Theramenes (d. 404/3) is the Athenian politician famous for his tergiversations at the end of the fifth century; cf. theta 342, theta 343, theta 344; and see generally OCD(4) s.v., with references to the 'Theramenes papyrus'.
The quotations here are from Aristophanes [= "he" in the second sentence], Frogs 968-70, produced the year before the man's execution in a political battle among the "Thirty Tyrants" (see OCD(4) s.v.). The entry is based on the scholia on the passage, already more fully at theta 344.
[1] This phrase spoken by Dionysus is clearly sarcastic. The tone is carried by the ambiguities of sofo/s, 'wise, sophistic', and deino/s 'dreadfully good, dreadful'.
[2] See alpha 4250. This clause is a paraphrase of Aristophanes, whose own language more clearly reveals its dicing metaphors (see theta 344). It is taken from the scholia, with the otherwise unknown verb there for throwing badly.
[3] Aristophanes uses as a subtle and devastating characterization of Theramenes a proverb explained by Tzetzes in his Commentarium ad loc.: "when the Athenians were in a hostile mood towards the Chian people, if ever someone from Chios was captured by them and about to be beaten, he used to shout, 'Not a Chian but a Cean!'" This shout was intended to be a pun on the names of the throws in knucklebones, with the losing throw Chios; but in the place of the winning throw Coös, similar to the adjective for an inhabitant of the island Cos, in the Athenian sphere of influence but Dorian in origin (thus Spartan in sentiment), the speakers used the adjective for an inhabitant of the island Ceôs, an Ionian island more closely allied to Athens. Theramenes is described as a man who, when caught on the losing side, claims with sophistic wit that he had never really belonged to it and has thrown the dice of the winning side. In an interesting critical notice Eustathius (on Homer, Iliad 4. 691) explores the intertextual relationship between the proverbial phrase in Aristophanes and the proverb concerning the winning and losing throws in knucklebones: "Chios standing beside does not allow Coös" (cf. kappa 2290). The rare compound verb used in his notice, para-lalei=n, for talking off the top of one's head (Hesychius, accepted by LSJ), is a favorite of Eustathius, who uses it 79 times in a quite different and literary sense for relationships including or similar to those of parody between texts. Indeed on Odyssey 1.29 to summarize his argument he uses the verb for parody, (parw/|dhtai).
[4] Eustathius gives as an alternative explanation for the phrase in Aristophanes that *Kei=os may be an error for *Kw=os in the transmission of the text (on Odyssey 1. 29, 120), and this view is widely accepted.
[5] Or possibly 'under' the Thirty. At any rate, the sentence comes from Harpokration s.v., commenting on Th.'s appearances in Lysias 12. For the episode in question see generally Xenophon, Hellenica 2.3.15-56.
[6] This is simply untrue in fact, for, as all compound names in -menês, Theramenes belongs to the third declension, with a genitive in -ous.