After Odysseus realizes he is not lost, but is in fact in Ithaca, the narrative describes him preparing to speak.
“So she spoke, and much-enduring, shining Odysseus
Was delighting in his own paternal land which Pallas Athena
Declared to him, the daughter of Aegis-bearing Zeus.
Then he responded to her with winged words—
He didn’t speak the truth, but he chose the opposite to that,
Since he was always fostering very-profitable thought in his chest.”
ὣς φάτο, γήθησεν δὲ πολύτλας δῖος ᾿Οδυσσεὺς
χαίρων ᾗ γαίῃ πατρωΐῃ, ὥς οἱ ἔειπε
Παλλὰς ᾿Αθηναίη, κούρη Διὸς αἰγιόχοιο·
καί μιν φωνήσας ἔπεα πτερόεντα προσηύδα· —
οὐδ’ ὅ γ’ ἀληθέα εἶπε, πάλιν δ’ ὅ γε λάζετο μῦθον,
αἰὲν ἐνὶ στήθεσσι νόον πολυκερδέα νωμῶν·
Schol.HV ad Od. 254 ex:
“Odysseus turned to the opposite; to the opposite of the truth which is he took up a story for a second time.”
πάλιν δ’ ὅγε λάζετο] εἰς τὸ ἐναντίον ἔστρεφεν. H. εἰς τοὐναντίον τοῦ ἀληθοῦς, ὅ ἐστιν, ἐκ δευτέρου δὲ τὸν λόγον ἀνελάβετο. V.
The scholia says this but misses the fact that in archaic and classical Greek poetry this compound is only applied to Odysseus.
“fostering a polykerdea mind: This means turning his deceptive and lying thought to many things, devising different thoughts for different matters”
νόον πολυκερδέα νωμῶν· τὸν ἀπατηλὸν καὶ ψεύστην νοῦν ἐπὶ πολλὰ τρέπων· ἄλλο ἐπ’ ἄλλο διανοούμενος (ν 255)
πολυκερδέα· πανοῦργον: polykerdea: doing anything, i.e. wicked.
But: πολὺ κέρδιον· πολὺ βέλτιον: polu kerdion [means] much better.
23.77 Eurykleia speaking to Penelope about Odysseus
“He would not allow me to say anything, thanks to the [devious thoughts] of his mind”
οὐκ εἴα εἰπεῖν πολυκερδείῃσι νόοιο.
24.167-8 Amphimedon telling the story of the slaughter
“But he ordered his wife with [very devious thoughts]
To set out the bow and gray iron for the suitors…”
αὐτὰρ ὁ ἣν ἄλοχον πολυκερδείῃσιν ἄνωγε
τόξον μνηστήρεσσι θέμεν πολιόν τε σίδηρον