If Russia were so inclined (I don't think they are and don't see why they would be) they could turn the Island of Taiwan into a pile of gravel on the floor of the China Sea. They have several thousand nuclear warheads with the means to deliver them; more than enough to overwhelm any extant ABM system.

For that reason if for no other, I think an American conflict with China is more likely than a conflict with Russia. China still has hundreds of nukes too, which is hundreds too many, but that's many times less than what Russia has.

To be clear, a direct war between any three of these countries would be a stupid, horrible idea.