Etymology
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draw (n.)

c. 1400, "act of pulling," from draw (v.). Meaning "game or contest that ends without a winner," is attested first in drawn match (1610s), but the signification is uncertain origin; some speculate it is from withdraw. Hence, as a verb, "to leave (a game, etc.) undecided," from 1837.

Colloquial sense of "anything that can draw a crowd" is from 1881 (from the verb in the related sense). 

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draw (v.)

"give motion to by the act of pulling," c. 1200, drauen, spelling alteration of Old English dragan "to drag, to draw, protract" (class VI strong verb; past tense drog, past participle dragen), from Proto-Germanic *draganan "to draw, pull" (source also of Old Norse draga "to draw, drag, pull," Old Saxon dragan "to carry," Old Frisian drega, draga, Middle Dutch draghen "to carry, bring, throw," Old High German tragan "carry, bring, lead," German tragen "to carry, bear"), from PIE root *dhregh- (see drag (v.)).

Sense of "make a line or figure" (by "drawing" a pencil across paper) is from c. 1200. Meaning "remove or extract (a weapon) by pulling" is from late 12c., originally of a sword. Sense of "to pull (a bowstring)" is from c. 1200. To draw a criminal (drag him at the tail of a horse to the place of execution) is from c. 1300.

Meaning "select one (from a number of lots, etc.)" is from c. 1300. Sense of "bring (a crowd, an audience, etc.) by inducement or attraction" is from 1580s. Of a ship or boat, "to displace (a specified amount) of water," 1550s. In card-playing, "to take or receive (a card)," by 1772; draw-poker is by 1850. To draw out "lengthen, protract" is from 1550s; to draw the line in the figurative sense of "make a limit" is by 1793. To draw blood is from c. 1400.

The difference between [Draw Poker] and Poker is, that the player can draw from the pack as many cards as he may wish,—not exceeding five,—which must be given him by the dealer; but previous to drawing he must take from his original hand the game number as he may wish to draw, and lay them in the centre of the table. ["Bohn's New Hand-Book of Games," Philadelphia, 1850]
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away (adv.)

Middle English awei, from late Old English aweg, earlier on weg "on from this (that) place;" see a- (1) + way (n.).

The meaning "from one's own or accustomed place" is from c. 1300; that of "from one state or condition to another" is from mid-14c.; that of "from one's possession (give away, throw away) is from c. 1400. Colloquial use for "without delay" (fire away, also right away) is from the earlier sense of "onward in time" (16c.). The meaning "at such a distance" (a mile away) is by 1712. Intensive use (as in away back) is American English, attested by 1818. Of sporting events played at the other team's field or court, by 1893.

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lay-away (n.)

also lay-away, 1961 in reference to a system of payments for reserved merchandise, from the verbal phrase (attested from c. 1400 as "to put away," especially "place in store for future use"); see lay (v.) + away (adv.). Earlier in the same sense, as an adjective, was Australian lay-by (1930).

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draw-string (n.)

string, cord, lace, or rope used to "draw" (gather, or shorten) fabric or other material by 1831, from draw (v.) + string (n.). Also draw-cord (1840); drawing-string (1784).

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get-away (n.)

also getaway, 1852, "an escape," originally in fox hunting, from verbal phrase get away "escape" (early 14c.); see get (v.) + away (adv.). Of prisoners or criminals from 1893.

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keep-away (n.)

as a game, 1925, from verbal phrase (attested from late 14c.); see keep (v.) + away (adv.).

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give-away (n.)

also giveaway, "act of giving away," 1872, from verbal phrase give away, c. 1400 (of brides from 1719); see give (v.) + away (adv.). The phrase in the meaning "to betray, expose, reveal" is from 1878, originally U.S. slang. Hence also Related: give-away (n.) "inadvertent betrayal or revelation" (1882).

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far-away (adj.)

also faraway, "distant, remote," 1816, from far + away.

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cut-away (adj.)

of coats, "cut back from the waist," 1841, from the verbal phrase; see cut (v.) + away. As a noun, "coat cut back from the waist," by 1849. In reference to models, drawings, etc., of which a part is cut away to reveal the interior, by 1946. The verbal phrase is from c. 1300 as "cut (something) off or away." 

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