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In chess, AlphaZero first outperformed Stockfish after just 4 hours in shogi, AlphaZero first outperformed Elmo after 2 hours and in Go, AlphaZero first outperformed the version of AlphaGo that beat the legendary player Lee Sedol in 2016 after 30 hours. Note: each training step represents 4,096 board positions.

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To learn each game, an untrained neural network plays millions of games against itself via a process of trial and error called reinforcement learning. At first, it plays completely randomly, but over time the system learns from wins, losses, and draws to adjust the parameters of the neural network, making it more likely to choose advantageous moves in the future. The amount of training the network needs depends on the style and complexity of the game, taking approximately 9 hours for chess, 12 hours for shogi, and 13 days for Go. Some of its moves, such as moving the King to the centre of the board, go against shogi theory and - from a human perspective - seem to put AlphaZero in a perilous position. Yoshiharu Habu, 9-Dan professional, only player in history to hold all seven major shogi titles Its unique playing style shows us that there are new possibilities for the game.īut incredibly it remains in control of the board. The trained network is used to guide a search algorithm – known as Monte-Carlo Tree Search (MCTS) – to select the most promising moves in games.

For each move, AlphaZero searches only a small fraction of the positions considered by traditional chess engines. In Chess, for example, it searches only 60 thousand positions per second in chess, compared to roughly 60 million for Stockfish.

The fully trained systems were tested against the strongest hand-crafted engines for chess ( Stockfish) and shogi ( Elmo), along with our previous self-taught system AlphaGo Zero, the strongest Go player known.

Each program ran on the hardware for which they were designed.

Stockfish and Elmo used 44 CPU cores (as in the TCEC world championship), whereas AlphaZero and AlphaGo Zero used a single machine with 4 first-generation TPUs and 44 CPU cores.

A first generation TPU is roughly similar in inference speed to commodity hardware such as an NVIDIA Titan V GPU, although the architectures are not directly comparable.

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All matches were played using time controls of three hours per game, plus an additional 15 seconds for each move.

In each evaluation, AlphaZero convincingly beat its opponent:.

In chess, AlphaZero defeated the 2016 TCEC (Season 9) world champion Stockfish, winning 155 games and losing just six games out of 1,000.

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To verify the robustness of AlphaZero, we also played a series of matches that started from common human openings. In each opening, AlphaZero defeated Stockfish.

We also played a match that started from the set of opening positions used in the 2016 TCEC world championship, along with a series of additional matches against the most recent development version of Stockfish, and a variant of Stockfish that uses a strong opening book.

In shogi, AlphaZero defeated the 2017 CSA world champion version of Elmo, winning 91.2% of games.