The story on how Putin likely came to power is bone chilling.

Basically he was minister of war under Yeltsin, who was facing corruption scandals. An election for president was coming up. Putin was polling at 2 percent. A series of bombings in apt buildings was killing Russian civilians, hundreds. Putin said it was Chechen rebels and went to war. Six months later he was president, absolved Yeltsin.

The evidence is very very strong that it was Putin and the secret police who did the bombings, not the Chechens, as a pretext for war. That you can read about in depth, lots of investigative journaling on that.

Based on that, odds of a nuclear war are probably more like 1:50.