How computers play chess

How Computers
Play Chess
Wednesday, September 25, 13

A bit about me
Carlos Justiniano (carlos.justiniano@gmail.com)
Started playing chess at age 7, reached master
strength in (slow) online play.
Project Manager / Team Lead on the Chessmaster
series.
Founded ChessBrain - a distributed computing project
which earned a Guinness 2005 world record as the
world’s largest chess computer.

Overview
In this talk we’ll look at how computers play
chess.
We’ll begin with a brief history of chess.
Then we’ll look at the core modules which
make up all chess programs.
We’ll end with a look inside an actual chess
program.

Chess History
Chess is well over 1000 years old.
Believed to have originated in India before
spreading to Persia.
The style of chess we play today took form
in Europe during the 15th century.
At about the that time chess books were
written.

Chess History
During the 18th century,
Philidor wrote The Analysis of
Chess (L’analyse des échecs).
He was considered to be one
of the World’s best chess
players in his time.
François-André
Danican Philidor

It’s been said that more books have been
written about chess than for all other
games combined!

So why this fascination
with Chess?
Long considered an
intellectual game - the
game of kings, queens
and generals.
A game which embodies
the struggles of common
men to entire kingdoms.
A epic battle of life and
death.

Fast forward to the future...

Chess Today
Today, chess is played around the globe. It’s
estimated that out of 7 billion people about
700 million have played chess at one point in
their lives.
Computers have surpassed the best human
players.
Today competitive chess players use
computers in order to prepare for their
human opponents.

The creation has
surpassed its creator
So, although we humans
have had over 1000 years
to invent, study and
understand the ﬁner
points of chess - machines
are now better at playing
chess than we are!

Whoa! No way dude!
How did this happen?

It didn’t happen
over night
As early inventors created machines, public
fascination grew for some of the more clever
machines exhibiting human characteristics.
Early inventor, Al Jazari, described many such
inventions in his book “The Book of Knowledge of
Ingenious Mechanical Devices” which he wrote in
1206.
Surely, it was only a matter of time before
machines could play chess.

The Turk, Chess Playing
Automaton
Built in 1769 by Wolfgang von
Kempelen.
The Turk beat many players
but lost to the strongest
players of the time, such as
Philidor.
It won many more games than
it lost and was a sensation
throughout Europe.

The Turk, Chess Playing
Automaton
Sadly, however, it was an
elaborate hoax.
The Turk concealed a
human chess master.
The world would not see a
true chess playing machine
for another 180 years.

Fast forward to the late
1930s
The creation of electronic
computers began in the
1930s.
By the late 40s,
computers were used as
research and military
tools in the US, England,
Germany and the former
USSR.
The ENIAC, which became operational in 1946, is
considered to be the ﬁrst general-purpose electronic
computer. Programmers Betty Jean Jennings (left)
and Fran Bilas (right) are depicted here operating the
ENIAC's main control panel.

Early research papers in
Computer Chess
In 1945, Konrad Zuse, the German pioneer of
computer science ﬁrst wrote about the
possibility of creating a chess program.
Although Konrad developed one of the ﬁrst
electronic computers, the Zuse-1, there’s no
record of him actually creating a chess
program.

Early research papers in
Computer Chess
Four years later, in 1949, Claude
Shannon (a research scientist at Bell
Labs) authored a seminal paper
entitled “Programming a Computer for
Playing Chess”.
Many of Shannon’s ideas are still in
use today!

Turing takes things a
few steps further
In 1951, British mathematician and
early computer scientist, Alan Turing
wrote about computer chess.
He later completed a one move chess
analyzer called TUROCHAMP.
Turing’s chess analyzer didn’t run on
an actual computer, but was rather a
set of instructions he could execute
by hand.

Turing takes things a
few steps further
Turing simply calculated chess moves by
looking ahead one move at a time and scoring
them.
Although played on paper, this was the ﬁrst
program to play a complete game of chess.
Turing believed that games such as chess
served as ideal models in which to study
machine intelligence.

No worries!
We’re not going to cover all
of computer chess history.
Let’s speed things
up a bit...

The 50s - 80s
In 1957, Chess programs using a 6x6 board instead of the 8x8 board began
playing simple chess.
By 1957, the first program to play a game of chess was developed by Alex
Bernstein in the US and one by programmers in Russia.
In 1961 a Russian chess program played a game against a human chess
amateur. This was the first recorded game of man vs machine. Although the
machine lost, it wouldn’t be long before the tables would turn.
Along with advances in main-frame and mini computers, chess programs also
continued to improve during the 60s and 70s.
During the 70s and 80s, Joe Condon and Ken Thompson at Bell Labs created
Belle, the first chess machine to reach master strength play. Side note: you
may remember Ken Thompson as the creator of the UNIX operating system.

The 80s also ushered in
low cost chess computers

The 80s and 90s
During the 80s we also started seeing chess programs for
the early personal computers as well as dedicated chess
machines for consumers.
The 90s were an exciting time in computer chess history as
chess programs began challenging International Chess
masters and later Grandmasters.
This progress was fueled by faster computers, improvements
in software and advances in computing science.

IBM’s Deep Blue
By 1997 IBM’s Deep Blue
chess machine beat then
World Champion, Garry
Kasparov by two wins
against one win and three
draws.
This marked the ﬁrst time
in human history that a
machine had ever defeated
a World Champion.

Early 2000s
Deep Blue was a highly specialized machine designed to play
chess. However, PCs were also getting better!
In the early 2000s there were three high proﬁle matches between
world-class chess players and PCs.
Keep in mind that these games where played against “gamer-class”
PCs and not large mini and super computers. Not bad for machines
less powerful than Deep Blue.
In 2002 Vladimir Kramnik and Deep Fritz competed an eight game match
ending in a draw.
In 2003, Garry Kasparov played Junior, The match ended a draw with 3–3.
Later that year, Kasparov played X3D Junior in a match also ending in a
draw.

In 2005, Human chess
dominance ends
In 2005, Hydra (a specialized Chess machine using 64
processors) defeated the 6th ranked player in the
world, Michael Adams 5½ to ½ in a six-game match.
In 2006 undisputed World Champion Vladimir Kramnik
played Deep Fritz and lost by a score of 2 to 4.
Today chess programs running on our mobile phones
play better than all but the world’s top human
players.

Today, all competitive
chess players train using
machines - most have no
chance of winning
against the machines in
actual tournament play

Speed in perspective
In the 1980s a microcomputer could execute just
over 2 million instructions per second, by the 90s
they were executing well over 50 million
instructions per second.
Today, the processors in our tablets and phone are
capable of executing over a billion instructions per
second.
Advances in computer science and software tools
have also helped considerably, but advances in raw
processing speed can’t be ignored.

Thinking Games
To understand how computers play chess it’s
important to understand how they play simpler
games.

Thinking Games
We’ve all played
simple games like
tic-tac-toe and the
15 tile sliding game.
These games require
us to consider which
moves will bring us
closer to winning.

Thinking Games
The process of thinking about how to win
involves employing strategies which bring us
closer to achieving a solution.
All games have strategies. In Monopoly it’s
important to obtain high priced properties, in
Reversi/Othello controlling the corner square
is vital.
For computer programs these strategies are
described using Heuristics and Algorithms.

Heuristics and
Algorithms
In computer science the term Heuristic refers
to a method of solving a problem by getting
closer to a solution or end goal.
In contrast the term algorithm refers to a
method (approach) of solving a particular
problem.
It’s common for Heuristics to involve one or
more algorithms.

Most non-trivial games
can’t be realistically solved
with an algorithm -
largely because it would
take too damn long

Solving Chess
Take chess for example: there exists a way
of ﬁnding the best move at the start of the
game.
However, it involves looking at all possible
moves and the replies to each of those
moves -- followed by replies to those moves,
and so on until an end is reached.
Not a bad plan if it were not for the shear
number of possible chess moves in a given
game.

If we assume an average chess
game of 40 moves, there are...
10^120 possible moves, or
10,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,00
0,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000
At a calculation speed of 1/1000 of a second
for each move - it would take a computer
10^90 years to make the ﬁrst move.

10^120 is a really really
(yes really) big number!
Fictional side note:
It turns out that it’s
considerably larger
than the seven
million years
required for Deep
Thought to arrive at
the answer: 42

Can’t win by brute force
Brute force refers to an approach which
explores all possibilities.
Complex intelligent games can’t be solved by
brute force.
So moves have to be selectively chosen.
This realization is what has driven advances
in how intelligent games are built.

Evaluating choices
So if choices have to be evaluated then we
need a way of performing an evaluation.
In the ﬁeld of intelligent games this is
referred to as an evaluation function.
The function says: Given a known move
return a score.
The best move in a list of choices is the
move which scored the highest.

How a machine sees
Before a chess program can evaluate a move,
we must ﬁrst teach it how to represent a
chess position.
This is unsurprisingly known as “Board
representation”.

How a machine sees
A chess board can be
represented as a
numbered list of
squares.

How a machine sees
The chess pieces
themselves can be
represented using the
numbers -1 through 6.
Piece colors are
indicated using positive
and negative numbers.

How a machine sees
This is by no means the only way to
represent a board and pieces.
Other methods exist with names such as
“bitboards” and “Forsyth-Edwards Notation”.
In this talk we’ll stick with our earlier
method.

How a machine sees
Following our earlier example, it’s necessary
to expand upon our simplistic board
representation in order to detect chess
moves which fall out of bounds.
Essentially we need to encode the board’s
boundaries.

How a machine sees
This results in a
larger board which
includes our actual
chess board within.
A value of -99 is
used to represent
out of bound
areas.

How a machine sees
Thus our numbered
list of squares also
changes to allow
for our expanded
board.

How a machine sees
Next, we need to help the machine
understand what it sees.
We need to teach it how each piece moves,
and ﬁnally chess rules which further
constrain legal moves.
For example, the King chess piece can’t move into a
square which is already under attack by the
opposing side.

How a machine sees
Let’s consider the Knight
chess piece.
It moves in an L shaped
path: two squares in a
horizontal or vertical
direction and then one
square to either side.

How a machine sees
With a black Knight on
square 78 we can see that it
can move to squares 53, 55,
64, 68, 88, 92, 101, and 103.
We can encode the Knight’s
movements as the difference
between the square it can
move to and the square its
currently on.

How a machine sees
A movement to square 53
involves a subtraction
53-78=-25 So we encode
that move as -25.
Moving to square 101 involves
101-78=23 so we encode that
as +23.
This encoding works no
matter where we place the
Knight.

How a machine sees
Lets place our Knight in the
lower corner of the board.
Notice how most of its moves
fall out of bounds.
This is why we use a larger
board: in order to detect
piece moves which aren’t
valid.

How a machine sees
A chess programmer proceeds to encode the
offset differences for each piece.
This algorithm is known as a legal move
generator.
With a list of legal moves the program can
then run the evaluation function against
each resulting move to begin to isolate a
best move.

Inside an evaluation
function
In chess an evaluation function would
essentially weigh various desirable
characteristics in a chess position and return
a score.
This is one of the earliest methods used in
computer chess.

function
A simple evaluation function would ask
questions like: “how many moves do I have
available?”, “is my King safe?”.
Evaluation functions are typically
implemented using a weighted sum model.
This approach assigns relative values to
various chess factors to arrive at a weighed
score.

function
Before we can assign values in a weighed
sum function we have to agree on a basic
unit of measurement.

function
In computer chess a pawn is assigned the value of 100, a
knight is assigned 300, a bishop 350, a rook 500 and a
Queen is valued at 900. A king is assigned a large number
because capturing the king marks the end of the game.

function
Each factor of an evaluation function is assigned a
value relative to a centipawn, that's 1/100 of a pawn.
For each desired factor, a chess programmer asks,
"how much of a pawn is that factor worth?".

function
Evaluation functions also contain a measure of
material balance - that is, by a show of remaining
pieces - who is winning?. This is determined by
adding up the value of each side’s pieces, which are
already measured in centipawns. So a knight and
two pawns is equal to 500 or equal in value to a
Rook.

function
Here is another example: A chess game begins with
each side having two bishops. It's considered
advantageous to retain both bishops for as long as
possible.
So an evaluation function might value the present of
both bishops as equal to half a centipawn or 50. Once
a player no longer has both bishops an evaluation
function would cease to add 50 to its overall score.

function
Many factors go into an evaluation function, such as
king safety (can the king be attacked, is it safe?) and
Piece Mobility (how many moves are available to a
given piece) greater mobility often equates to more
options or opportunities.
The presence or absence of various factors is what
determines how a position is scored.

function
Here is a really crude evaluation function where
Queen=900, Rook=500, Bishop=350, Knight=300,
Pawn=100.
f below is our evaluation function, the parameter p is
the position to be evaluated, M is a measure of
mobility.
f(p) = QueenWeight X (Qw-Qb) + RookWeight X (Rw -
Rb) + BishopWeight X (Bw-Bb) + KnightWeight X (Nw-
Nb) + (Pw-Pb)+ 0.1 X (Mw-Mb)

function
Simpler evaluation functions model how beginners
see chess positions, while more complex evaluation
functions model how very strong players see a
position.
Complex evaluation functions take more time to
execute than simpler ones.
Thus, other algorithms need to be employed to
speed up the selection process.

Searching for a best
move
So now that we’ve seen how a chess set
(position) can be represented and how a it
can be evaluated - we’re ready to consider
how good moves can be found.

Look ahead
In order for a chess program to decide on a
best move it must also take into account its
opponents move - followed by its own replies
and so on.
This is known as looking ahead. Good chess
players look ahead a few moves while great
chess players have been known to look
ahead a dozen or so moves.

Keeping track of
evaluations
We’ve seen how computers represent chess positions
and how they evaluate them - but how do they
keep track of what they’ve evaluated?
Enter: game trees a tool used to graph positions
(nodes) and moves (vertices) and their relative
evaluations.

When inverted a
game tree appears
more like a natural
tree with a trunk,
branches and leaves
moving upward.

Game Trees
In computer science a tree is also known as
a data structure.
Common data structures include arrays and
hash tables (also known as dictionary or
associative arrays).
Trees can be implemented as array of nodes
- where each node contains both a pointer to
its parent and an array with sibling nodes.

Game Trees
Game Trees, like other data structure, are
useful for more than just storing data.
Algorithms typically operate on data
structures.
For example, a sorted array may contain a
list of places and an algorithm (binary
search) might be used to ﬁnd a speciﬁc
location.

Game Trees and Search
Algorithms
A game tree is built using a legal move generator
and nodes are evaluated using an evaluation function
- which was described earlier.
Search algorithms navigate the game tree while
looking at the score left by an evaluation function.
As a search algorithm visits a node (position) it may
further update other node values along the way.

Search Algorithms
Over the years many search algorithms
have been devised.

Search Algorithms
The Minimax algorithm was the first search method
used in computer chess. MAX values (positive) are
assigned to moves for the first player, while MIN
values are assigned to the moves of the second
player. The game tree is filled with MIN and MAX
values and ordered so that any given node contains
the MIN value or MAX value of the best replies
below it.
In this way a path to the best (highest scoring)
move is identified.

Search Algorithms
Alpha-Beta Pruning is a search algorithm which
improves upon the Minimax algorithm by reducing
the number of nodes which need to be evaluated.
It does this by discarding a move branch when it’s
proven to be worse than one already identiﬁed.
We humans do this when we consider a choice which
is so bad that we stop considering it and move on to
more promising options.

Alpha beta pruning on a
minimax tree

Improved Alpha/Beta
Over the years, many improvements have
been made to the Alpha Beta Pruning
algorithm.
If you’re interested, checkout NegaScout,
PVS and MTF(f).

Key components
we’ve covered
Board representation / game state: How to
represent a given position.
Move Generation: Given a position, determine
all of the legal moves.

Key components
we’ve covered
Static Evaluation: How to assess a given
position based on various factors.
Search: How to locate the best move in a game
tree of chess positions.

That’s how computers
play chess
The areas we’ve covered should give you a
sense of how computers play chess.
Naturally this talk is a gross
oversimpliﬁcation but with additional
research into the ideas we’ve covered most
talented programmers should be able to build
their own chess program.

Ideas in action
Let’s take a brief look at an actual chess
program...
There are hundreds of chess programs
available on the web. For this talk I choose
GarboChess by Gary Linscott.
GarboChess is written in simple JavaScript
and can run locally on your computer.

Now you know how
computers play chess!
The ideas we’ve looked at apply to a wide
range of games.
There are many sites online which further
elaborate on the materials we’ve covered.

How computers play chess

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