CS 61A Project 1 The Game of Hog

Introduction

Important submission note: For full credit:

Submit with Phase 1 complete by Tuesday, Feb 7, worth 1 pt.
Submit the complete project by Friday, Feb 10.

Try to attempt the problems in order, as some later problems will depend on
earlier problems in their implementation and therefore also when running ok

You may complete the project with a partner.

You can get 1 bonus point by submitting the entire project by Thursday, Feb 9
You can receive extensions on the project deadline and checkpoint
deadline, but not on the early deadline, unless you’re a DSP student with an
accommodation for assignment extensions.

In this project, you will develop a simulator and multiple strategies for the
dice game Hog. You will need to use control statements and higher-order
functions together, as described in Sections 1.2 through 1.6 of Composing
Programs, the online textbook.

When students in the past have tried to implement the functions without
thoroughly reading the problem description, they’ve often run into issues.
Read each description thoroughly before starting to code.

In Hog, two players alternate turns trying to be the first to end a turn with
at least GOAL total points, where GOAL defaults to 100. On each turn, the current player chooses some number
of dice to roll, up to 10. That player’s score for the turn is the sum of the
dice outcomes. However, a player who rolls too many dice risks:

Sow Sad. If any of the dice outcomes is a 1, the current player’s score
for the turn is 1.

Examples (enable JavaScript)

Example 1: The current player rolls 7 dice, 5 of which are 1’s. They
score 1 point for the turn.
Example 2: The current player rolls 4 dice, all of which are 3’s. Since
Sow Sad did not occur, they score 12 points for the turn.

In a normal game of Hog, those are all the rules. To spice up the game, we’ll
include some special rules:

Pig Tail. A player who chooses to roll zero dice scores
2 * abs(tens – ones) + 1 points; where tens, ones are the
tens and ones digits of the opponent’s score. The ones digit refers to the
rightmost digit and the tens digit refers to the second-rightmost digit.

Examples (enable JavaScript)

Example 1:

The opponent has 46 points, and the current player chooses to roll
zero dice. 2 * abs(4 – 6) + 1 = 5, so the player gains 5 points.

Example 2:

The opponent has 73 points, and the current player chooses to roll
zero dice. 2 * abs(7 – 3) + 1 = 9.

Square Swine. After a player gains points for their turn, if the
resulting score is a perfect square, then increase their score to the next
higher perfect square. A perfect square is any integer n where n = d * d for some integer d.

Examples (enable JavaScript)

Example 1:

A player has 12 points and rolls 3 dice that total 13 points. Their
new score would be 25, but since 25 is 5 squared, their score is
increased to 6 squared: 36.

Example 2:

A player has 12 points and rolls 3 dice that total 12 point. Their new
score would be 24, which is not a perfect square.

Example 3:

A player has 0 points and rolls 5 dice, but one is a 1, so their new
score would be 1. 1 is a perfect square, and so their score is
increased to 4.

Example 4:

A player has 80 points and rolls 10 dice, but three are 1’s, so their
new score would be 1. 81 is 9 squared, so their new score is 10
squared: 100. They win the game.

Download starter files

To get started, download all of the project code as a zip archive.
Below is a list of all the files you will see in the archive once unzipped.
For the project, you’ll only be making changes to hog.py.

hog.py: A starter implementation of Hog
dice.py: Functions for making and rolling dice
hog_gui.py: A graphical user interface (GUI) for Hog (updated)
ucb.py: Utility functions for CS 61A
hog_ui.py: A text-based user interface (UI) for Hog
ok: CS 61A autograder
tests: A directory of tests used by ok
gui_files: A directory of various things used by the web GUI

You may notice some files other than the ones listed above too—those are needed for making the autograder and portions of the GUI work. Please do not modify any files other than hog.py.

The project is worth 25 points, of which 1 point is for submitting
Phase 1 by the checkpoint date of Tuesday, Feb 7.

You will turn in the following files:

You do not need to modify or turn in any other files to complete the
project. To submit the project, submit the required files to the appropriate Gradescope assignment.

For the functions that we ask you to complete, there may be some
initial code that we provide. If you would rather not use that code,
feel free to delete it and start from scratch. You may also add new
function definitions as you see fit.

However, please do not modify any other functions or edit any files not
listed above. Doing so may result in your code failing our autograder tests.
Also, please do not change any function signatures (names, argument order, or
number of arguments).

Throughout this project, you should be testing the correctness of your code.
It is good practice to test often, so that it is easy to isolate any problems.
However, you should not be testing too often, to allow yourself time to
think through problems.

We have provided an autograder called ok to help you
with testing your code and tracking your progress. The first time you run the
autograder, you will be asked to log in with your Ok account using your web
browser. Please do so. Each time you run ok, it will back up
your work and progress on our servers.

The primary purpose of ok is to test your implementations.

If you want to test your code interactively, you can run

python3 ok -q [question number] -i

with the appropriate question number (e.g. 01) inserted.
This will run the tests for that question until the first one you failed,
then give you a chance to test the functions you wrote interactively.

You can also use the debugging print feature in OK by writing

print(“DEBUG:”, x)

which will produce an output in your terminal without causing OK tests to fail
with extra output.

Graphical User Interface

A graphical user interface (GUI, for short) is provided for you. At the moment, it doesn’t work because you haven’t implemented the game logic. Once you complete the play function, you will be able to play a fully interactive version of Hog!

Once you’ve done that, you can run the GUI from your terminal:

python3 hog_gui.py

Getting Started Videos

These videos may provide some helpful direction for tackling the coding
problems on this assignment.

To see these videos, you should be logged into your berkeley.edu email.

YouTube link

Phase 1: Rules of the Game

In the first phase, you will develop a simulator for the game of Hog.

Problem 0 (0 pt)

The dice.py file represents dice using non-pure zero-argument functions.
These functions are non-pure because they may have different return values each
time they are called, and so a side-effect of calling the function may be
changing what will happen when the function is called again. The documentation
of dice.py describes the two different types of dice used in the project:

Fair dice produce each possible outcome with equal probability. The
four_sided and six_sided functions are examples.
Test dice are deterministic: they always cycle through a fixed sequence
of values that are passed as arguments. Test dice are generated by the
make_test_dice function.

Before writing any code, read over the dice.py file and check your
understanding by unlocking the following tests.

python3 ok -q 00 -uCopy

This should display a prompt that looks like this:

=====================================================================
Assignment: Project 1: Hog Ok, version v1.18.1
=====================================================================

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Unlocking tests

At each “? “, type what you would expect the output to be. Type exit() to quit

———————————————————————
Question 0 > Suite 1 > Case 1
(cases remaining: 1)

>>> test_dice = make_test_dice(4, 1, 2)
>>> test_dice()

You should type in what you expect the output to be. To do so, you need to
first figure out what test_dice will do, based on the description above.

You can exit the unlocker by typing exit().

Typing Ctrl-C on Windows to exit out of the unlocker has been known to cause
problems, so avoid doing so.

Problem 1 (2 pt)

Implement the roll_dice function in hog.py. It takes two arguments: a
positive integer called num_rolls giving the number of dice to roll and a
dice function. It returns the number of points scored by rolling the dice
that number of times in a turn: either the sum of the outcomes or 1 (Sow

Sow Sad. If any of the dice outcomes is a 1, the current player’s score
for the turn is 1.

Examples (enable JavaScript)

To obtain a single outcome of a dice roll, call dice(). You should call
dice() exactly num_rolls times in the body of roll_dice.

Remember to call dice() exactly num_rolls times even if Sow Sad happens
in the middle of rolling. By doing so, you will correctly simulate rolling
all the dice together (and the user interface will work correctly).

Note: The roll_dice function, and many other functions throughout the
project, makes use of default argument values—you can see this in the
function heading:

def roll_dice(num_rolls, dice=six_sided): …

The argument dice=six_sided means that when roll_dice is called, the
dice argument is optional. If no value for dice is provided, then
six_sided is used by default.

For example, calling roll_dice(3, four_sided), or equivalently roll_dice(3,
dice=four_sided), simulates rolling 3 four-sided dice, while calling roll_dice(3)
simulates rolling 3 six-sided dice.

Understand the problem:

Before writing any code, unlock the tests to verify your understanding of the question:
python3 ok -q 01 -uCopy

Note: You will not be able to test your code using ok until you unlock
the test cases for the corresponding question.

Write code and check your work:

Once you are done unlocking, begin implementing your solution. You can check your correctness with:
python3 ok -q 01Copy

Debugging Tips (enable JavaScript)

Check out the Debugging Guide!

Debugging Tips

If the tests don’t pass, it’s time to debug. You can observe the behavior of
your function using Python directly. First, start the Python interpreter and
load the hog.py file.

python3 -i hog.py

Then, you can call your roll_dice function on any number of dice you want.
The roll_dice function has a default argument value for dice that is a
random six-sided dice function. Therefore, the following call to roll_dice
simulates rolling four fair six-sided dice.

>>> roll_dice(4)

You will find that the previous expression may have a different result each
time you call it, since it is simulating random dice rolls. You can also use
test dice that fix the outcomes of the dice in advance. For example, rolling
twice when you know that the dice will come up 3 and 4 should give a total
outcome of 7.

>>> fixed_dice = make_test_dice(3, 4) roll_dice(2, fixed_dice)

On most systems, you can evaluate the same expression again by pressing the
up arrow, then pressing enter or return. To evaluate earlier commands, press
the up arrow repeatedly.

If you find a problem, you first need to change your hog.py file to fix the
problem, and save the file. Then, to check whether your fix works, you’ll
have to quit the Python interpreter by either using exit() or Ctrl^D, and
re-run the interpreter to test the changes you made. Pressing the up arrow in
both the terminal and the Python interpreter should give you access to your
previous expressions, even after restarting Python.

[default argument value]:
http://composingprograms.com/pages/14-designing-functions.html#default-argument-values

Continue debugging your code and running the ok tests until they all pass.

One more debugging tip: to start the interactive interpreter automatically
upon failing an ok test, use -i. For example, python3 ok -q 01 -i will
run the tests for question 1, then start an interactive interpreter with
hog.py loaded if a test fails.

Problem 2 (2 pt)

Implement tail_points, which takes the player’s opponent’s current score
opponent_score, and returns the number of points scored by Pig Tail when the
player rolls 0 dice.

Examples (enable JavaScript)

Example 1:

The opponent has 46 points, and the current player chooses to roll
zero dice. 2 * abs(4 – 6) + 1 = 5, so the player gains 5 points.

Example 2:

The opponent has 73 points, and the current player chooses to roll
zero dice. 2 * abs(7 – 3) + 1 = 9.

Don’t assume that scores are below 100. Write your tail_points function so
that it works correctly for any non-negative score.

Important: Your implementation should not use str, lists, or
contain square brackets [ ]. The test cases will check if those have
been used.

Before writing any code, unlock the tests to verify your understanding of the question:
python3 ok -q 02 -uCopy

Once you are done unlocking, begin implementing your solution. You can check your correctness with:
python3 ok -q 02Copy

You can also test tail_points interactively by running python3 -i hog.py
from the terminal and calling tail_points on various inputs.

Problem 3 (2 pt)

Implement the take_turn function, which returns the number of points scored
for a turn by rolling the given dice num_rolls times.

Your implementation of take_turn should call both roll_dice and
tail_points rather than repeating their implementations.

Before writing any code, unlock the tests to verify your understanding of the question:
python3 ok -q 03 -uCopy

Once you are done unlocking, begin implementing your solution. You can check your correctness with:
python3 ok -q 03Copy

Problem 4 (1 pt)

Add functions perfect_square and next_perfect_square so that
square_update returns a player’s total score after they roll num_rolls. You
do not need to edit the body of square_update.

Examples (enable JavaScript)

Example 1:

A player has 12 points and rolls 3 dice that total 13 points. Their
new score would be 25, but since 25 is 5 squared, their score is
increased to 6 squared: 36.

Example 2:

A player has 12 points and rolls 3 dice that total 12 point. Their new
score would be 24, which is not a perfect square.

Example 3:

A player has 0 points and rolls 5 dice, but one is a 1, so their new
score would be 1. 1 is a perfect square, and so their score is
increased to 4.

Example 4:

A player has 80 points and rolls 10 dice, but three are 1’s, so their
new score would be 1. 81 is 9 squared, so their new score is 10
squared: 100. They win the game.

Before writing any code, unlock the tests to verify your understanding of the question:
python3 ok -q 04 -uCopy

Once you are done unlocking, begin implementing your solution. You can check your correctness with:
python3 ok -q 04Copy

Problem 5 (5 pt)

Implement the play function, which simulates a full game of Hog. Players take
turns rolling dice until one of the players reaches the goal score, and the
final scores of both players are returned by the function.

To determine how many dice are rolled each turn, call the current player’s
strategy function (Player 0 uses strategy0 and Player 1 uses strategy1). A
strategy is a function that, given a player’s score and their opponent’s
score, returns the number of dice that the current player will roll in the
turn. An example strategy is always_roll_5 which appears above play.

To determine the updated score for a player after they take a turn, call the
update function. An update function takes the number
of dice to roll, the current player’s score, the opponent’s score, and the
dice function used to simulate rolling dice. It returns the updated score
of the current player after they take their turn. Two examples of update functions
are simple_update andsquare_update.

If a player achieves the goal score by the end of their turn, i.e. after all
applicable rules have been applied, the game ends. play will then return the
final total scores of both players, with Player 0’s score first and Player 1’s
score second.

Some example calls to play are:

play(always_roll_5, always_roll_5, simple_update) simulates two players
that both always roll 5 dice each turn, playing with just the Sow Sad and Pig
Tail rules.
play(always_roll_5, always_roll_5, square_update) simulates two players
that both always roll 5 dice each turn, playing with the Square Swine rule in
addition to the Sow Sad and Pig Tail rules (i.e. all the rules).

Important: For the user interface to work, a strategy function should be
called only once per turn. Only call strategy0 when it is Player 0’s turn
and only call strategy1 when it is Player 1’s turn.

If who is the current player, the next player is 1 – who.
To call play(always_roll_5, always_roll_5, square_update) and print out
what happens each turn, run python3 hog_ui.py from the terminal.

Before writing any code, unlock the tests to verify your understanding of the question:
python3 ok -q 05 -uCopy

Once you are done unlocking, begin implementing your solution. You can check your correctness with:
python3 ok -q 05Copy

Check to make sure that you completed all the problems in Phase 1:

python3 ok –score

Then, submit your work to Gradescope before the checkpoint deadline:

When you run ok commands, you’ll still see that some tests are locked
because you haven’t completed the whole project yet. You’ll get full credit for
the checkpoint if you complete all the problems up to this point.

Congratulations! You have finished Phase 1 of this project!

Interlude: User Interfaces

There are no required problems in this section of the project, just some
examples for you to read and understand. See Phase 2 for the remaining
project problems.

Printing Game Events

We have built a simulator for the game, but haven’t added any code to describe
how the game events should be displayed to a person. Therefore, we’ve built a
computer game that no one can play. (Lame!)

However, the simulator is expressed in terms of small functions, and we can
replace each function by a version that prints out what happens when it is
called. Using higher-order functions, we can do so without changing much of our
original code. An example appears in hog_ui.py, which you are encouraged to

The play_and_print function calls the same play function just implemented,
but using:

new strategy functions (e.g., printing_strategy(0, always_roll_5)) that
print out the scores and number of dice rolled.
a new update function (square_update_and_print) that prints the outcome of
each turn.
a new dice function (printing_dice(six_sided)) that prints the outcome of
rolling the dice.

Notice how much of the original simulator code can be reused.

Running python3 hog_ui.py from the terminal calls
play_and_print(always_roll_5, always_roll_5).

Accepting User Input

The built-in input function waits for the user to type a line of text and
then returns that text as a string. The built-in int function can take a
string containing the digits of an integer and return that integer.

The interactive_strategy function returns a strategy that let’s a person
choose how many dice to roll each turn by calling input.

With this strategy, we can finally play a game using our play function:

Running python3 hog_ui.py -n 1 from the terminal calls
play_and_print(interactive_strategy(0), always_roll_5), which plays a game
betweem a human (Player 0) and a computer strategy that always rolls 5.

Running python3 hog_ui.py -n 2 from the terminal calls
play_and_print(interactive_strategy(0), interactive_strategy(1)), which plays
a game between two human players.

You are welcome to change hog_ui.py in any way you want, for example to use
different strategies than always_roll_5.

Graphical User Interface (GUI)

We have also provided a web-based graphical user interface for the game using a similar approach as hog_ui.py called hog_gui.py. You can run it from the terminal:

python3 hog_gui.py

Like hog_ui.py, the GUI relies on your simulator implementation, so if you have any bugs in your code, they will be reflected in the GUI. This means you can also use the GUI as a debugging tool; however, it’s better to run the tests first.

The source code for the Hog GUI is publicly available on Github but involves several other programming languages: Javascript, HTML, and CSS.

Phase 2: Strategies

In this phase, you will experiment with ways to improve upon the basic
strategy of always rolling five dice. A strategy is a function that
takes two arguments: the current player’s score and their opponent’s score. It
returns the number of dice the player will roll, which can be from 0 to 10
(inclusive).

Problem 6 (2 pt)

Implement always_roll, a higher-order function that takes a number of dice
n and returns a strategy that always rolls n dice. Thus, always_roll(5)
would be equivalent to always_roll_5.

Before writing any code, unlock the tests to verify your understanding of the question:
python3 ok -q 06 -uCopy

Once you are done unlocking, begin implementing your solution. You can check your correctness with:
python3 ok -q 06Copy

Problem 7 (2 pt)

A strategy only has a fixed number of possible argument values. In a game to
100, there are 100 possible score values (0-99) and 100 possible
opponent_score values (0-99), giving 10,000 possible argument combinations.

Implement is_always_roll, which takes a strategy and returns whether that
strategy always rolls the same number of dice for every possible argument
combination.

Before writing any code, unlock the tests to verify your understanding of the question:
python3 ok -q 07 -uCopy

Once you are done unlocking, begin implementing your solution. You can check your correctness with:
python3 ok -q 07Copy

Problem 8 (2 pt)

Implement make_averaged, which is a higher-order function that
takes a function original_function as an argument.

The return value of make_averaged is a function that takes in the same
number of arguments as original_function. When we call this returned function
on the arguments, it will return the average value of repeatedly calling
original_function on the arguments passed in.

Specifically, this function should call original_function a total of
total_samples times and return the average of the results of these calls.

Important:
To implement this function, you will need to use a new piece of Python syntax.
We would like to write a function that accepts an arbitrary number of arguments,
and then calls another function using exactly those arguments. Here’s how

Instead of listing formal parameters for a function, you can write *args,
which represents all of the arguments that get passed into the
function. We can then call another function with these same arguments by
passing these *args into this other function. For example:

>>> def printed(f):
… def print_and_return(*args):
… result = f(*args)
… print(‘Result:’, result)
… return result
… return print_and_return
>>> printed_pow = printed(pow)
>>> printed_pow(2, 8)
Result: 256
>>> printed_abs = printed(abs)
>>> printed_abs(-10)
Result: 10

Here, we can pass any number of arguments into print_and_return via the
*args syntax. We can also use *args inside our print_and_return
function to make another function call with the same arguments.

Before writing any code, unlock the tests to verify your understanding of the question:
python3 ok -q 08 -uCopy

Once you are done unlocking, begin implementing your solution. You can check your correctness with:
python3 ok -q 08Copy

Problem 9 (2 pt)

Implement max_scoring_num_rolls, which runs an experiment to
determine the number of rolls (from 1 to 10) that gives the maximum average
score for a turn. Your implementation should use make_averaged and
roll_dice.

If two numbers of rolls are tied for the maximum average score, return the
lower number. For example, if both 3 and 6 achieve a maximum average score,

You might find it useful to read the doctest and the example shown in the doctest
for this problem before doing the unlocking test.

Important: In order to pass all of our tests, please make sure that you are
testing dice rolls starting from 1 going up to 10, rather than from 10 to 1.

Before writing any code, unlock the tests to verify your understanding of the question:
python3 ok -q 09 -uCopy

Once you are done unlocking, begin implementing your solution. You can check your correctness with:
python3 ok -q 09Copy

Running Experiments

The provided run_experiments function calls
max_scoring_num_rolls(six_sided) and prints the result. You will likely find
that rolling 6 dice maximizes the result of roll_dice using six-sided dice.

To call this function and see the result, run hog.py with the -r flag:

python3 hog.py -r

In addition, run_experiments compares various strategies to always_roll(6).
You are welcome to change the implementation of run_experiments as you wish.
Note that running experiments with tail_strategy and square_strategy will not
have accurate results until you implement them in the next two problems.

Some of the experiments may take up to a minute to run. You can always reduce
the number of trials in your call to make_averaged to speed up experiments.

Running experiments won’t affect your score on the project.

Problem 10 (2 pt)

A strategy can try to take advantage of the Pig Tail rule by rolling 0 when
it is most beneficial to do so. Implement tail_strategy, which returns 0
whenever rolling 0 would give at least threshold points and returns
num_rolls otherwise. This strategy should not also take into account
the Square Swine rule.

Hint: You can use the tail_points function you defined in Problem 2.

Before writing any code, unlock the tests to verify your understanding of the question:
python3 ok -q 10 -uCopy

Once you are done unlocking, begin implementing your solution. You can check your correctness with:
python3 ok -q 10Copy

You should find that running python3 hog.py -r now shows a win rate for
tail_strategy close to 57%.

Problem 11 (2 pt)

A better strategy will take advantage of both Pig Tail and Square Swine in
combination. Even a small number of pig tail points can lead to large gains.
For example, if a player has 31 points and their opponent has 42, rolling 0
would bring them to 36 which is a perfect square, and so they would end the
turn with 49 points: a gain of 49 – 31 = 18!

The square_strategy returns 0 whenever rolling 0 would result in a score that
is at least threshold points more than the player’s score at the
start of turn.

Hint: You can use the square_update function.

Before writing any code, unlock the tests to verify your understanding of the question:
python3 ok -q 11 -uCopy

Once you are done unlocking, begin implementing your solution. You can check your correctness with:
python3 ok -q 11Copy

You should find that running python3 hog.py -r now shows a win rate for
square_strategy close to 62%.

Optional: Problem 12 (0 pt)

Implement final_strategy, which combines these ideas and any other ideas you
have to achieve a high win rate against the baseline strategy. Some
suggestions:

If you know the goal score (by default it is 100), there’s no benefit to
scoring more than the goal. Check whether you can win by rolling 0, 1 or 2
dice. If you are in the lead, you might decide to take fewer risks.
Instead of using a threshold, roll 0 whenever it would give you more points
on average than rolling 6.

You can check that your final strategy is valid by running ok.

python3 ok -q 12Copy

Project submission

Run ok on all problems to make sure all tests are unlocked and pass:

python3 ok

You can also check your score on each part of the project:

python3 ok –score

Once you are satisfied, submit this assignment by uploading hog.py to Gradescope. For a refresher on how to do this, refer to Lab 00.

You can add a partner to your Gradescope submission by clicking on + Add Group Member under your name on the right hand side of your submission. O