Some background from over in the chess engine community.
The big press announcements about AlphaZero and Stockfish were against Stockfish 8 with terrible settings. However, even cranking up the most recent version of Stockfish (v11 any day now) on great hardware (say 43 core just to be concrete), AlphaZero and Stockfish are more or less even. It is really hard to pin down which is better because either can always make use of better hardware, though in my opinion it currently looks like Stockfish scales better with better hardware. That is Stockfish on 128 core is a lot better than the same Stockfish on 64 core.
It is a "problem" that we don't really have AlphaZero to play with and do comparisons, since Deepmind Does not release a version for us to use.
There are a couple of open source community projects to repeat the Deepmind/AlphaZero approach in the public eye. The most notable is LeelaChessZero. A lot of indirect evidence suggests that Leela (for short) is very much comparable to AlphaZero in strength. Leela on very good hardware is more or less equal to Stockfish on very good hardware, thoush as mentioned above, Stockfish seems to benefit more from even better hardware at the moment.
Chess engines on computers have been much better than the human world champions for 20 years now, or more. Your phone is better than Magnus Carlsen. A human would be considered lucky to get even a draw once in a great while.
It is often said that AlphaZero learned to play chess in only 4 hours of self play. This is true, but sort of bogus. It was four hours on 5000 super strong computers. If it had only been one computer, it would have been 20,000 hours. By comparison, Leela takes months to teach itself chess, but that is because the Leela team only has a few hundred computers to train on, some of which are quite slow.
Last factoid: One of the things that makes it hard to compare Stockfish and its kin (Houdini, Komodo, and others) with AlphaZero, Leela and their kin is that they use different types of computer hardware. Stockfish runs fine on an ordinary CPU core, the more the better. AlphaZero and Leela can run on ordinary cores, but on ordinary cores, even a lot of them, are not very strong. To be strong they need high end vector co-processors. GPUs contain vector processing subunits (alongside all the graphics stuff, like skeletons and physics and muzzle blasts and smoke). This is why AlphaZero and Leela require good GPUs but do't really need more than a few CPU core.
Enough for now. Agree or die.