Green’s Dictionary of Slang

best (of it) n.

[19C+] an advantage.

In phrases

get the best of it (v.)

[19C–1940s] (Aus./US) to gain an advantage, typically in a gambling game.

give someone best (v.) (also give it best, give something best)

[late 19C–1950s] to leave, to abandon, to acknowledge defeat.

give someone the best of it (v.) (also give someone/something best)

[late 19C–1940s] (Aus./US) to allow someone the advantage, typically in a gambling game.