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Adversarial Search: 2048 game
Adversarial Search: 2048 game
INSTRUCTIONS
In this assignment you will create an agent to intelligently play the 2048-puzzle game, using
more advanced techniques to probe the search space than the simple methods used in the
previous assignment. If you have not played the game before, you may do so
at gabrielecirulli.github.io/2048 to get a sense of how the game works. You will implement
an adversarial search algorithm that plays the game intelligently, perhaps much more
so than playing by hand. Please read all sections of the instructions carefully.
I. Introduction
II. Algorithm Review
III. Using The Skeleton Code
IV. What You Need To Submit
V. Important Information
VI. Before You Submit
I. Introduction
An instance of the 2048-puzzle game is played on a 4×4 grid, with numbered tiles that slide
in all four directions when a player moves them. Every turn, a new tile will randomly
appear in an empty spot on the board, with a value of either 2 or 4. Per the input direction
given by the player, all tiles on the grid slide as far as possible in that direction, until they
either (1) collide with another tile, or (2) collide with the edge of the grid. If two tiles of the
same number collide while moving, they will merge into a single tile, valued at the sum of
the two original tiles that collided. The resulting tile cannot merge with another tile again in
the same move.
In the first assignment, you had ample experience with the process of abstracting ideas and
designing functions, classes, and data structures. The goal was to get familiar with how
objects, states, nodes, functions, and implicit or explicit search trees are implemented and
interact in practice. This time, the focus is strictly on the ground-level details of the
algorithms. You will be provided with all the skeleton code necessary to get started, so that
you can focus solely on optimizing your algorithm.
With typical board games like chess, the two players in the game (i.e. the "Computer AI"
and the "Player") take similar actions in their turn, and have similar objectives to achieve in
the game. In the 2048-puzzle game, the setup is inherently asymmetric; that is, the computer
and player take drastically different actions in their turns. Specifically, the computer is
responsible for placing random tiles of 2 or 4 on the board, while the player is responsible
for moving the pieces. However, adversarial search can be applied to this game just the
same.
II. Algorithm Review
Before you begin, review the lecture slides on adversarial search. Is this a zero-sum game?
What is the minimax principle? In the 2048-puzzle game, the computer AI is technically not
"adversarial". In particular, all it does is spawn random tiles of 2 and 4 each turn, with a
designated probability of either a 2 or a 4; it certainly does not specifically spawn tiles at the
most inopportune locations to foil the player's progress. However, we will create a "Player
AI" to play as if the computer is completely adversarial. In particular, we will employ
the minimax algorithm in this assignment.
Remember, in game-playing we generally pick a strategy to employ. With the minimax
algorithm, the strategy assumes that the computer opponent is perfect in minimizing the
player's outcome. Whether or not the opponent is actually perfect in doing so is another
question. As a general principle, how far the actual opponent's actual behavior deviates
from the assumption certainly affects how well the AI performs [1]. However, you will see
that this strategy works well in this game. In this assignment, we will implement and
optimize the minimax algorithm.
.
[1] As we saw in the case of a simple game of tic-tac-toe, it is useful to employ the minimax
algorithm, which assumes that the opponent is a perfect "minimizing" agent. In practice,
however, we may encounter a sub-par opponent that makes silly moves. When this
happens, the algorithm's assumption deviates from the actual opponent's behavior. In this
case, it still leads to the desired outcome of never losing. However, if the deviation goes the
other way (e.g. suppose we employ a "maximax" algorithm that assumes that the opponent
wants us to win), then the outcome would certainly be different.
III. Using The Skeleton Code
To let you focus on the details of the algorithm, a skeleton code is provided to help you get
started, and to allow you to test your algorithm on your own. The skeleton code includes
the following files. Note that you will only be working in one of them, and the rest of them
are read-only:
• Read-only: GameManager.py. This is the driver program that loads your Computer AI and
Player AI, and begins a game where they compete with each other. See below on how to
execute this program.
• Read-only: Grid.py. This module defines the Grid object, along with some useful
operations: move(), getAvailableCells(), insertTile(), and clone(), which you may use in your
code. These are available to get you started, but they are by no means the most efficient
methods available. If you wish to strive for better performance, feel free to ignore these and
write your own helper methods in a separate file.
• Read-only: BaseAI.py. This is the base class for any AI component. All AIs inherit from this
module, and implement the getMove() function, which takes a Grid object as parameter and
returns a move (there are different "moves" for different AIs).
• Read-only: ComputerAI.py. This inherits from BaseAI. The getMove() function returns a
computer action that is a tuple (x, y) indicating the place you want to place a tile.
• Writable: PlayerAI.py. You will create this file, and this is where you will be doing your
work. This should inherit from BaseAI. ThegetMove() function, which you will need to
implement, returns a number that indicates the player’s action. In particular, 0 stands for
"Up", 1 stands for "Down", 2 stands for "Left", and 3 stands for "Right". You need to
create this file and make it as intelligent as possible. You may include other files in your
submission, but they will have to be included through this file.
• Read-only: BaseDisplayer.py and Displayer.py. These print the grid.
.
To test your code, execute the game manager like so:
$ python GameManager.py
The progress of the game will be displayed on your terminal screen, with one snapshot
printed after each move that the Computer AI or Player AI makes. The Player AI is
allowed 0.2 seconds to come up with each move. The process continues until the game is
over; that is, until no further legal moves can be made. At the end of the game,
the maximum tile value on the board is printed.
IMPORTANT: Do not modify the files that are specified as read-only. When your
submission is graded, the grader will first automatically over-write all read-only files in the
directory before executing your code. This is to ensure that all students are using the same
game-play mechanism and computer opponent, and that you cannot "work around" the
skeleton program and manually output a high score.
IV. What You Need To Submit
Your job in this assignment is to write PlayerAI.py, which intelligently plays the 2048-
puzzle game. Here is a snippet of starter code to allow you to observe how the game looks
when it is played out. In the following "naive" Player AI. The getMove() function simply
selects a next move in random out of the available moves:
from random import randint
from BaseAI import BaseAI
class PlayerAI(BaseAI):
def getMove(self, grid):
moves = grid.getAvailableMoves()
return moves[randint(0, len(moves) - 1)] if moves else None
Of course, that is indeed a very naive way to play the 2048-puzzle game. If you submit this
as your finished product, you will likely receive a low grade. You should implement your
Player AI with the following points in mind:
• Employ the minimax algorithm. This is a requirement. There are many viable strategies to
beat the 2048-puzzle game, but in this assignment we will be practicing with the minimax
algorithm.
• Implement alpha-beta pruning. This is a requirement. This should speed up the search
process by eliminating irrelevant branches. In this case, is there anything we can do about
move ordering?
• Use heuristic functions. What is the maximum height of the game tree? Unlike elementary
games like tic-tac-toe, in this game it is highly impracticable to search the entire depth of the
theoretical game tree. To be able to cut off your search at any point, you must
employ heuristic functions to allow you to assign approximate values to nodes in the tree.
Remember, the time limit allowed for each move is 0.2 seconds, so you must implement a
systematic way to cut off your search before time runs out.
• Assign heuristic weights. You will likely want to include more than one heuristic function.
In that case, you will need to assign weights associated with each individual heuristic.
Deciding on an appropriate set of weights will take careful reasoning, along with
careful experimentation. If you feel adventurous, you can also simply write an optimization
meta-algorithm to iterate over the space of weight vectors, until you arrive at results that
you are happy enough with.
V. Important Information
Please read the following information carefully. Before you post a clarifying question on the
discussion board, make sure that your question is not already answered in the following
sections.
1. Note on Python 3
.
Each file in the skeleton code actually comes in two flavors: [filename].py (written in
Python 2) and [filename]_3.py (written in Python 3). If you prefer to develop in Python 3,
you will be using the latter version of each file in the skeleton code provided. In addition,
you will have to name your player AI file PlayerAI_3.py as well, so that the grader will be
alerted to use the correct version of Python during grading. For grading purposes, please
only submit one of the following, but not both:
• PlayerAI.py (developed in Python 2, and relying on the Python 2 version of each skeleton
code file), or
• PlayerAI_3.py (developed in Python 3, and relying on the Python 3 version of each skeleton
code file).
If you submit both versions, the grader will only grade one of them, which probably not
what you would want. To test your algorithm in Python 3, execute the game manager like
so:
$ python3 GameManager_3.py
2. Basic Requirements
Your submission must fulfill the following requirements:
• You must use adversarial search in your PlayerAI (minimax with alpha-beta pruning).
• You must provide your move within the time limit of 0.2 seconds.
• You must name your file PlayerAI.py (Python 2) or PlayerAI_3.py (Python 3).
• Your grade will depend on the maximum tile values your program usually gets to.
3. Grading Submissions
Grading is exceptionally straightforward for this project: the better your Player AI
performs, the higher your grade. While this is straightforward, we admit that this
Adversarial Search project is the most difficult project in this class because of its openendedness. Your Player AI will be pitted against the standard Computer AI for a total
of 10 games, and the maximum tile value of each game will be recorded. Among the 10
runs, we pick and average top 5 maximum tile values. Based on the average of these 5
maximum tile values, your submission will be assessed out of a total of 100 points.
• Submissions that are no better than random will receive a score of zero.
• Submissions which contains two 1024 runs and three 2048 runs will receive full
credit. For example, [256, 512, 512, 512, 1024, 1024, 1024, 2048, 2048, 2048] will receive full
credit.
• Submissions that fall somewhere in between will receive partial credit on
a logarithmic scale. That is, every time you manage to double your average maximum tile
value, you will be moving your final grade up in equally-spaced notches (instead of
doubling as well). For other credit examples, please see the FAQs.
VI. Before You Submit
• Make sure your code executes. In particular, make sure you name your file correctly
according to the instructions specified above, especially regarding different Python
versions.
• Make sure your PlayerAI.py does not print anything to the screen. Printing gameplay
progress is handled by Grid.py, and there should ideally be nothing else printed.
INSTRUCTIONS
In this assignment you will create an agent to intelligently play the 2048-puzzle game, using
more advanced techniques to probe the search space than the simple methods used in the
previous assignment. If you have not played the game before, you may do so
at gabrielecirulli.github.io/2048 to get a sense of how the game works. You will implement
an adversarial search algorithm that plays the game intelligently, perhaps much more
so than playing by hand. Please read all sections of the instructions carefully.
I. Introduction
II. Algorithm Review
III. Using The Skeleton Code
IV. What You Need To Submit
V. Important Information
VI. Before You Submit
I. Introduction
An instance of the 2048-puzzle game is played on a 4×4 grid, with numbered tiles that slide
in all four directions when a player moves them. Every turn, a new tile will randomly
appear in an empty spot on the board, with a value of either 2 or 4. Per the input direction
given by the player, all tiles on the grid slide as far as possible in that direction, until they
either (1) collide with another tile, or (2) collide with the edge of the grid. If two tiles of the
same number collide while moving, they will merge into a single tile, valued at the sum of
the two original tiles that collided. The resulting tile cannot merge with another tile again in
the same move.
In the first assignment, you had ample experience with the process of abstracting ideas and
designing functions, classes, and data structures. The goal was to get familiar with how
objects, states, nodes, functions, and implicit or explicit search trees are implemented and
interact in practice. This time, the focus is strictly on the ground-level details of the
algorithms. You will be provided with all the skeleton code necessary to get started, so that
you can focus solely on optimizing your algorithm.
With typical board games like chess, the two players in the game (i.e. the "Computer AI"
and the "Player") take similar actions in their turn, and have similar objectives to achieve in
the game. In the 2048-puzzle game, the setup is inherently asymmetric; that is, the computer
and player take drastically different actions in their turns. Specifically, the computer is
responsible for placing random tiles of 2 or 4 on the board, while the player is responsible
for moving the pieces. However, adversarial search can be applied to this game just the
same.
II. Algorithm Review
Before you begin, review the lecture slides on adversarial search. Is this a zero-sum game?
What is the minimax principle? In the 2048-puzzle game, the computer AI is technically not
"adversarial". In particular, all it does is spawn random tiles of 2 and 4 each turn, with a
designated probability of either a 2 or a 4; it certainly does not specifically spawn tiles at the
most inopportune locations to foil the player's progress. However, we will create a "Player
AI" to play as if the computer is completely adversarial. In particular, we will employ
the minimax algorithm in this assignment.
Remember, in game-playing we generally pick a strategy to employ. With the minimax
algorithm, the strategy assumes that the computer opponent is perfect in minimizing the
player's outcome. Whether or not the opponent is actually perfect in doing so is another
question. As a general principle, how far the actual opponent's actual behavior deviates
from the assumption certainly affects how well the AI performs [1]. However, you will see
that this strategy works well in this game. In this assignment, we will implement and
optimize the minimax algorithm.
.
[1] As we saw in the case of a simple game of tic-tac-toe, it is useful to employ the minimax
algorithm, which assumes that the opponent is a perfect "minimizing" agent. In practice,
however, we may encounter a sub-par opponent that makes silly moves. When this
happens, the algorithm's assumption deviates from the actual opponent's behavior. In this
case, it still leads to the desired outcome of never losing. However, if the deviation goes the
other way (e.g. suppose we employ a "maximax" algorithm that assumes that the opponent
wants us to win), then the outcome would certainly be different.
III. Using The Skeleton Code
To let you focus on the details of the algorithm, a skeleton code is provided to help you get
started, and to allow you to test your algorithm on your own. The skeleton code includes
the following files. Note that you will only be working in one of them, and the rest of them
are read-only:
• Read-only: GameManager.py. This is the driver program that loads your Computer AI and
Player AI, and begins a game where they compete with each other. See below on how to
execute this program.
• Read-only: Grid.py. This module defines the Grid object, along with some useful
operations: move(), getAvailableCells(), insertTile(), and clone(), which you may use in your
code. These are available to get you started, but they are by no means the most efficient
methods available. If you wish to strive for better performance, feel free to ignore these and
write your own helper methods in a separate file.
• Read-only: BaseAI.py. This is the base class for any AI component. All AIs inherit from this
module, and implement the getMove() function, which takes a Grid object as parameter and
returns a move (there are different "moves" for different AIs).
• Read-only: ComputerAI.py. This inherits from BaseAI. The getMove() function returns a
computer action that is a tuple (x, y) indicating the place you want to place a tile.
• Writable: PlayerAI.py. You will create this file, and this is where you will be doing your
work. This should inherit from BaseAI. ThegetMove() function, which you will need to
implement, returns a number that indicates the player’s action. In particular, 0 stands for
"Up", 1 stands for "Down", 2 stands for "Left", and 3 stands for "Right". You need to
create this file and make it as intelligent as possible. You may include other files in your
submission, but they will have to be included through this file.
• Read-only: BaseDisplayer.py and Displayer.py. These print the grid.
.
To test your code, execute the game manager like so:
$ python GameManager.py
The progress of the game will be displayed on your terminal screen, with one snapshot
printed after each move that the Computer AI or Player AI makes. The Player AI is
allowed 0.2 seconds to come up with each move. The process continues until the game is
over; that is, until no further legal moves can be made. At the end of the game,
the maximum tile value on the board is printed.
IMPORTANT: Do not modify the files that are specified as read-only. When your
submission is graded, the grader will first automatically over-write all read-only files in the
directory before executing your code. This is to ensure that all students are using the same
game-play mechanism and computer opponent, and that you cannot "work around" the
skeleton program and manually output a high score.
IV. What You Need To Submit
Your job in this assignment is to write PlayerAI.py, which intelligently plays the 2048-
puzzle game. Here is a snippet of starter code to allow you to observe how the game looks
when it is played out. In the following "naive" Player AI. The getMove() function simply
selects a next move in random out of the available moves:
from random import randint
from BaseAI import BaseAI
class PlayerAI(BaseAI):
def getMove(self, grid):
moves = grid.getAvailableMoves()
return moves[randint(0, len(moves) - 1)] if moves else None
Of course, that is indeed a very naive way to play the 2048-puzzle game. If you submit this
as your finished product, you will likely receive a low grade. You should implement your
Player AI with the following points in mind:
• Employ the minimax algorithm. This is a requirement. There are many viable strategies to
beat the 2048-puzzle game, but in this assignment we will be practicing with the minimax
algorithm.
• Implement alpha-beta pruning. This is a requirement. This should speed up the search
process by eliminating irrelevant branches. In this case, is there anything we can do about
move ordering?
• Use heuristic functions. What is the maximum height of the game tree? Unlike elementary
games like tic-tac-toe, in this game it is highly impracticable to search the entire depth of the
theoretical game tree. To be able to cut off your search at any point, you must
employ heuristic functions to allow you to assign approximate values to nodes in the tree.
Remember, the time limit allowed for each move is 0.2 seconds, so you must implement a
systematic way to cut off your search before time runs out.
• Assign heuristic weights. You will likely want to include more than one heuristic function.
In that case, you will need to assign weights associated with each individual heuristic.
Deciding on an appropriate set of weights will take careful reasoning, along with
careful experimentation. If you feel adventurous, you can also simply write an optimization
meta-algorithm to iterate over the space of weight vectors, until you arrive at results that
you are happy enough with.
V. Important Information
Please read the following information carefully. Before you post a clarifying question on the
discussion board, make sure that your question is not already answered in the following
sections.
1. Note on Python 3
.
Each file in the skeleton code actually comes in two flavors: [filename].py (written in
Python 2) and [filename]_3.py (written in Python 3). If you prefer to develop in Python 3,
you will be using the latter version of each file in the skeleton code provided. In addition,
you will have to name your player AI file PlayerAI_3.py as well, so that the grader will be
alerted to use the correct version of Python during grading. For grading purposes, please
only submit one of the following, but not both:
• PlayerAI.py (developed in Python 2, and relying on the Python 2 version of each skeleton
code file), or
• PlayerAI_3.py (developed in Python 3, and relying on the Python 3 version of each skeleton
code file).
If you submit both versions, the grader will only grade one of them, which probably not
what you would want. To test your algorithm in Python 3, execute the game manager like
so:
$ python3 GameManager_3.py
2. Basic Requirements
Your submission must fulfill the following requirements:
• You must use adversarial search in your PlayerAI (minimax with alpha-beta pruning).
• You must provide your move within the time limit of 0.2 seconds.
• You must name your file PlayerAI.py (Python 2) or PlayerAI_3.py (Python 3).
• Your grade will depend on the maximum tile values your program usually gets to.
3. Grading Submissions
Grading is exceptionally straightforward for this project: the better your Player AI
performs, the higher your grade. While this is straightforward, we admit that this
Adversarial Search project is the most difficult project in this class because of its openendedness. Your Player AI will be pitted against the standard Computer AI for a total
of 10 games, and the maximum tile value of each game will be recorded. Among the 10
runs, we pick and average top 5 maximum tile values. Based on the average of these 5
maximum tile values, your submission will be assessed out of a total of 100 points.
• Submissions that are no better than random will receive a score of zero.
• Submissions which contains two 1024 runs and three 2048 runs will receive full
credit. For example, [256, 512, 512, 512, 1024, 1024, 1024, 2048, 2048, 2048] will receive full
credit.
• Submissions that fall somewhere in between will receive partial credit on
a logarithmic scale. That is, every time you manage to double your average maximum tile
value, you will be moving your final grade up in equally-spaced notches (instead of
doubling as well). For other credit examples, please see the FAQs.
VI. Before You Submit
• Make sure your code executes. In particular, make sure you name your file correctly
according to the instructions specified above, especially regarding different Python
versions.
• Make sure your PlayerAI.py does not print anything to the screen. Printing gameplay
progress is handled by Grid.py, and there should ideally be nothing else printed.
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