Computers Playing Games
Arif Zaman
CS 101
Acknowledgements
Portions of this are taken from MIT’s
open-courseware http://ocw.mit.edu/
 Some items are adapted from Chapter 5
on Games by some professor who
adapted it from notes by Charles R.
Dyer, University of Wisconsin-Madison
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Why Play?
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Humans play for enjoyment, but computers…?
Games of strategy and skill require
“intelligence”. We may learn about thinking by
learning how to teach computers.
Hard but well defined problems, unlike other AI
problems like speech, ethics etc.
Competition, knowledge-representation, …
To provide entertainment, competition and
training to humans (that play or program).
Game Theory
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Von Neumann and
Morgenstern analyzed
two person zero-sum
games, where each
person takes a decision
simultaneously, and then
gets paid according to a
payoff matrix.
Economic games, can
be multi-person, multistage.
Enemy
Strategy
My
Stra
tegy
A
B
X
10
-10
Y
-2
40
Board Games
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Two Person
Alternating moves
Zero Sum
Deterministic (not
Backgammon or
Ludo)
Perfect Information
(not Bridge, Hearts)
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Examples
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Tic-Tac-Toe
Checkers
Chess
Go
Reversi (Othello)
History
1949 Claude Shannon
paper on Chess
 1951 Alan Turing
simulation on Checkers
 1955 Chess Program
using α-β.
 1966 MacHack
 1990 Belle (harware
assist)
 2000 Deep Blue (serious
hardware)
3500
3000
2500
2000
1500
Deep
Blue
USCF Rating

Belle
Mac
Hack
1000
500
Depth (ply)
0
3
6
9
12
Top-down Program
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Repeat Until Done
DrawBoard
 GetPlayerMove
 CheckLegalMove ‘also check if game over
 MakePlayerMove
 DrawBoard
 FindLegalMoves ‘also check if game over
 EvaluateLegalMoves
 MakeBestMove
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Static Position Evaluator
Given a position, come up with a “value”.
Values are 0…1 or 0…infinity or –
infinity…infinity.
 0..1 can represent “probability” of my lose/win
 In chess can count
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my pieces – enemy pieces.
my total piece value – enemy total piece value.
Add points for Mobility
Add points for Center Control
Negative points for exposed king, etc.
This is where humans experts excel.
Game Tree Mini-Max
Crude Evaluator
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You can start off with
a crude static
evaluator, and a high
ply minimax.
 Russians believed
that better would be
an excellent but slow
static evaluator with
lower plies.
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The extreme
strategies are of
course a perfect
evaluator with 1-ply
 Or the complete
game-tree search
with trivial evaluator.
Deep Blue
32 node supercomputer, each with eight
special chess processors.
 50 – 100 billion moves in 3 mins with a
13-30 ply search
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Other Tricks
α-β pruning: We do  Lookup Tables: for
not need to look at
opening moves.
every possible move,  Special program:
especially if we have
for endgames.
a good candidate.
 Quiessence: Static
evaluate at peaceful
situations. Go
deeper into fights.
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Other Games
Go is much harder. The best computer is
far worse than the best human, even
though the rules are very simple
 Checkers computers are far better than
the best humans
 Tic-Tac-Toe is still a great mystry
 Othello has a very interesting story.
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Rules of the game
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Start with four squares
filled.
Move next to opposite
colored square.
Change color of all
opposite colored
squared surrounded by
moved piece and
another piece of the
same color.
Must capture.
Reversi (Othello)
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D E Moriarty and R
Miikkulainen,
“Discovering Complex
Othello Strategies
Through Evolutionary
Neural Networks”
Created a strong player
without any initial
knowledge, by breeding
a program!
Evolutionary
 Start with a “population”
of 100 “random”
programs.
 Have a competition, and
kill the 90 losers. Breed
the 10 winners by
“mixing” their “genes”
with a bit of “mutation.”
 Do the same for many
generations (1000’s).
Positional Strategy
Positional Strategy
 Programs quickly
learned the basic
positional strategy:
 Take corners.
 Avoid neighbors of
corners
 Take neighbors of
neighbors of corners.
Mobility Strategy
 Keep low piece
count
 Restrict opponents
moves
 Discovered only
once in Japan, and
then everyone learnt
it from them.
Mobility vs Positional
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The mobility strategy
(learned by the ENN)
looks like it is
loosing, but converts
it to a win in the last
3-4 moves!
But…
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Specially designed programs to play
Othello still do even better eg. Bill or
Logistello.