Etymology
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pool (n.1)

"small body of standing water," Old English pol "small body of water; deep, still place in a stream," from Proto-West Germanic *pōl- (source also of Old Frisian and Middle Low German pol, Dutch poel, Old High German pfuol, German Pfuhl "pool, puddle"), which is of uncertain origin, perhaps a substratum word [Boutkan]. As a short form of swimming pool it is recorded from 1901. Pool party "party at a swimming pool" is by 1965.

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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.

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pool (v.2)

"to make a common interest or fund, put things into one common fund or stock for the purpose of dividing or redistribution in certain proportions," 1871, from pool (n.2). Related: Pooled; pooling.

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pool (v.1)

of liquid, "to form a pool or pools," 1620s, from pool (n.1). Earlier, of land, "to be full of pools" (polen, mid-15c.). Related: Pooled; pooling.

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pool-ball (n.)

"ivory ball used in the game of pool," by 1871, from pool (n.2) + ball (n.1).

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pool-hall 

"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.

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car-pool (n.)
also carpool, "the sharing of a car ride by more than one person going to the same destination," 1942, American English, from car + pool (n.2). As a verb from 1962. Related: Carpooled; carpooling.
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whirlpool (n.)
1520s, from whirl (v.) + pool (n.1). Old English had hwyrfepol and wirfelmere.
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Liverpool 
English city on the River Mersey, c.1190, Liuerpul "Pool with Muddy Water," from Old English lifer "thick, clotted water" + pol (see pool (n.1)). "The original reference was to a pool or tidal creek now filled up into which two streams drained" [Victor Watts, "Cambridge Dictionary of English Place-Names," 2004]. The adjective and noun Liverpudlian (with jocular substitution of puddle for pool) is attested from 1833.
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*pau- (1)

Proto-Indo-European root meaning "few, little."

It forms all or part of: catchpoll; encyclopedia; filly; foal; few; hypnopedia; impoverish; orthopedic; Paedophryne; paraffin; parvi-; parvovirus; paucity; Paul; pauper; pedagogue; pederasty; pedo-; pedophilia; poco; poltroon; pony; pool (n.2) "game similar to billiards;" poor; poulterer; poultry; poverty; puericulture; puerile; puerility; puerperal; pullet; pullulate; Punch; Punchinello; pupa; pupil (n.1) "student;" pupil (n.2) "center of the eye;" puppet; pusillanimous; putti.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit potah "a young animal," putrah "son;" Avestan puthra- "son, child;" Greek pauros "few, little," pais (genitive paidos) "child," pōlos "foal;" Latin paucus "few, little," paullus "little," parvus "little, small," pauper "poor," puer "child, boy," pullus "young animal;" Oscan puklu "child;" Old English feawe "not many, a small number," fola "young horse;" Old Norse fylja "young female horse;" Old Church Slavonic puta "bird;" Lithuanian putytis "young animal, young bird;" Albanian pele "mare."

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