The key part of Alphago is a convolutional neural network. These are usually used for recognizing cat pictures and other visual tasks, and progress in the last five years has been incredible.
Alphago went from the level of a novice pro last October to world champion level for this match. It did so by playing itself over and over again.
Chess programs are well understood because they are programmed by humans. Alphago is uses an algorithm to pick a winning move in a given go position. But the heart of the program is a learning program to find that algorithm, not the algorithm itself.
Go programs made steady progress for a decade with improved tree pruning methods, which reduce the total number of positions the program has to evaluate. The cleverest method is Monte Carlo pruning, which simply prunes at random.
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