Unstable great power groupings, how dangerous.

As we now live in a tri-polar world, USA, The Russian Commonwealth, and the People's Republic of China, how likely is the chance of a major, possibly nuclear war.
The history of WWI could be defined as an unstable system, Russia plus Great Britain and France against the Central Powers who were really Germany. Three powers, =WWI.
For WWII; USSR, Great Britain and the USA versus the Third Reich and Friends (like Japan, Hungary, and Roumania)?

I think a world war is very unlikely, but can well imagine we'll see a terror incident or a contained use in confrontation (e.g. North Korea). It's much more difficult to imagine that Nagasaki will have been the last time ever.

I hesitate to say it, but I can imagine world leaders becoming cynical enough to discreetly encourage a localized nuclear war, in order to reap the climate-calming effects. Nothing too dire; just a flare-up between India and Pakistan, or maybe North Korea could be encouraged to provoke its own destruction.

The effect on the balance of power in Asia would probably occupy more of their thought than the deaths of millions, the suffering of millions more (including future generations), or the devastation of the environment with famine likely to follow.

I hope I'm being ridiculous.

Well, I do not like the argument that"Since it's going to happen anyway, I might as well do it."
Remember that to many in the Vienna and Berlin, in August 1914, it seemed likely that a swift and judicious use of the Austrian Army would bring those upstart Serbs to heel, without involving Russia or France, which in turn would lead to a serious crisis. But the dirt in the system of the Austrian army meant that they could not be swiftly used....So the Genie came out of the bottle.

The world would be happy if Nagasaki was the last use of Nuclear weapons....very, very happy. Ask Rick Perry (Rick Perry?), how many megatons it would take to clear the planet of all intelligent life. The radiation of a major exchange would kill billions, and drive the survivors underground to a slow death from cancer and starvation.
The nightmare scenario is that Putin put DuDonald in office so that the USA would launch a nuclear strike on N. Korea... And no-one else would use their nukes after the public service act...
But I said nightmare.

No major war has been fought in the last 200+ years when there weren't competing military alliances - a situation that easily leads to war by accident. In this world we only really have NATO and it's junior equivalents like ANZUS. The Warsaw Pact obviously no longer exists. Russia has a couple of satellite states that really add nothing to its military capability, and China doesn't even have those (I don't think North Korea would count as a satellite, it's too erratic).