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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The United States has a little over 300,000,000 citizens. That's the same number as Chinas entire draftable population. They also have the second largest military budget. However ours is twice theirs. Our tech and training is better too, but their numbers are massive... Assuming they could train and arm most of their draftable population it would be close.