"steal game," 1520s, "to push, poke," from Middle French pocher "to thrust, poke," from Old French pochier "poke out, gouge, prod, jab," from a Germanic source (compare Middle High German puchen "to pound, beat, knock," German pochen, Middle Dutch boken "to beat") related to poke, v.. Sense of "trespass for the sake of stealing" is first attested 1610s, perhaps via notion of "thrusting" oneself onto another's property, or perhaps from French pocher "to pocket" (see poach, v.2). Related: Poached; poaching.

"cook in liquid," early 15c., from Old French poché, past participle of pochier (12c.), literally "put into a pocket" (as the white of an egg forms a pocket for the yolk), from poche "bag, pocket," from Frankish *pokka "bag," from Proto-Germanic *puk- (see poke, n.). Related: Poached; poaching.