This is one hundred percent hypothetical, so bear with me[url=http://lh6.ggpht.com/__zoKJ77EvEc/TJJU_wxYXPI/AAAAAAAAHhM/Fdy3Kc9RNWs/bear-yoga%20(1)%5B2%5D.jpg?imgmax=800].[/url]
Let's pretend that for whatever reason, each country simultaneously declares war on each other the second you read this. Each country's eventual goal is to eliminate the other, or to absorb the other country into their own empire.
[b]What would happen first? Who would each country ally with? Who would win in the end?[/b]
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US should easily win because of superior technology. The only way it could get close is if China could get a strong foothold on American soil, and the US would focus too much on minimizing collateral damage.