The main reason AlphaGo Zero learns so much faster than its predecessors is because it uses temporal-difference learning.[1] This effectively removes a huge amount of the value network's state space for the learning algorithm to search through, since it bakes in the assumption that a move's value ought to equal that of the best available move in the following board position, which is exactly what you'd expect for a g…
(Eg AlphaGo using two different networks for policy and valuation was a big breakthrough back when it was young, because people couldn't make the single network one work so well.)
For temporal difference learning the article about TD-Gammon, a backgammon AI from the early 90s, is great: http://www.bkgm.com/articles/tesauro/tdl.html (It's linked from the Wikipedia article you referenced, too.)