I agree that Stockfish should probably have access to opening books at least and maybe some better hardware. I also think, based on the limited information, that it is likely that the AZ evaluation process gained by training its neural network, are a match for Stockfish, at the very least.
Though, it is also possible the more it plays Stockfish, the better it will get against the engine and might show weaknesses in the the Stockfish evaluation and pruning functions. That is, it should be able to learn from the games against Stockfish and play a little better.
Interestingly, everyone is debating on hardware issues. Obviously, alpha-zero is an advanced system and require a complex system to work. In my understanding, instead of looking at hardware, we should look at how many moves they are evaluating per minute.
Alpha-zero 80k moves per second
Stockfish 70 million moves per second
Stockfish is evaluating a higher number of moves than alpha-zero and has a great advantage over alpha-zero. Still, alpha-zero evaluates the position better and predicts a better move than stockfish. In four hours, alpha-zero has created better position evaluation criteria than human-knowledge-based position evaluation criteria in stockfish.
What do you think about this?