Paul writes to the Ephesians: ὅτι οὐκ ἔστιν ἡμῖν ἡ πάλη πρὸς αἷμα καὶ σάρκα, ἀλλὰ πρὸς τὰς ἀρχάς, πρὸς τὰς ἐξουσίας, πρὸς τοὺς κοσμοκράτορας τοῦ σκότους τούτου, πρὸς τὰ πνευματικὰ τῆς πονηρίας ἐν τοῖς ἐπουρανίοις. (Ephesians 6:12 UBS5).
H.I. Marrou (A History of Education in Antiquity) reports that physical training was the "most characteristic part" of Greek education "at least at the beginning of the Hellenistic period" (p. 116). One activity that was used to educate young Greeks in times of antiquity was "wrestling" (ἡ πάλη) or hand to hand grappling. Marrou points out that ancient Greek wrestling was more popular than running. For the Greeks, wrestling in the strictest sense was "standing wrestling" (ORQIA PALH or STADIAIA PALH) in which a wrestler would try throwing his opponent to the ground "without falling himself" (p. 122). If one of the grapplers did fall, the throw would not be counted.
Other points about πάλη are "πάλη (#4097) struggle, wrestling. The word refers particularly to a hand-to-hand fight (Barth). Wrestling was a fight characterized by trickery, cunning, and strategy (Rogers, Cleon L., Jr. and Cleon L. Rogers III. The New Linguistic and Exegetical Key to the Greek New Testament. Grand Rapids: Zondervan, 1998, page 446).
"PALH, PALHS, hH (PALAIW 'wrestle'; Hom. et. al.; ins; Sb 678, 6) engagement in a challenging contest (orig. 'wrestling' Il. 23, 635 al., then of fights or battles Aeschyl., Ch. 866; Eur., Heracl. 159) struggle against . . . of Christians' fight against powers of darkness Eph 6:12 (the opponent is introduced by PROS w. the acc. as in Philo above [Sobr. 65], but the context suggests military imagery" (BDAG).
"Our wrestling is not (οὐκ ἔστιν ἡμῖν ἡ πάλη). 'To us the wrestling is not.' πάλη is an old word from PALLW, to throw, to swing (from Homer to the papyri, though here only in N.T.), a contest between two till one hurls the other down and holds him down (KATECW). Note PROS again (five times) in sense of 'against,' face to face conflict to the finish" (Robertson's WP).