You will never defeat australia due to our resources. If america attacked, china and/or russia would back us due to ore and food resources that they require. If china attacked, america would need to back us for continual access to our resources. No matter who attacks, the enemy of our enemy becomes our friend and prevents defeat. Checkm8
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Easy solution for America, provide food/ resources to Russia/ control Australia's waters so china would have to go thru America for access to Australian shipping lanes. Checkm8 emus
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Thats the thing. Russia and china have large investments in australian resources. China legit owns 1/10 or so of our farms and russia, around 1/12. Canada and UK own about 1/8 each. With all this money and dependence tied up in our land, the respective countries would be stupid not to defend their considerable investments. America would never be able to control Australian waters due to their size and location. China pretty much owns the south china sea, which is positioned to control all of northern australia. You would not beat china in a race to the west or southern coast. Your only chance at securing our waters would be across the south east coast, of which owning does not constitute a strong region from which to invade the rest of australia as well as control resources. Darwin, port headland and cairns tie us to china thoroughly enough and in such a way that america cannot bar.
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China wouldn't interfere because they have way more invested in The U.S. Drones can secure the waters around Australia so we would only need a few aircraft carriers and maybe a few other ships for support. it wouldn't be a race because a large chunk of our fleet is already located there due to North Korea. And we could turn around after decimating the Australian population and sell the continent to the Chinese and pay off our debt. we wouldn't even need to deploy troops just massive carpet bombing of all the crops and resources and just squeeze off all the shipping lanes till the Australians are starving and demoralized and give up. We could keep Russia out by just allowing them to build army bases in the EU in places they want to control.
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You cannot starve australia by isolation because we produce more than enough to feed ourselves, hence foreign investment and interest. China will definitely intervene and you will reach a similar outcome to both vietnam and korea: china/russia back us with money, arms, technology and even people so that their enemy, or threats, do not gain access to their backyard. Australia is the hub of southeast asia which china cannot stand to lose to america. You would never be able to achieve your stated russia scenario, where you allow them to build shit in europe. That would destroy all european alliances with america. Europe similarly has a lot of investments in australia and would turn to aiding us in that event. Due to our location, resources and allies, it is not possible for america to defeat us. [spoiler]also, your idea of carpet bombing the sixth largest country in the world to oblivion is not only impossible, but of no gain to america. Assume you manage to pull it off, you have just sent the country back to the stone age and lost all productive infrastructure such that you gain absolutely nothing from wasting a large amount of time and money to level the place. [/spoiler]