AlphaZero

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GerdIsenberg GerdIsenberg Feb 10, 2018 

**[[Home]] * [[Engines]] * AlphaZero**
|| [[image:258px-Krampus_at_Perchtenlauf_Klagenfurt.jpg link="https://commons.wikimedia.org/wiki/File:Krampus_at_Perchtenlauf_Klagenfurt.jpg"]] ||~   || **AlphaZero**,
a chess and [[Go]] playing entity by [[Google]] [[DeepMind]] based on a general [[Reinforcement Learning|reinforcement learning]] algorithm with the same name. On [[https://en.wikipedia.org/wiki/December_5#Holidays_and_observances|December 5]], [[https://en.wikipedia.org/wiki/Portal:Current_events/2017_December_5|2017]], the DeepMind team around [[David Silver]], [[Thomas Hubert]], and [[Julian Schrittwieser]] along with former [[Giraffe]] author [[Matthew Lai]], reported on their generalized algorithm, combining [[Deep Learning|Deep learning]] with [[Monte-Carlo Tree Search]] (MCTS) <ref>[[David Silver]], [[Thomas Hubert]], [[Julian Schrittwieser]], [[Ioannis Antonoglou]], [[Matthew Lai]], [[Arthur Guez]], [[Marc Lanctot]], [[Laurent Sifre]], [[Dharshan Kumaran]], [[Thore Graepel]], [[Timothy Lillicrap]], [[Karen Simonyan]], [[Demis Hassabis]] (**2017**). //Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm//. [[https://arxiv.org/abs/1712.01815|arXiv:1712.01815]]</ref> .

A 100 game match versus [[Stockfish|Stockfish 8]] using 64 [[Thread|threads]] and a [[Transposition Table|transposition table]] size of 1GiB, was won by AlphaZero using a single machine with 4 [[https://en.wikipedia.org/wiki/Tensor_processing_unit|Tensor processing units]] (TPUs) with +28=72-0. Despite a possible hardware advantage of AlphaZero and criticized playing conditions <ref>[[http://www.open-chess.org/viewtopic.php?f=5&t=3153|Alpha Zero]] by [[Mark Watkins|BB+]], [[Computer Chess Forums|OpenChess Forum]], December 06, 2017</ref>, this seems a tremendous achievement. ||
|| The Krampus has come <ref>[[https://en.wikipedia.org/wiki/Krampus|Krampus]] at [[https://en.wikipedia.org/wiki/Pre-Christian_Alpine_traditions#Perchten|Perchtenlauf]] in [[https://en.wikipedia.org/wiki/Klagenfurt|Klagenfurt]], Image by [[https://www.flickr.com/people/15501382@N00|Anita Martinz]], December 02, 2006, [[https://creativecommons.org/licenses/by/2.0/deed.en|CC BY 2.0]], [[https://en.wikipedia.org/wiki/Wikimedia_Commons|Wikimedia Commons]]</ref> <ref>"5th of December - The [[https://en.wikipedia.org/wiki/Krampus|Krampus]] has come" was suggested by [[Michael Scheidl]] in [[http://forum.computerschach.de/cgi-bin/mwf/topic_show.pl?tid=9635|AlphaZero]] by Peter Martan, [[Computer Chess Forums|CSS Forum]], December 06, 2017, with further comments by [[Ingo Althöfer]]</ref> ||~   ||^   ||
[[toc]]
=Description= 
Starting from random play, and given no domain knowledge except the game rules, AlphaZero achieved a superhuman level of play in the games of chess and [[Shogi]] as well as in [[Go]]. The algorithm is a more generic version of the [[AlphaGo#Zero|AlphaGo Zero]] algorithm that was first introduced in the domain of Go <ref>[[https://deepmind.com/blog/alphago-zero-learning-scratch/|AlphaGo Zero: Learning from scratch]] by [[Demis Hassabis]] and [[David Silver]], [[DeepMind]], October 18, 2017</ref> . AlphaZero [[Evaluation|evaluates]] [[Chess Position|positions]] using non-linear function approximation based on a [[Neural Networks|deep neural network]], rather than the [[Evaluation#Linear|linear function approximation]] as used in classical chess programs. This neural network takes the board position as input and outputs a vector of move probabilities. The MCTS consists of a series of simulated games of self-play whose move selection is controlled by the neural network. The search returns a vector representing a probability distribution over moves, either proportionally or greedily with respect to the visit counts at the root state.

==Network Architecture==
The network is a [[Neural Networks#Deep|deep]] [[Neural Networks#Residual|residual]] [[Neural Networks#Convolutional|convolutional neural network]] <ref>The principle of residual nets is to add the input of the layer to the output of each layer. With this simple modification training is faster and enables deeper networks, see  [[Tristan Cazenave]] (**2017**). //[[http://ieeexplore.ieee.org/document/7875402/|Residual Networks for Computer Go]]//.  [[IEEE#TOCIAIGAMES|IEEE Transactions on Computational Intelligence and AI in Games]], Vol. PP, No. 99, [[http://www.lamsade.dauphine.fr/~cazenave/papers/resnet.pdf|pdf]]</ref> <ref>[[http://www.talkchess.com/forum/viewtopic.php?t=65923|Residual Networks for Computer Go]] by Brahim Hamadicharef, [[CCC]], December 07, 2017</ref> with many layers of spatial NxN planes - [[8x8 Board|8x8 board]] arrays for chess. The input describes the [[Chess Position|chess position]] from [[Side to move|side's to move]] point of view - that is [[Color Flipping|color flipped]] for black to move. Each square cell consists of 12 [[Pieces#PieceTypeCoding|piece-type]] and [[Color|color]] bits, e.g. from the current [[Bitboard Board-Definition|bitboard board definition]], and to address [[Graph History Interaction|graph history]] and [[Path-Dependency|path-dependency]] - times eight, that is up to seven predecessor positions as well - so that [[En passant|en passant]], immediate [[Repetitions|repetitions]], or some sense of progress is implicit. Additional inputs, redundant inside each square cell  to be conform to the convolution net, consider [[Castling rights|castling rights]], [[Halfmove Clock|halfmove clock]], total move count and side to move. 

The deep hidden layers connect the pieces on different squares to each other due to consecutive 3x3 convolutions, where a cell of a layer is connected to the correspondent 3x3 [[https://en.wikipedia.org/wiki/Receptive_field|receptive field]] of the previous layer, so that after 4 layers, each square is connected to every other cell in the original input layer <ref>[[http://www.talkchess.com/forum/viewtopic.php?t=65937&start=10|Re: AlphaZero is not like other chess programs]] by [[Rein Halbersma]], [[CCC]], December 09, 2017</ref>. The output of the neural network is finally represented as an 8x8 board array as well, for every [[Origin Square|origin square]] up to 73 [[Target Square|target square]] possibilities ([[Direction#MoveDirections|NRayDirs]] x [[Rays|MaxRayLength]] + [[Direction#KnightDirections|NKnightDirs]] + NPawnDirs * [[Promotions|NMinorPromotions]]), encoding a probability distribution over 64x73 = 4,672 possible moves, where illegal moves were masked out by setting their probabilities to zero, re-normalising the probabilities for remaining moves.

==Training==
AlphaZero was trained in 700,000 steps or mini-batches of size 4096 each, starting from randomly initialized parameters, using 5,000 [[https://en.wikipedia.org/wiki/Tensor_processing_unit#First_generation|first-generation TPUs]] <ref>[[https://www.nextplatform.com/2017/04/05/first-depth-look-googles-tpu-architecture/|First In-Depth Look at Google’s TPU Architecture]] by [[https://www.nextplatform.com/author/nicole/|Nicole Hemsoth]], [[https://www.nextplatform.com/|The Next Platform]], April 05, 2017</ref> to generate self-play games and 64 [[https://en.wikipedia.org/wiki/Tensor_processing_unit#Second_generation|second-generation TPUs]] <ref>[[http://www.talkchess.com/forum/viewtopic.php?t=65945|Photo of Google Cloud TPU cluster]] by [[Norman Schmidt]], [[CCC]], December 09, 2017</ref> <ref>[[https://www.nextplatform.com/2017/05/17/first-depth-look-googles-new-second-generation-tpu/|First In-Depth Look at Google’s New Second-Generation TPU]] by [[https://www.nextplatform.com/author/nicole/|Nicole Hemsoth]], [[https://www.nextplatform.com/|The Next Platform]], May 17, 2017</ref> <ref>[[https://www.nextplatform.com/2017/05/22/hood-googles-tpu2-machine-learning-clusters/|Under The Hood Of Google’s TPU2 Machine Learning Clusters]] by Paul Teich, [[https://www.nextplatform.com/|The Next Platform]], May 22, 2017</ref> to train the neural networks <ref>[[David Silver]], [[Thomas Hubert]], [[Julian Schrittwieser]], [[Ioannis Antonoglou]], [[Matthew Lai]], [[Arthur Guez]], [[Marc Lanctot]], [[Laurent Sifre]], [[Dharshan Kumaran]], [[Thore Graepel]], [[Timothy Lillicrap]], [[Karen Simonyan]], [[Demis Hassabis]] (**2017**). //Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm//. [[https://arxiv.org/abs/1712.01815|arXiv:1712.01815]]</ref> .

=See also= 
* [[Alpha-Beta]]
* [[Alpha I]]
* [[AlphaGo]]
* [[Neural Networks#engines|Chess Engines with Neural Networks]]
* [[Learning#Programs|Learning Chess Programs]]
* [[LCZero]]

=Publications= 
* [[David Silver]], [[Julian Schrittwieser]], [[Karen Simonyan]], [[Ioannis Antonoglou]], [[Shih-Chieh Huang|Aja Huang]], [[Arthur Guez]], [[Thomas Hubert]], [[Lucas Baker]], [[Matthew Lai]], [[Adrian Bolton]], [[Yutian Chen]], [[Timothy Lillicrap]], [[Fan Hui]], [[Laurent Sifre]], [[George van den Driessche]], [[Thore Graepel]], [[Demis Hassabis]] (**2017**). //[[https://www.nature.com/nature/journal/v550/n7676/full/nature24270.html|Mastering the game of Go without human knowledge]]//. [[https://en.wikipedia.org/wiki/Nature_%28journal%29|Nature]], Vol. 550, [[https://www.gwern.net/docs/rl/2017-silver.pdf|pdf]]
* [[David Silver]], [[Thomas Hubert]], [[Julian Schrittwieser]], [[Ioannis Antonoglou]], [[Matthew Lai]], [[Arthur Guez]], [[Marc Lanctot]], [[Laurent Sifre]], [[Dharshan Kumaran]], [[Thore Graepel]], [[Timothy Lillicrap]], [[Karen Simonyan]], [[Demis Hassabis]] (**2017**). //Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm//. [[https://arxiv.org/abs/1712.01815|arXiv:1712.01815]]

=Forum Posts= 
==2017==
* [[http://www.talkchess.com/forum/viewtopic.php?t=65909|Google's AlphaGo team has been working on chess]] by [[Peter Kappler]], [[CCC]], December 06, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=65910|Historic Milestone: AlphaZero]] by Miguel Castanuela, [[CCC]], December 06, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=65911|AlphaZero beats AlphaGo Zero, Stockfish, and Elmo]] by Carl Lumma, [[CCC]], December 06, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=65919|AlphaZero vs Stockfish]] by Bigler, [[CCC]], December 06, 2017
* [[https://groups.google.com/forum/#!topic/fishcooking/pcFRIurN_l4|Deepmind drops the bomb]] by Leebot, [[Computer Chess Forums|FishCooking]], December 06, 2017
* [[http://rybkaforum.net/cgi-bin/rybkaforum/topic_show.pl?tid=32392|AlphaZero beats Stockfish 8 by 64-36]] by [[Jeroen Noomen|Venator]], [[Computer Chess Forums|Rybka Forum]], December 06, 2017
* [[http://www.open-chess.org/viewtopic.php?f=5&t=3153|Alpha Zero]] by [[Mark Watkins|BB+]], [[Computer Chess Forums|OpenChess Forum]], December 06, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=65924|AlphaGo Zero And AlphaZero, RomiChess done better]] by [[Michael Sherwin]], [[CCC]], December 07, 2017 » [[RomiChess]]
* [[http://www.hiarcs.net/forums/viewtopic.php?t=8709|BBC News; 'Google's ... DeepMind AI claims chess crown']] by pennine22, [[Computer Chess Forums|Hiarcs Forum]], December 07, 2017
* [[https://groups.google.com/d/msg/fishcooking/S5W57LgDHQ8/WNiGb_25BgAJ|Press Release Stockfish vs. AlphaZero]] by Michael Whiteley, [[Computer Chess Forums|FishCooking]], December 08, 2017
* [[http://rybkaforum.net/cgi-bin/rybkaforum/topic_show.pl?tid=32398|AlphaZero reinvents mobility and romanticism]] by [[Chris Whittington]], [[Computer Chess Forums|Rybka Forum]], December 08, 2017 » [[AlphaZero#ImmortalZugzwang|Alpha Zero's "Immortal Zugzwang Game"]]
* [[http://www.talkchess.com/forum/viewtopic.php?t=65934|Reactions about AlphaZero from top GMs...]] by [[Norman Schmidt]], [[CCC]], December 08, 2017 » [[AlphaZero#Reactions|Reactions From Top GMs, Stockfish Author]]
* [[http://www.talkchess.com/forum/viewtopic.php?t=65937|AlphaZero is not like other chess programs]] by [[Dann Corbit]], [[CCC]], December 08, 2017
> [[http://www.talkchess.com/forum/viewtopic.php?t=65937&start=10|Re: AlphaZero is not like other chess programs]] by [[Rein Halbersma]], [[CCC]], December 09, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=65945|Photo of Google Cloud TPU cluster]] by [[Norman Schmidt]], [[CCC]], December 09, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=65983|Cerebellum analysis of the AlphaZero - Stockfish Games]] by [[Thomas Zipproth]], [[CCC]], December 11, 2017 » [[Cerebellum]]
* [[https://groups.google.com/d/msg/fishcooking/ExSnY8xy7sY/_x32q6INCAAJ|Open letter to Google DeepMind]] by Michael Stembera, [[Computer Chess Forums|FishCooking]], December 12, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=66005|recent article on alphazero ... 12/11/2017 ...]] by Dan Ellwein, [[CCC]], December 14, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=66013|An AlphaZero inspired project]] by [[Truls Edvard Stokke]], [[CCC]], December 14, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=66026|AlphaZero - Tactical Abilities]] by [[David Rasmussen]], [[CCC]], December 16, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=66047|In chess,AlphaZero outperformed Stockfish after just 4 hours]] by [[Ed Schroder]], [[CCC]], December 18, 2017
* [[http://forum.computerschach.de/cgi-bin/mwf/topic_show.pl?tid=9653|AlphaZero - Youtube Videos]] by Christoph Fieberg, [[Computer Chess Forums|CSS Forum]], December 18, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=66062|AlphaZero Chess is not that strong ...]] by [[Vincent Lejeune]], [[CCC]], December 19, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=66087|David Silver (Deepmind) inaccuracies]] by [[Ed Schroder]], [[CCC]], December 21, 2017
* [[http://rybkaforum.net/cgi-bin/rybkaforum/topic_show.pl?tid=32423|AZ vs SF - game 99]] by [[Ed Schroder|Rebel]], [[Computer Chess Forums|Rybka Forum]], December 23, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=66121|AlphaZero performance]] by [[Martin Sedlak]], [[CCC]], December 25, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=66179|A Simple Alpha(Go) Zero Tutorial]] by Oliver Roese, [[CCC]], December 30, 2017
* [[http://www.talkchess.com/forum/viewtopic.php?t=66184|AlphaZero: The 10 Top Shots]] by [[Walter Eigenmann]], [[CCC]], December 30, 2017
==2018==
* [[http://www.talkchess.com/forum/viewtopic.php?t=66214|SF was more seriously handicapped than I thought]] by [[Kai Laskos]], [[CCC]], January 02, 2018
* [[http://www.talkchess.com/forum/viewtopic.php?t=66299|Chess World to Google Deep Mind..Prove You beat Stockfish 8!]] by AA Ross, [[CCC]], January 11, 2018
* [[http://www.talkchess.com/forum/viewtopic.php?t=66349|Article:"How Alpha Zero Sees/Wins"]] by AA Ross, [[CCC]], January 17, 2018  » [[AlphaZero#DanaMackenzie|How AlphaZero Wins]]
* [[http://www.talkchess.com/forum/viewtopic.php?t=66443|Connect 4 AlphaZero implemented using Python...]] by [[Steve Maughan]], [[CCC]], January 29, 2018 » [[Connect Four]], [[Python]]
* [[http://www.talkchess.com/forum/viewtopic.php?t=66546|Seeing Alphazero in perspective ...]] by Dan Ellwein, [[CCC]], February 10, 2018 

=External Links= 
* [[https://en.wikipedia.org/wiki/AlphaZero|AlphaZero from Wikipedia]]
* [[https://en.wikipedia.org/wiki/AlphaGo_Zero#AlphaZero|AlphaGo Zero - AlphaZero from Wikipedia]]
* [[#Keynote]]Keynote [[David Silver]] [[https://nips.cc/Conferences/2017|NIPS 2017]] [[https://youtu.be/A3ekFcZ3KNw|Deep Reinforcement Learning Symposium AlphaZero]], December 06, 2017, [[https://en.wikipedia.org/wiki/YouTube|YouTube]] Video <ref>[[http://www.talkchess.com/forum/viewtopic.php?t=66059|AlphaZero explained by one creator]] by [[Mario Carbonell Martinez]], [[CCC]], December 19, 2017</ref>
> [[media type="youtube" key="A3ekFcZ3KNw"]]
* [[http://web.stanford.edu/~surag/posts/alphazero.html|A Simple Alpha(Go) Zero Tutorial]] by [[Surag Nair]], [[Stanford University]], December 29, 2017 <ref>[[http://www.talkchess.com/forum/viewtopic.php?t=66179|A Simple Alpha(Go) Zero Tutorial]] by Oliver Roese, [[CCC]], December 30, 2017</ref>
> [[https://github.com/suragnair/alpha-zero-general|GitHub - suragnair/alpha-zero-general: A clean and simple implementation of a self-play learning algorithm based on AlphaGo Zero (any game, any framework!)]]
==Reports==
* [[https://www.theverge.com/2017/12/6/16741106/deepmind-ai-chess-alphazero-shogi-go|DeepMind’s AI became a superhuman chess player in a few hours, just for fun]] by [[https://www.theverge.com/users/James%20Vincent|James Vincent]], [[https://en.wikipedia.org/wiki/The_Verge|The Verge]], December 06, 2017
* [[http://www.telegraph.co.uk/science/2017/12/06/entire-human-chess-knowledge-learned-surpassed-deepminds-alphazero/|Entire human chess knowledge learned and surpassed by DeepMind's AlphaZero in four hours]] by [[http://www.telegraph.co.uk/authors/sarah-knapton/|Sarah Knapton]], and [[http://www.telegraph.co.uk/authors/leon-watson/|Leon Watson]], [[https://en.wikipedia.org/wiki/Telegraph_Media_Group|The Telegraph]], December 06, 2017
* [[http://www.bbc.co.uk/news/technology-42251535|Google's 'superhuman' DeepMind AI claims chess crown]], [[https://en.wikipedia.org/wiki/BBC_News|BBC News]], December 06, 2017 <ref>[[http://www.hiarcs.net/forums/viewtopic.php?t=8709|BBC News; 'Google's ... DeepMind AI claims chess crown']] by pennine22, [[Computer Chess Forums|Hiarcs Forum]], December 07, 2017</ref>
* [[https://chess24.com/en/read/news/deepmind-s-alphazero-crushes-chess|DeepMind’s AlphaZero crushes chess]] by [[https://chess24.com/en/profile/colin|Colin McGourty]],  [[https://en.wikipedia.org/wiki/Chess24.com|Chess24.com]], December 06, 2017
* [[http://www.danamackenzie.com/blog/?p=5068|One Small Step for Computers, One Giant Leap for Mankind]] by [[Dana Mackenzie]], [[http://www.danamackenzie.com/blog/|Dana Blogs Chess]], December 06, 2017
* [[https://www.chess.com/news/view/google-s-alphazero-destroys-stockfish-in-100-game-match|Google's AlphaZero Destroys Stockfish In 100-Game Match]] by [[https://www.chess.com/member/mikeklein|Mike Klein]], [[https://en.wikipedia.org/wiki/Chess.com|Chess.com]], December 06, 2017
* [[https://en.chessbase.com/post/the-future-is-here-alphazero-learns-chess|The future is here – AlphaZero learns chess]] by [[Albert Silver]], [[ChessBase|ChessBase News]], December 06, 2017
* [[#Reactions]][[https://www.chess.com/news/view/alphazero-reactions-from-top-gms-stockfish-author|AlphaZero: Reactions From Top GMs, Stockfish Author]] by [[http://www.chessvibes.com/?q=peterdoggers|Peter Doggers]], [[https://en.wikipedia.org/wiki/Chess.com|Chess.com]], December 08, 2017 » [[Stockfish]], [[Tord Romstad]] <ref>[[http://www.talkchess.com/forum/viewtopic.php?t=65934|Reactions about AlphaZero from top GMs...]] by [[Norman Schmidt]], [[CCC]], December 08, 2017</ref>
* [[https://medium.com/@josecamachocollados/is-alphazero-really-a-scientific-breakthrough-in-ai-bf66ae1c84f2|Is AlphaZero really a scientific breakthrough in AI?]] by [[https://scholar.google.com/citations?user=NP4KdQQAAAAJ&hl=en|Jose Camacho Collados]], [[https://medium.com/|Medium]], December 11, 2017 <ref>[[http://www.talkchess.com/forum/viewtopic.php?t=66005|recent article on alphazero ... 12/11/2017 ...]] by Dan Ellwein, [[CCC]], December 14, 2017</ref>
* [[https://en.chessbase.com/post/alpha-zero-comparing-orang-utans-and-apples|Alpha Zero: Comparing "Orangutans and Apples"]] by [[https://en.chessbase.com/author/andre-schulz|André Schulz]], [[ChessBase|ChessBase News]], December 13, 2017
* [[https://en.chessbase.com/post/kasparov-on-deep-learning-in-chess|Kasparov on Deep Learning in chess]] by [[Frederic Friedel]], [[ChessBase|ChessBase News]], December 13, 2017
==[[#StockfishMatch]]Stockfish Match==
* [[https://lichess.org/study/wxrovYNH|AlphaZero vs Stockfish Games • lichess.org]]
* [[http://www.chessgames.com/perl/chessplayer?pid=160016|The chess games of AlphaZero (Computer)]] from [[http://www.chessgames.com/index.html|chessgames.com]]
* [[http://www.zipproth.de/Brainfish/Cerebellum_AlphaZero.html|Cerebellum AlphaZero Analysis]] » [[Cerebellum]] <ref>[[http://www.talkchess.com/forum/viewtopic.php?t=65983|Cerebellum analysis of the AlphaZero - Stockfish Games]] by [[Thomas Zipproth]], [[CCC]], December 11, 2017</ref>
* [[#ImmortalZugzwang]][[https://youtu.be/lFXJWPhDsSY|Deep Mind Alpha Zero's "Immortal Zugzwang Game" against Stockfish]] by [[https://www.facebook.com/AGADMATOR|Antonio Radic]], December 07, 2017,  [[https://en.wikipedia.org/wiki/YouTube|YouTube]] Video <ref>[[http://rybkaforum.net/cgi-bin/rybkaforum/topic_show.pl?tid=32398|AlphaZero reinvents mobility and romanticism]] by [[Chris Whittington]], [[Computer Chess Forums|Rybka Forum]], December 08, 2017</ref> <ref>[[https://en.wikipedia.org/wiki/Immortal_Zugzwang_Game|Immortal Zugzwang Game from Wikipedia]]</ref> » [[Zugzwang]]
> [[media type="youtube" key="lFXJWPhDsSY"]]
* [[https://youtu.be/pcdpgn9OINs|Deep Mind AI Alpha Zero Dismantles Stockfish's French Defense]] by [[https://www.facebook.com/AGADMATOR|Antonio Radic]], December 08, 2017, [[https://en.wikipedia.org/wiki/YouTube|YouTube]] Video
* [[#DanaMackenzie]][[http://www.danamackenzie.com/blog/?p=5072|How AlphaZero Wins]] by [[Dana Mackenzie]], [[http://www.danamackenzie.com/blog/|Dana Blogs Chess]], December 15, 2017 <ref>[[http://www.talkchess.com/forum/viewtopic.php?t=66349|Article:"How Alpha Zero Sees/Wins"]] by AA Ross, [[CCC]], January 17, 2018</ref>
==Misc==
* [[https://medium.com/applied-data-science/how-to-build-your-own-alphazero-ai-using-python-and-keras-7f664945c188|How to build your own AlphaZero AI using Python and Keras]] by [[https://www.linkedin.com/in/davidtfoster/|David Foster]], January 26, 2018 » [[Connect Four]], [[Python]] <ref>[[http://www.talkchess.com/forum/viewtopic.php?t=66443|Connect 4 AlphaZero implemented using Python...]] by [[Steve Maughan]], [[CCC]], January 29, 2018</ref>
* [[Videos#Can|Can]] - [[https://en.wikipedia.org/wiki/Halleluhwah|Halleluwah]], from [[https://en.wikipedia.org/wiki/Tago_Mago|Tago Mago]] 1971, [[https://en.wikipedia.org/wiki/YouTube|YouTube]] Video 
> lineup: [[https://en.wikipedia.org/wiki/Irmin_Schmidt|Irmin Schmidt]], [[https://en.wikipedia.org/wiki/Michael_Karoli|Michael Karoli]],  [[https://en.wikipedia.org/wiki/Holger_Czukay|Holger Czukay]], [[https://en.wikipedia.org/wiki/Damo_Suzuki|Damo Suzuki]], [[https://en.wikipedia.org/wiki/Jaki_Liebezeit|Jaki Liebezeit]]
> [[media type="youtube" key="2dZbAFmnRVA"]]

=References= 
<references />
=What links here?= 
[[include component="backlinks" page="AlphaZero" limit="80"]]
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