I think you are quite naive in your assumption and calculation.
When there is a nuclear exchange, its not as simple as "I fire x number of missiles, so I deduct the number I fired and I still have the rest to play with". That's your first erroneous assumption. In a nuclear exchange between Russia and China, both side practically has to throw everything they have at each other, because :
1. China has, and is developing/advancing its ABM systems. With ABM, it is a great equalizer - it means even when Russian have more nuclear warheads/launchers/missiles, it will have to use "mass swarming" to overcome the ABM system to ensure destruction of the other side. Firing one or two at a target the old way is not going to work, because it makes it easy to intercept as ABM advances. Both side will have to throw as many nukes at the target as possible in hope of overcoming the ABM.
2. In a nuclear exchange, its not just firing the missile and "we are all fine and dandy", the incoming missiles will also destroy your silos/missiles/places where you can launch, so, that reduce the number even further.
So it is very costly for Russian to attack China with nukes, it will leave Russia hugely weaken if not make Russian spent almost its entire nuclear arsenals just to ensure it can win the war.
Now, a bit of historical perspective - Just after the cold war ended, the Russians expected huge help from American, but instead, they were given the cold shoulder intentionally, as American sees no reason to help Russian in anyway except in arms reduction treaties to "de-fang" the Russians further while watching Russian's arm industries collapse. It is clear that American wants its strongest rival to weaken and collapse so its easy picking for later. The Russians calls the 90s the "lost decade" and it gave them a new perspective on the world - that American were never meant anything good for Russian. That's the reason why Putin become so wildly popular in Russia even today, even of an idol status.
That brings us to my third point :
3. In the future IF (BIG IF) this conflict is to occur, its is likely the world is running almost out of resources (and we already are). With Russian hugely weaken (if not devoid almost of no nuclear weapon as it spent it all to overcome ABM) it set itself up as a prime lamb to be slaughter. Russia is rich with resources, and America is already fast running out of resources and still hungry for more everyday (average american energy usage is still increasing steadily). Russian are not stupid. It will be stupid to think America will pass the the chance to get rid of its old prime rival who ALSO HAPPEN TO HAVE THE MOST NATURAL RESOURCES ON EARTH, with low population count (and hence military/army to fight with - especially after nuclear war). Like I said, its fat lamb ready to be strip and slaughter. America will not pass up this chance.
Also, to Martian, the reason why Russia/China/USA don't want war with each other, is because its most likely to benefit the side that sits it out. The winner of the duel will be FAR TOO WEAK TO FEND OFF AN ATTACK FROM BYSTANDER. History has shown that when super powers goes into war and weakens each other, it only benefits the bystanders.
