Perhaps I should resist the play on words, but odd really is odd. At school, I was never able to get a good explanation why half of all numbers were said to be odd. What was strange about 3 or 255 or 1729?
Even is easier to explain. It’s from Old English efen, derived from a Germanic source, but nobody has yet been able to say for sure whether it originally meant “level” or “equal, like”. The Old English word, however, definitely meant a flat piece of ground, hence level or smooth. It began to be applied to numbers in the late 1500s with the idea that an even one could be divided into two equal parts, figuratively on a level with each other. We know this because even had been applied rather earlier in the century to accounts that were in balance or square.
Odd began life in the various Scandinavian languages. In Old Norse an oddr was a spear point, while in Old Icelandic oddi meant a point or tongue of land, a word that still appears in one or two ancient English place names. The figurative idea common to both was a point, hence a triangle and from that the number three. In Old Icelandic an oddamaðr was the third man, who had a casting vote; English obtained odd man out from it. From all this came the idea of numbers with an unpaired unit, originally the number three, that left a remainder of one after dividing by two. Odd also came to refer to an indefinite or unknown remainder above a round number such as ten, a dozen or 100, giving us phrases like “her 50-odd years” and “the book has 300-odd pages” as well as odds and ends for miscellaneous remnants, stuff left over. It can also be a single item left over, as when we say that a game was won by the odd goal.
The plural odds came to mean unequal things and then an abstract noun for inequality or difference, as in it makes no odds. Two contending parties may be said to be at odds with each other. The difference might be the extent to which one has superior capability or strength, which led to the probability that some contest or game would have a particular result, and from there to odds in the gambling sense. It turns up in other places, too, such as odds-on for something likely to happen.
Our common modern sense of an odd person being peculiar or strange is a development of the old idea of odd man out that began to be recorded in the late sixteenth century. Though he didn’t invent it, Shakespeare is an early user in Love’s Labour’s Lost in 1598: “He is too picked, too spruce, too affected, too odd as it were.”