Back in the 1940s, vodka was a very unpopular spirit in the US, and it was apparently joked that Russian vodka was too terrible. However, this did not scare John Martin, who bought the American rights to the Smirnoff brand in 1939. However, he soon found out that it was impossible to sell it, because no one drank vodka.
One gloomy evening, John Martin sat in the bar “Cock 'n' Bull” in Los Angeles and lamented to the bar owner, Jack Morgan, about his inability to sell the vodka. The bar owner had the same problem, but only with ginger beer, and funnily enough, a whole 3rd businessman had a problem getting rid of copper mugs.
After a few drinks and some ingenuity, they came up with the Moscow Mule — a vodka and ginger beer cocktail served in a copper mug. The cocktail was marketed all they could and people embraced it. Suddenly, vodka had become accepted on the American cocktail scene.
The name of the cocktail is chosen purely at random. Moscow is probably chosen because of the association between vodka and Russia, but why mules are included is not known. Some claim it's added because the ginger beer gives a kick of flavor.
In the 8th century, the Poles invented a spirit called vodka, and the reason why vodka is usually associated with Russia is because, after the invention, the Russians had the greatest influence on the product that we associate with vodka today.
Vodka had better opportunities to develop into the crystal clear liquid that we know in Russia, as there was the possibility to freeze the liquid and then collect the alcoholic liquid. You freeze to pure alcohol instead of heating, distillation also first came to Russia in the middle of the 15th century. It was also during this time that vodka was produced and consumed for its medicinal benefits, which is why it was named "Zhiznennia Voda" (water of life). In the 18th century it came to be called "vodka" (little water).
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