σοφοκλεῖ καὶ πεσσὰ πεντέγραμμα καὶ κύβαν βολαί: τῶν δὲ πέντε τῶν ἑκατέρωθεν γραμμῶν μέση τις ἧν ἱερὰ γραμμή: καὶ δ̔ τὸν ἐεῖθεν κινῶν ἐποίει παροιμίαν: κίνει τὸν ἀφ᾽ ἱερᾶς.
I'll have another post up soon with some proposed rules for Five Lines.