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Keno originated way back in the mists of time where fact and fantasy tend to blur, but here's how the generally accepted story goes.
The game is originally Chinese, although its name is French (we'll get to that part in a moment). The concept of what eventually became modern keno owes its origins to one Chéung Léung a couple of thousand years ago, early in the Han Dynasty. Finding himself hard up for cash after a prolonged period spent defending his besieged city from marauders, Chéung needed a means to provision his army. But he'd already taxed his people to the limit through the normal channels. So in order to raise the cash, he came up with the idea of a lottery, whereby the good citizens of his town would be encouraged to risk their property for a chance of greater financial rewards, via a game of chance. The idea proved so successful that it was later used to finance all kinds of projects, including the Great Wall of China, imperial palaces, and overseas exploration.
Instead of numbers, the original game used characters from the "Thousand Character Classic," a famous poem that was used as an aid for teaching children and contained each different character only once. As the game spread far and wide, carrier pigeons were used to communicate the winning results to remote locations. Hence, it became known as the "Game of the White Dove."
Having become popular throughout China, the game was then spread all over the world by Chinese immigrants. In the 1800s it was brought to the U.S. by workers imported to help build the railroads, and at first was known as the "Chinese lottery." When numbers were substituted for the original Chinese characters, the popularity spread to the non-Chinese population, in particular the gambling halls of New Orleans. That's where the French connection comes in, with the name "keno" evolving from the French "quine," meaning a set of five winning numbers.
When gambling was legalized in Nevada in 1931, the new law didn't apply to lotteries, which remained illegal. So the game's name was changed to "racehorse keno," a subterfuge by which the numbers players were betting on supposedly represented horses (individual rounds of keno are still sometimes colloquially referred to as "races.") Then the government decided to tax off-track betting, so the name changed yet again, this time simply to keno.
