Erasmus, Adagia 1.25: 

“Diogenianus thinks that this has roughly the same force as the previous saying: Κινῶ τὸν ἀφ᾿ ἱερᾶς, that is, I move my die from the sacred line. This is said of those who are about to make a last desperate attempt at something. Julius Pollux, explaining the saying in his ninth book, says that the adage comes from a certain game of dice, which was set up such that each of the contestants had five stones placed on as many lines. From this, even Sophocles said πεσσὰ πεντέγραμμα, that is, dice of five lines. Between those lines, each one a fifth, there was one in the middle which they called sacred. One who moved the die from the middle was said to have moved it from the sacred line. But that didn’t hapen, except when the matter demanded it, as when a player resorted to desperate remedies. Plato takes up this adage in the fifth book of his Laws: Καθάπερ πεττῶν ἀφ᾿ ἱεροῦ, that is, just as from the sacred die. 

Plutarch, in the book which is called Whether the Republic Should Be Run By An Old Man, Τελευταίαν ὥσπερ τὴν ἀφ᾿ ἱερᾶς ἐπάγουσιν ἡμῖν τὸ γῆρας, that is, They allege that old age is to us the end, as if it were the sacred line, which is understood to be a most grave charge. Plutarch also says in his commentary On the Comparison of Terrestrial and Marine Animals: Φέρε κινήσαντες τὴν ἀφ᾿ ἱερᾶς βραχέα περὶ θειότητος αὐτῶν καὶ μαντικῆς εἴπωμεν, that is, Come on, having removed the die from the sacred line, we will say a bit about their divinity and divination. Again, in Against Colotes the Epicurean, Εὐθὺς οὖν τὸν ἀφ᾿ ἱερᾶς κεκίνηκεν ὁ Κολώτης, that is, Colotes moved his die from the sacred line straightaway, which is to say that Colotes took the most extreme step at the outset, so that he could attack the judgment of Apollo concerning Socrates. He also writes, in the life of Martius Coriolanus about the Roman state disturbed by Coriolanus’ threats, Ἄρα τὴν ἀφ᾿ ἱερᾶς ἀφῆκεν, that is, He tossed away the die taken from the sacred line. For, in desperate matters, one takes refuge in supplication by sacrifices, priestesses, initiators, augurs, etc. Theocritus even alluded to this in his Bucolics:

Καὶ τὸν ἀπὸ γραμμᾶς κινεῖ λίθον

that is,

‘And he moves the stone from the little line’

about which I have written elsewhere.”

Movebo talum a sacra linea.xxv

Idem pollere putat Diogenianus : Κινῶ τὸν ἀφ᾿ ἱερᾶς, id est Sacrae lineae talum moveo. De iis, qui extrema parant experiri. Id Julius Pollux libro nono exponens ait a ludo quopiam tesserarum natum esse adagium. Lusum autem fuisse hujusmodi, ut utrique ludentium essent calculi quinque totidem impositi lineis  ; unde et Sophocles dixerit πεσσὰ πεντέγραμμα, id est tesserae quinque linearum. Inter eas lineas, utrimque quinas, unam fuisse mediam, quam sacram vocabant ; unde qui talum movisset, is sacrae lineae talum movere dicebatur. Id vero non fiebat, nisi cum res posceret, ut ludens ad extrema confugeret auxilia. Usurpat hoc adagium Plato libro De legibus quinto : Καθάπερ πεττῶν ἀφ᾿ ἱεροῦ, id est Tanquam a sacra tessera. Plutarchus in libro, qui inscribitur An seni sit gerenda respublica : Τελευταίαν ὥσπερ τὴν ἀφ᾿ ἱερᾶς ἐπάγουσιν ἡμῖν τὸ γῆρας, id est Postremam nobis tanquam a sacra linea senectam allegant, hoc est veluti causam gravissimam. Idem commentario De comparatione terrestrium ac marinorum : Φέρε κινήσαντες τὴν ἀφ᾿ ἱερᾶς βραχέα περὶ θειότητος αὐτῶν καὶ μαντικῆς εἴπωμεν, id est Age moto talo a sacra linea paucis de divinitate eorum et divinatione dicamus. Rursum idem Adversus Colotam Epicureum : Εὐθὺς οὖν τὸν ἀφ᾿ ἱερᾶς κεκίνηκεν ὁ Κολώτης, id est Protinus igitur talum a sacra movit Colotes, hoc est statim id quod est gravissimum aggressus est, ut impugnaret Apollinis de Socrate judicium. Idem in vita Martii Coriolani de civitate Romana ob Coriolani minas perturbata : Ἄρα τὴν ἀφ᾿ ἱερᾶς ἀφῆκεν, id est Sublatam a sacra linea tesseram misit. Desperatis enim rebus ad deorum religionem confugiebat supplicatum missis sacrificis, aedituis, initiatoribus, auguribus etc. Huc allusit Theocritus in Bucoliastis :

Καὶ τὸν ἀπὸ γραμμᾶς κινεῖ λίθον,

id est

Atque a lineola lapidem movet,

de quo nobis et alias facta mentio.