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Quoridor and Artificial
Intelligence
Jeremy Alberth
Quoridor
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
Quoridor is played on a 9x9 grid.
Starting positions are shown for two players.
Quoridor
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Red moves his pawn down. The objective for both
players is to be first to reach the opposite side.
Quoridor
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Blue moves his pawn up. Players may either move their
pawn or place a wall on a move.
Quoridor
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Red places a wall horizontally in front of blue’s pawn.
Walls must block movement from four squares.
Quoridor
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Blue moves his pawn left so that he is no longer
impeded on his journey upward.
Quoridor
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Blue places a wall vertically to the right of red’s pawn.
Wall orientations can be horizontal or vertical.
Quoridor
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Red moves his pawn down.
Quoridor
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Blue places a wall horizontally in front of red’s pawn.
Players are limited to ten walls.
Quoridor
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Red moves his pawn left, continuing on his shortest path
to his goal row.
Quoridor
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Blue places a wall to the left of red’s pawn, continuing
his devious wall-placing behavior.
Quoridor
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Blue eventually wins the game when he paths his pawn
to the opposite side of the board.
My Work
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
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Created an implementation of Quoridor
Implemented AI players using the
minimax algorithm
Modified minimax and AI strategies
Analyzed performance of computer players
against one another and against a random
player
Minimax

Minimax is a method
which finds the best
move by using adversarial
tree search.

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The game tree represents
every possible move for
both players.
Branching factor is the
number of moves at each
step (here, branching
factor = 3)
Static Evaluation
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In complex games, a depth limited search
will be used.
Upon reaching a depth cutoff, the search
will employ a static evaluation function.
This function must give a value to a game
state, often revolving around a board state
and the player to move.
Managing the Tree

Branching factor is initially 132.

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5 moves ahead: 132^5 = 40074642432
states
Minimax must be modified to make use of
a restricted move set.
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The branching factor can be reduced to a
manageable size of ~10.
5 moves ahead: 10^5 = 100000 states
Wall Selection
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Best strategy for shrinking the move set is
reducing the number of walls considered.
Use a heuristic to determine which.
Walls close to or directly next to the
opposing player are a way to prevent an
opponent’s quick victory.
Might not consider wall placements by the
opponent.
Problem
Problem
Problem
Solution
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Computer players may not consider wall
placements by the opponent.
Considerations should be made for
repeated states.
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Minimax can avoid repeating game states by
assigning undesirable values to them.
The game can prevent this by forcing a draw
after a certain number of repeated states.
Strategies and Evaluations
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Strategies for computer players were
reliant on their static evaluators.
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[P] Shortest path: Considered shortest path
values for both players.
[B] Bird’s eye: Considered the distance to the
goal row without regard to walls.
[C] Close distance: Only one player’s path.
[PR] Shortest path with random element
[BR] Bird’s eye with random element
Do We Consider Opponent’s Wall
Placement?
P, wall
B, wall C, wall PR,wall BR,wall
P, no
183
199
167
195
199
B, no
21
117
74
147
159
C, no
133
172
198
187
196
PR, no
23
82
74
136
133
BR, no
14
53
72
137
120

No.
AI Effectiveness
AI Outcomes
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Strategies with
random elements
were the worst,
followed by the bird’s
eye strategy.
Shortest path and
“close distance”
strategies
outperformed the
others.
P
B
C
PR BR
P
48 98 55 98 99
B
0
C
43 88 47 98 97
42 31 67 79
PR 1
32 0
48 55
BR 0
15 3
39 42
Data Trends
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AIs using wall heuristic not successful
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Repeated state flag generated more non-draw
outcomes
Shortest path was the most effective
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Considered walls that were not useful
Players not considering opponent’s walls were able to
path more successfully
Randomness added variation but often removed
effectiveness
References
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Abramson, B. 1989. Control strategies for two-player games. ACM
Comput. Surv. 21, 2 (Jun. 1989), 137-161. DOI=
http://doi.acm.org/10.1145/66443.66444
Thuente, D. J. and Jones, R. P. 1991. Beyond minimaxing for games
with draws. In Proceedings of the 19th Annual Conference on
Computer Science (San Antonio, Texas, United States). CSC '91.
ACM Press, New York, NY, 551-557. DOI=
http://doi.acm.org/10.1145/327164.328771
Slagle, J. R. and Dixon, J. E. 1969. Experiments With Some
Programs That Search Game Trees. J. ACM 16, 2 (Apr. 1969), 189207. DOI= http://doi.acm.org/10.1145/321510.321511
Previous Quoridor Software Work
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Xoridor (Java Quoridor Project)
Glendenning: Genetic algorithms research
Mertenz: AI Comparisons
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Used different board representation,
strategies, evaluations, and random elements