Solving Ponnuki-Go on Small Board
Paper: Solving Ponnuki-Go on small board
Authors: Erik van der Werf, Jos Uiterwijk,
Jaap van den Herik
Presented by: Niu Xiaozhen
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Outline
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Introduction
Motivation
Method Summary
Results and Analysis
Conclusions
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Introduction
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Ponnuki-Go (also known as Atari-Go),
the goal is to be the first to capture one
or more of the opponent’s stones
Two rules are different with Go:
 Capturing
directly ends the game
 Passing is not allowed (no tie)
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Simpler than Go (no ko-fights)
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Motivation
Why we study Atari-Go?
 It
contains major concepts of Go
such as capturing stones,
determining life or death and
making territory
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Motivation (2)
Why we study Atari-Go?
 A good
benchmark for testing the
performance of algorithms
 Successful algorithms in small
board Atari-Go might be useful for
computer Go
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Outline
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
Introduction
Motivation
Method Summary
Results and Analysis
Conclusions
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Method Summary
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Standard alpha-beta framework with
many enhancements:
 Iterative
deepening Principal Variation
Search (PVS)
 Transposition table
 History heuristic
 Enhanced transposition cutoffs
 Move ordering
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Transposition Table
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Use the two-deep replacement
scheme:
225 (32M) double entries
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History Heuristic
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History Heuristic employs one
table for both black and white
moves, utilizing the Go proverb
“the important move of my
opponent is important to me as
well”
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Move Ordering
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First the transposition move is
tested
Second are the killer moves
Third the rest of the moves are
ordered by the history heuristic
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Evaluation Function
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Simple evaluation function is to
use a three-valued scheme [1(win),
0(unknown), -1(loss)]
Efficient for small boards
Becomes useless for strong play
on large boards
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Evaluation Function (2)
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Proposed heuristic evaluation function
is based on four principles:
 Maximizing
liberties
 Maximizing territory
 Connecting stones
 Making eyes
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Maximizing Liberties and Territory
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The number of liberties is a lower
bound on the number of moves
that is needed to capture a stone
Maximizing territory is a long-term
goal since it allows the player put
more stones inside his own
territory (before filling it completely)
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Connecting and Making Eyes
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Why should connect stones to a
larger group?
 A small
number of larger groups is
easier to defend than a large
number of small groups

Making eyes is derived from
normal Go.
 After
a player has run out of
alternative moves, he might be
forced to fill his own eyes
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Implementation
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Use bit-boards for fast
computation of the
board features
Territory is estimated
by a weighted sum of
the number of first-,
second- and thirdorder liberties
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Implementation (2)
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Connections and eyes are more
costly to calculate than the liberties
Use Euler number to estimate the
connections and eyes
The Euler Number of a binary image
is:
 The
number of objects minus the
number of holes
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Euler Number
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Minimizing the Euler Number thus
connects stones as well as creates eyes
E = 3 - 19 = - 16
E = 1 - 18 = - 17
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Outline
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Introduction
Motivation
Method Summary
Results and Analysis
Conclusions
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Results and Analysis
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The program solved the empty
square boards up to 5x5
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First Play First Win?
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2x2 board:
3x3 board:
4x4 board:
5x5 board:
6x6 board:
no
yes
no
yes
don’t know yet!
Test on 6x6 board took a few weeks
(before system crash), the solution
is at least 24-ply deep!
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Experiment Results
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The table shows the winner, the depth (in plies)
of the shortest solutions, the number of nodes,
time and the effective branching factor
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6x6 board
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Two alternative way are used for
testing:
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Another Approach
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In 2002, Cazenave solved Atari-Go
on 6x6 with crosscut starting
Use Gradual Abstract Proof Search
(GAPS) algorithm, which is an
combination of alpha-beta with a
clever threat-extension scheme
Proved a win at depth 17 in around
10 minutes
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Comparison
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The authors’ algorithm found the shortest win at depth
15 in a comparable time frame
Using the same search enhancements into GAPS,
Cazenave also found the solution at depth 15 in 26
seconds
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6x6 board with Stable Starting
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Still too difficult! (estimates that about one
month of computation time!)
Prove the black win (at the depth of 31) by
manually playing the first move
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Solutions for Non-empty 6x6 board
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Impact of Search Enhancements
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Experiment results show that, on
larger boards the enhancements
become increasingly effective
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Comparison of Evaluation Functions
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Authors’ heuristic evaluation
function performs better!
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Program Performance
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Against Rainer Schutze’s freeware
“AtariGo 1.0” in 10x10 board, won
most of the game
After adding an implementation
about extending ladders, won all!
Against an amateur 1D in a 9x9
board, sometimes the program
was able to win, but most of the
games was lost!
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Future Work
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Solve the empty 6x6 board and
solving the 8x8 board with crosscut
starting
Since search extensions for
ladders are essential for strong
play on larger board, future work
will focus on selective searchextensions
Test the algorithm in Go!
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Conclusions
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Authors‘ conclusions:
 solved Atari-Go on the 3x3, 4x4, 5x5 and
some non-empty 6x6 boards
 the combination of enhancements and the
heuristic evaluation fucntion is effective
My conclusions:
 Focusing on enhancements, or trying to solve
larger board one by one might not be a right
direction
 We need something different!
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