outplay v.

in Old English a common prefix with nouns, adjectives, adverbs, and verbs, "out, outward, outer; forth, away," from out (adv.). The use was even more common in Middle English, and also with the senses "outer, outside, on the outside, from without, external, externally; apart; greatly, extremely; completely, thoroughly, to completion." Other senses of out that extended into the use as a prefix include "beyond the surface or limits; to the utmost degree; to an explicit resolution."

In composition out has either its ordinary adverbial sense, as in outcast, outcome, outlook, etc., or a prepositional force, as in outdoors, or forms transitive verbs denoting a going beyond or surpassing of the object of the verb, in doing the act expressed by the word to which it is prefixed, as in outrun, outshine, outvenom, etc. In the last use especially out may be used with almost any noun or verb. [Century Dictionary]

Middle English pleien, from Old English plegan, plegian "move lightly and quickly, occupy or busy oneself, amuse oneself; engage in active exercise; frolic; engage in children's play; make sport of, mock; perform music," from Proto-West Germanic *plegōjanan "occupy oneself about" (source also of Old Saxon plegan "vouch for, take charge of," Old Frisian plega "tend to," Middle Dutch pleyen "to rejoice, be glad," German pflegen "take care of, cultivate"), which is apparently connected to the root of plight (v.), but the ultimate etymology is uncertain and the phonetic development is difficult to explain.

Meaning "to take part in" a martial or athletic game is from c. 1200. It has been opposed to work (v.) since late 14c. Meaning "perform or act on the stage" (transitive) is by late 14c., as are the senses of "take the role of" and "make a pretense of, make believe" and "act thoughtlessly or wantonly." Sense of "put forward, move, throw, lay on the table, etc." in the course of a game or contest is by 1560s of chess pieces, 1670s of playing cards. Sense of "operate or cause to operate with continuous or repeated action" is from 1590s. Meaning "to cause (a recording) to reproduce what is on it" is by 1903, probably from the "make music" sense. Related: Played; playing.

Many expressions are from the stage, sports and games, or music, and it is not always easy to say which is from which. To play up "emphasize" is from 1909 (perhaps originally "play music more vigorously"); to play down "minimize" is from 1930; to play along "pretend to agree or cooperate" is from 1929. To play fair "be nice" is from mid-15c. To play house as a children's activity is from 1958.

To play for keeps is from 1861, originally of marbles or other children's games with tokens. To play (something) safe is from 1911; to play favorites is attested from 1902.  To play second fiddle in the figurative sense is from 1809 ("Gil Blas"). To play into the hands (of someone) "act in such a way as to give the advantage to one's opponent or a third party" is from 1705. For play the _______ card see card (n.1). For play the field see field (n.). To play with oneself "masturbate" is from 1896 (to play with "have sexual intercourse with" is from mid-13c.). Playing-card "one of a pack of cards used for playing games" is from 1540s.