"establishment outfitted for playing pool, billiards, etc.," by 1883, from pool (n.2) + hall (n.). Pool-room in the billiards sense is attested by 1851.
Entries linking to pool-hall
pool n.2
game similar to billiards, 1848, originally (1690s) the name of a card game played for collective stakes, from pool "collective stakes of players in a game," which is from French poule "stakes, booty, plunder," literally "hen," from Old French poille "hen, young fowl," from Vulgar Latin *pulla, fem. of Latin pullus "young animal," especially "young fowl," from PIE root *pau- (1) "few, little."
Perhaps the original notion is from jeu de la poule, supposedly a game in which people threw things at a chicken and the player who hit it, won it, which speaks volumes about life in the Middle Ages. The notion behind the word, then, is "playing for money." The connection of "hen" and "stakes" is also present in Spanish polla and Walloon paie.
By 1868 it came to mean "combination of a number of persons, each staking a sum of money on the success of a horse in a race, a contest in a game, etc., the money to be divided among the successful bettors," thus also "collective stakes" in betting. The sense of "common reservoir of resources" is from 1917. Meaning "group of persons who share duties or skills" (typist pool, etc.) is from 1928. From 1933 as short for football pool in wagering.
Pool shark is from 1898. The phrase dirty pool "underhanded or unsportsmanlike conduct," especially in politics (1951), seems to belong here now, but the phrase dirty pool of politics, with an image of pool (n.1) is recorded from 1871 and was in use early 20c.
hall n.
Old English heall "spacious roofed residence, house; temple; law-court," any large place covered by a roof, from Proto-Germanic *hallo "covered place, hall" (source also of Old Saxon, Old High German halla, German halle, Dutch hal, Old Norse höll "hall;" Old English hell, Gothic halja "hell"), from PIE root *kel- (1) "to cover, conceal, save."
Sense of "passageway in a building" evolved 17c., from the time when the doors to private rooms opened onto the large public room of the house. Older sense preserved in town hall, music hall, etc., in use of the word in Britain and Southern U.S. for "manor house," also "main building of a college" (late 14c.). French halle, Italian alla are from Middle High German. Hall of fame attested by 1786 as an abstract concept; in sporting sense first attested 1901, in reference to Columbia College; the Baseball Hall of Fame opened in 1939. Related: Hall-of-famer.