Its just a giant flexing game. Neither the US or Russia will get into an armed conflict based solely on common allies(China). America doesnt have the will to fight an actual standing army, and Russia is far from being equipped enough to face a stand up fight and protect its borders. Although China and Russia are allies, I wouldnt be surprised if China would use any opportunity to do a land grab for its self since there have been several land disputes between China and Russia. Besides its fairly safe to say no first world country would use nuclear weapons(bounceback damage). Perhaps in the case of a complete loss of state but highly unlikely to see any 1st world country invading another. Nuclear weapons are more of a rogue nation and or madman's weapon of preferred choice.