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