Project 1: The Game of Hog

• hog.zip

Introduction

Important submission note: For full credit:

• Submit with Phase 1 complete by Thursday, June 27, worth 1 pt.
• Submit the complete project by Tuesday, July 2.

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 tests.

You may complete the project with a partner.

You can get 1 bonus point by submitting the entire project by Monday, July 1. 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.

Rules

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 together, 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, regardless of the other values rolled.

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

• Boar Brawl. A player who chooses to roll zero dice scores three times the absolute difference between the tens digit of the opponent’s score and the ones digit of the current player’s score, or 1, whichever is greater. The ones digit refers to the rightmost digit and the tens digit refers to the second-rightmost digit. If a player's score is a single digit (less than 10), the tens digit of that player's score is 0.

• Sus Fuss. We call a number sus if it has exactly 3 or 4 factors, including 1 and the number itself. If, after rolling, the current player's score is a sus number, their score instantly increases to the next prime number.

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.

Logistics

The project is worth 25 points, of which 1 point is for submitting Phase 1 by the checkpoint date of Thursday, June 27.

You will turn in the following files:

• hog.py

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 

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

 print("DEBUG:", x) 

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 and play Hog in your browser:

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 is changing what will be returned when the function is called again.

Here's the documentation from dice.py that you need to read in order to simulate dice in this project.

A dice function takes no arguments and returns a number from 1 to n
(inclusive), where n is the number of sides on the dice.

Fair dice produce each possible outcome with equal probability.
Two fair dice are already defined, four_sided and six_sided,
and are generated by the make_fair_dice function.

def make_fair_dice(sides):
    """Return a die that generates values ranging from 1 to SIDES, each with an equal chance."""
    ...

four_sided = make_fair_dice(4)
six_sided = make_fair_dice(6)

Test dice are deterministic: they always cycles through a fixed
sequence of values that are passed as arguments.
Test dice are generated by the make_test_dice function.

def make_test_dice(...):
    """Return a die that cycles deterministically through OUTCOMES.

    >>> dice = make_test_dice(1, 2, 3)
    >>> dice()
    1
    >>> dice()
    2
    >>> dice()
    3
    >>> dice()
    1
    >>> dice()
    2

Check your understanding by unlocking the following tests.

python3 ok -q 00 -u
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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, which specifies the number of times to roll a die, and a dice function. It returns the number of points scored by rolling the die that number of times in a turn: either the sum of the outcomes or 1 (Sow Sad).

• Sow Sad. If any of the dice outcomes is a 1, the current player's score for the turn is 1, regardless of the other values rolled.

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 indicates that the dice parameter in the roll_dice function is optional. If no value is provided for dice, then six_sided will be used by default.

For example, calling roll_dice(3, four_sided), simulates rolling 3 four-sided dice, while calling roll_dice(3) simulates rolling 3 six-sided dice due to the default argument.

Understand the problem:

Before writing any code, unlock the tests to verify your understanding of the question:

python3 ok -q 01 -u
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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 01
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python3 -i hog.py

>>> roll_dice(4)

>>> fixed_dice = make_test_dice(3, 4)
>>> roll_dice(2, fixed_dice)
7

Problem 2 (2 pt)

Implement boar_brawl, which takes the player's current score player_score and the opponent's current score opponent_score, and returns the number of points scored when the player rolls 0 dice and Boar Brawl is invoked.

• Boar Brawl. A player who chooses to roll zero dice scores three times the absolute difference between the tens digit of the opponent’s score and the ones digit of the current player’s score, or 1, whichever is greater. The ones digit refers to the rightmost digit and the tens digit refers to the second-rightmost digit. If a player's score is a single digit (less than 10), the tens digit of that player's score is 0.

Don't assume that scores are below 100. Write your boar_brawl 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 -u
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Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 02
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You can also test boar_brawl interactively by running python3 -i hog.py from the terminal and calling boar_brawl 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 the roll_dice and boar_brawl functions rather than repeating their implementations.

Before writing any code, unlock the tests to verify your understanding of the question:

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

python3 ok -q 03
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Problem 4 (2 pt)

First, implement num_factors, which takes in a positive integer n and determines the number of factors that n has.

1 and n are both factors of n!

After, implement sus_points and sus_update.

• sus_points takes in a player's score and returns the player's new score after applying the Sus Fuss rule, even if the score remains unchanged. For example, sus_points(5) should return 5 and sus_points(21) should return 23. You should use num_factors and the provided is_prime function in your implementation.
• sus_update returns a player's total score after they roll num_rolls dice, taking both Boar Brawl and Sus Fuss into account. You should use sus_points in this function.

Hints:

• You can look at the implementation of simple_update provided in hog.py and use that as a starting point for your sus_update function.
• Recall that take-turn already took the Boar Brawl rule into consideration!

• Sus Fuss. We call a number sus if it has exactly 3 or 4 factors, including 1 and the number itself. If, after rolling, the current player's score is a sus number, their score instantly increases to the next prime number.

Before writing any code, unlock the tests to verify your understanding of the question:

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

python3 ok -q 04
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Problem 5 (4 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. The function then returns the final scores of both players.

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 that turn. A simple 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 and sus_update. Remember, update functions return the player's total score after their turn, not just the change in score.

The game ends when a player reaches or exceeds the goal score by the end of their turn, after all applicable rules have been applied. 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 Boar Brawl rules.
• play(always_roll_5, always_roll_5, sus_update) simulates two players that both always roll 5 dice each turn, playing with the Sus Fuss rule in addition to the Sow Sad and Boar Brawl 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.

Hints:

• If who is the current player, the next player is 1 - who.
• To call play(always_roll_5, always_roll_5, sus_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 -u
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Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 05
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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 read.

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 (sus_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 simple always_roll_five 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 function 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 -u
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Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 06
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Problem 7 (2 pt)

A strategy has a fixed number of possible argument values. For example, in a game with a goal of 100, there are only 100 possible score values (0-99) and 100 possible opponent_score values (0-99), resulting in 10,000 possible argument combinations to a strategy function.

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, where each score is up to goal points.

Reminder: The game continues until one player reaches goal points (in the above example goal is set to 100, but it could be any number). Ensure your solution considers every possible combination of score and opponent_score for the specified goal.

Before writing any code, unlock the tests to verify your understanding of the question:

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

python3 ok -q 07
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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 arguments as original_function. When called with specific arguments, this function should repeatedly call original_function on those same arguments, samples_count times, and return the average of the results. Take a look at the make_averaged doctest. Be sure to keep track of what values are being passed into the function!

Doctest Walkthrough: Take a close look at the make_averaged doctest. Here, original_function is roll_dice. Notice the line averaged_dice(1, dice). This implies that the arguments for roll_dice are (1, dice) (think about why!) Observe how averaged_dice accepts the same arguments as roll_dice. The arguments are not passed directly to roll_dice but rather to averaged_dice. (Think about how this can be achieved!) Keep in mind, make_averaged should work with any original_function that shares the same argument structure as the function returned by make_averaged. In this example, rolling a single die is considered a sample (roll_dice(1, dice)). Since samples_count is set to 40, this sampling is repeated 40 times. The make_averaged function then calculates the average result of these 40 calls to roll_dice.

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 it works.

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)  # *args represents the arguments (2, 8)
Result: 256
256
>>> printed_abs = printed(abs)
>>> printed_abs(-10)  # *args represents one argument (-10)
Result: 10
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 -u
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Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 08
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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 the same maximum average score, return 3.

You might find it useful to read the doctest for this problem and make_averaged (Problem 8), 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 -u
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✂️

Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 09
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✂️

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 boar_strategy and sus_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 Boar Brawl rule by rolling 0 when it is most beneficial to do so. Implement boar_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 Sus Fuss rule.

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

Before writing any code, unlock the tests to verify your understanding of the question:

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

python3 ok -q 10
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You should find that running python3 hog.py -r now shows a win rate for boar_strategy close to 66-67%.

Problem 11 (2 pt)

A better strategy would take advantage of both Boar Brawl and Sus Fuss in combination. For example, if a player has 53 points and their opponent has 60, rolling 0 would bring them to 62, which is a sus number, and so they would end the turn with 67 points: a gain of 67 - 53 = 14!

The sus_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 sus_update function you defined in Problem 4.

Before writing any code, unlock the tests to verify your understanding of the question:

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

python3 ok -q 11
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You should find that running python3 hog.py -r now shows a win rate for sus_strategy close to 67-69%.

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 12
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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. Only one partner needs to submit to Gradescope.

Congratulations, you have reached the end of your first CS 61A project! If you haven't already, relax and enjoy a few games of Hog with a friend.