So I guess the ultimate proof that you're obsessed with a game is when you make a mod for it. I made one for Europa Universalis III over the last few days.
Drew Davidson is to blame; he's putting together a book titled Well Played (by analogy to "well read"), in which he's asked a bunch of people to write about particular games; I chose EU, and in preparing to write my chapter, got re-addicted.
For those of you who don't know, Europa Universalis is a vast grand-strategic game spanning the entire globe from the fall of Constantinople (1453) to the French Revolution (1797). Every country in the game is playable -- yes, even the Cree and the Congolese, although you likely won't get far playing them. Rich, deep, highly complicated, a true history buff's game, but definitely not for those who think no game should require a manual.
My mod adds three playable countries: Vinland, Roma Nova, and Fusang.
The Vinland colony established by Leif Eriksson is an historical reality, albeit a short-lived one. The mod assumes that a permanent colony survived, centered on Newfoundland, but lost contact with Europe through the start of EU III.
Most people who theorize pre-Columbian contact generally try to get explorers to North America. Actually, it would be far easier to get them to South America. Getting to North America from Europe means sailing against prevailing currents; getting from Gibraltar to the north coast of Brazil means sailing with the currents, and a shorter distance. Getting back to Europe would, of course, be much more difficult. The treasure hunter Robert Marx claims (controversially) to have discovered a Roman wreck off the coast of Rio de Janeiro. We posit that a large Roman fleet was blown off course by a storm some time in the 2nd century A.D., made landfall along Brazil's northern coast, and established a sustainable colony. This became the country of Roma Nova -- Latin in civilization, speaking a tongue that has no doubt drifted from classical Latin but is nonetheless Romance, and Catholic, more or less, in religion.
The 7th century Book of Liang, by Yao Silian, claims that in 499 A.D., the Buddhist monk Hui Shen sailed "20,000 li" east of China and visited the country of Fusang. "Li" is a measure with multiple meanings, the usual interpretation equates Fusang with Japan. However, "20,000 li" could mean as much as 10,000 miles, not a bad measure of the distance between China and the west coast of North America.
The idea of Chinese colonization of North America in the 6th century is absurd, but it is reasonable to think they might have named a later such colony "Fusang."
Between 1405 and 1433, fleets under the command of the Chinese admiral Zhen He sailed throughout the Indian ocean, visiting the spice islands, India, Ceylon, the east coast of Africa, and part of the Arabian peninsula. That much is well established. The records of the last two of Zhen He's seven expeditions were destroyed by the Ming Emperor, however, and where he went on those expeditions is uncertain. In his book 1421: THE YEAR CHINA DISCOVERED THE WORLD, Gavin Menzies, somewhat ludicrously, claims that Zhen He discovered both North and South America (as well as, well, just about everything else on the planet, including Antarctica and Iceland).
The mod makes the fairly absurd, but to my mind entertaining, assumption that a self-sufficient colony was established by Zhen He in California, centered on San Francisco Bay (the West Coast's finest harbor), but that with Ming China's gradual loss of interest in contact with the outer world, and the consequent decline in what had under Zhen He been the world's largest and most advanced navy, contact with the Chinese colony in "Fusang" was lost. The colony survived and, in the pioneer conditions of the New World, quickly came to think of itself as a new nation.