1911 Encyclopedia Britannica
ODD (in middle English odde, from old Norwegian oddi, an angle of a triangle; the old Norwegian oddamann is used of the third man who gives a casting vote in a dispute), that which remains over after an equal division, the unit in excess of an even number; thus in numeration the word is used of a number either above or below a round number, an indefinite cardinal number, as "eighty and odd," or "eighty odd." As applied to individuals, the sense of "one left after a division" leads to that of "solitary," and thus of "uncommon" or "strange." In the plural, "odds" was originally used to denote inequalities especially in the phrase "to make odds even." The sense of a difference in benefit leads to such colloquialisms as "makes no odds," while that of variance appears in the expression "to be at odds." In betting "the odds" is the advantage given by one person to another in proportion to the supposed chances of success.
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Chisholm, Hugh, General Editor. Entry for 'Odd'. 1911 Encyclopedia Britanica. https://www.studylight.org/encyclopedias/eng/bri/o/odd.html. 1910.