AlphaGo vs Fan Hui
How did AlphaGo do it?
While it is easy to imagine AlphaGo being able to master some local moves (called "small" moves in Go), there are mysterious "large" moves, often very far from the current fights on the board. Especially in the beginning, smaller fights break out in the corners, since you can secure territory in corners more easily; you only need two sides of a rectangle to secure a corner. Then fighting moves towards edges, which can be secured with three sides of a rectangle. It is uncommon and difficult to win by attacking the center, as you need to secure all four sides from your attacker.
The goal in Go is simple, try to link your stones to surround and secure the most territory. I used to play and study Go. I've read several books on common patterns (called "joseki") and graded Go problems. I played a dozen games a week for years and was undefeated in rural, farmland PA. Once I got to graduate school, I played against a Chinese graduate student in my lab, and never won a game against him, even with free stones as a handicap. He was a good, amateur-level Go player in China. He knew how to do big moves.
We'd start by putting some stones near corners, then we'd start duking it out in a particular corner. We were fairly even here. I had studied, and if you can look ahead a few moves you'll do OK. In Go this is called "reading". We would be settling in to a slow exchange of small moves, when, all of the sudden, he would place a stone on the opposite side of the board. I knew that was a big move, but it was completely inscrutable. Many, dozens of moves later, we'd be fighting somewhere else, and that one isolated stone would be in perfect position to destroy my attack! This happened over and over again, game after game. It was not an accident.
Clearly, Go players don't play big moves with an understanding of how the board will look, 100 moves later. Instead, they study how smaller patterns, standard joseki, interact with each other, sometimes clear across the board. This takes years of study in dedicated Go schools, where nothing else is taught. Most great players start early as children.
It should be clear by now, that just looking ten or twenty moves won't work in Go. Those computations would overwhelm all the computers on earth, and still not get you the big moves. For small moves, however, you have to have some capability to "read" the board. AlphaGo combines (monte-carlo) tree-searching for small moves with a neural network for big moves. Actually, there are lots of sub-systems in AlphaGo, but those are the main two. The neural network takes many, many games as input, and then "learns" how to predict human moves, especially big moves. The neural network needs a ton of data, more than all games played in history. Once it had exhausted all games in history, then it had to generate over one million games per day, playing itself! So there was a phase where AlphaGo was training itself with human games, supplementing this training with self-played games, leading up to the match with Fan Hui. This worked well, so they added more layers of processing, more computers, and then they let that new system play itself for months. This was the vastly stronger AlphaGo that Lee Sedol encountered. It's a total beast.