guess (v.) Look up guess at Dictionary.com
c. 1300, gessen "to estimate, appraise," originally "take aim," probably from Scandinavian (compare Middle Danish gitse, getze "to guess," Old Norse geta "guess, get"), possibly influenced by Middle Dutch gessen, Middle Low German gissen "to guess," all from Proto-Germanic *getiskanan "to get" (see get). Sense evolution is from "get," to "take aim at," to "to estimate." Meaning "to hit upon the right answer" is from 1540s. Spelling with gu- is late 16c., sometimes attributed to Caxton and his early experience as a printer in Bruges. Related: Guessed; guessing. Guessing game attested from 1650s.
[T]he legitimate, English sense of this word is to conjecture; but with us, and especially in New England, it is constantly used in common conversation instead of to believe, to suppose, to think, to imagine, to fancy. [Bartlett, "Dictionary of Americanisms," 1848]
guess (n.) Look up guess at Dictionary.com
c. 1300, from guess (v.). Verbal shrug phrase your guess is as good as mine attested from 1902.