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https://en.wikipedia.org/wiki/File:ST Battle Chess.png
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http://afflictor.com/2012/09/11/chess-programs-regularly-play-at-good-amateur-level/
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https://en.wikipedia.org/wiki/Deep Blue (chess computer)
Deep Blue
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https://stockfishchess.org/ Lang:C++ License:GPLv3
Stockfish
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Game tree
https://en.wikipedia.org/wiki/Game tree
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Optimal play
Terminal
min player
max player
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Optimal play
1 01 1 1Terminal
min player
max player
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Optimal play
1 01 1 1
0
Terminal
min player
max player
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Optimal play
1 01 1 1
0 1
Terminal
min player
max player
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Optimal play
1 01 1 1
0 1
1
Terminal
min player
max player
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Chess has about 1046 (2153) states!
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Minimax algorithm with heuristic score
Cut-off
min player
max player
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Minimax algorithm with heuristic score
.7 .1 .6 .9Cut-off
min player
max player
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Minimax algorithm with heuristic score
.7 .1 .6 .9
.1
Cut-off
min player
max player
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Minimax algorithm with heuristic score
.7 .1 .6 .9
.1 .6
Cut-off
min player
max player
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Minimax algorithm with heuristic score
.7 .1 .6 .9
.1 .6
.6
Cut-off
min player
max player
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https://tests.stockfishchess.org/
Testing AI changes is crucial
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Heuristic scores are hard!
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http://mathworld.wolfram.com/Go.html
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by Google Deepmind
https://deepmind.com/research/alphago/
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https://gogameguru.com/alphago-races-ahead-2-0-lee-sedol/
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http://pachi.or.cz/ Lang:C License:GPLv2
Pachi
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Monte Carlo evaluations
Cut-off
min player
max player
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Monte Carlo evaluations
Cut-off
min player
max player
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Monte Carlo evaluations
Cut-off
min player
max player
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Monte Carlo evaluations
Cut-off
min player
max player
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Monte Carlo evaluations
Cut-off
min player
max player
.7
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Monte Carlo Tree Search (MCTS)
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Some games have hidden information!
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http://magic.wizards.com/en/events/coverage/gpsin15/father-son-2015-06-27
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https://magarena.github.io Lang:Java License:GPLv3
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Choose a random instantiation of the hiddeninformation during simulation
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Theory Practice
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Theory Practice• Optimal play
• Minimax
• Monte Carlotree search
• Sampling hiddeninformation
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Theory Practice• Optimal play
• Minimax
• Monte Carlotree search
• Sampling hiddeninformation
Stockfish Pachi