Project 1: The Game of Hog

Files: hog.zip

Introduction

Important submission note: For full credit:

• Submit with Phase 1 complete by Wednesday 10 May (worth 1 pt).
• Submit with all phases complete by Saturday 13 May.

Although Phase 1 is due only a few days before the rest of the project, you should not put off completing Phase 1. We recommend starting and finishing Phase 1 as soon as possible.

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.

The entire project can be completed with a partner.

You can get 1 bonus point by submitting the entire project by Friday 12 May.

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 100 total points. 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

  • 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:

• Picky Piggy. A player who chooses to roll zero dice scores the nth digit of the decimal expansion of 1/7 (0.14285714…), where n is the opponent’s score. As a special case, if n is 0, the player scores 7 points.

  Examples

  • Example 1: The current player rolls zero dice and the opponent has a score of 3. The 3rd digit of the decimal expansion of 1/7 is 2: 0.14[2]85714285714285, The current player will receive 2 points.
  • Example 2: The current player rolls zero dice and the opponent has a score of 14. The 14th digit of the decimal expansion of 1/7 is 4: 0.1428571428571[4]285, so the current player will receive 4 points.
  • Example 3: The current player rolls zero dice and the opponent has a score of 0. The current player will receive 7 points.

• Hog Pile. After points for the turn are added to the current player’s score, if the players’ scores are the same, the current player’s score doubles.

  Examples

  • Both players start out at 0. (0, 0)
  • Player 0 rolls 2 dice and gets 5 points. (5, 0)
  • Player 1 rolls 1 dice and gets 5 points. Player 1’s score doubles. (5, 10)
  • Player 0 rolls 2 dice and gets 6 points. (11, 10)
  • Player 1 rolls 8 dice and gets 1 points. Player 1’s score doubles. (11, 22)

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 rolling dice
• hog_gui.py: A graphical user interface (GUI) for Hog (updated)
• ucb.py: Utility functions for CS 111
• ok: CS 111 autograder
• tests: A directory of tests used by ok
• gui_files: A directory of various things used by the web GUI
• calc.py: A file you can use to approximately test your final strategy (in progress)

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. 22 points are assigned for correctness, 2 points for composition, and 1 point for submitting Phase 1 by the checkpoint date.

Important points update: The points for the project have been updated to more accurately reflect the question weights including points for project composition.

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.

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. 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.

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!

Note: The GUI has been updated. See the announcement at the top of the page for instructions.

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

python3 hog_gui.py

Phase 1: Simulator

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. The documentation of dice.py describes the two different types of dice used in the project:

• A fair dice produces 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.
• A test dice is deterministic: it always cycles 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 -u

This should display a prompt that looks like this:

=====================================================================
Assignment: Project 1: Hog
Ok, version v1.18.2
=====================================================================

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.

In general, for each of the unlocking tests, you might find it helpful to read through the provided skeleton for that problem before attempting the unlocking test.

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 Sad).

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

  Examples

  • 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.

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. In this way, you correctly simulate rolling all the dice together.

Understand the problem:

Before writing any code, unlock the tests to verify your understanding of the question. Note: you will not be able to test your code using ok until you unlock the test cases for the corresponding question.

python3 ok -q 01 -u

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

python3 -i hog.py

>>> roll_dice(4)

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

Problem 2 (3 pt)

Implement picky_piggy, which takes the opponent’s current score and returns the number of points scored by rolling 0 dice.

• Picky Piggy. A player who chooses to roll zero dice scores the nth digit of the decimal expansion of 1/7 (0.14285714…), where n is the opponent’s score. As a special case, if n is 0, the player scores 7 points.

  Examples

  • Example 1: The current player rolls zero dice and the opponent has a score of 3. The 3rd digit of the decimal expansion of 1/7 is 2: 0.14[2]85714285714285, The current player will receive 2 points.
  • Example 2: The current player rolls zero dice and the opponent has a score of 14. The 14th digit of the decimal expansion of 1/7 is 4: 0.1428571428571[4]285, so the current player will receive 4 points.
  • Example 3: The current player rolls zero dice and the opponent has a score of 0. The current player will receive 7 points.

The goal of this question is for you to practice retrieving the digits of a number, so it may be helpful to keep in mind the techniques used in previous assignments for digit iteration.

However, your code should not use str, lists, or contain square brackets [ ] in your implementation. Aside from this constraint, you can otherwise implement this function how you would like to.

Note: Remember to remove the "*** YOUR CODE HERE ***" string from the function once you’ve implemented it so that you’re not getting an unintentional str check error.

If the syntax check isn’t passing on the docstring, try upgrading your Python version to 3.8 or 3.9. It seems that the docstring being included in the check is specific to Python version 3.7, so updating your Python version should resolve the issue.

Hint: The decimal expansion of 1/7 is a 6-digit repeating decimal with the digits 142857. Therefore, the 2nd digit is the same as the 8th digit, the 14th, 20th, 26th, 32nd, etc.

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

python3 ok -q 02 -u

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

python3 ok -q 02

You can also test picky_piggy interactively by entering python3 -i hog.py in the terminal and then calling picky_piggy with 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 picky_piggy when possible.

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

python3 ok -q 03 -u

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

python3 ok -q 03

👩🏽‍💻👨🏿‍💻 Pair programming? Remember to alternate between driver and navigator roles. The driver controls the keyboard; the navigator watches, asks questions, and suggests ideas.

Problem 4 (1 pt)

Implement hog_pile, which takes the current player and opponent scores and returns the points that the current player will receive due to Hog Pile. If Hog Pile is not applicable, the current player receives 0 additional points.

• Hog Pile. After points for the turn are added to the current player’s score, if the players’ scores are the same, the current player’s score doubles.

  Examples

  • Example:

  • Both players start out at 0. (0, 0)

  • Player 0 rolls 2 dice and gets 5 points. (5, 0)

  • Player 1 rolls 1 dice and gets 5 points. Player 1’s score doubles. (5, 10)

  • Player 0 rolls 2 dice and gets 6 points. (11, 10)

  • Player 1 rolls 8 dice and gets 1 points. Player 1’s score doubles. (11, 22)

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

python3 ok -q 04 -u

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

python3 ok -q 04

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. A turn is defined as one roll of the dice.

To determine how many dice are rolled each turn, each player uses their respective strategy (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. Don’t worry about implementing strategies yet; you’ll do that in Phase 3.

Important: Your implementation should only need to use a single loop; you don’t need multiple loops. This might not affect passing the test cases if your logic is correct overall, but this could affect your composition grade for the project. Here’s the section of the syllabus on composition for projects.

Additionally, each strategy function should be called only once per turn. This means you only want to call strategy0 when it is Player 0’s turn and only call strategy1 when it is Player 1’s turn. Otherwise, the GUI and some ok tests may get confused.

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.

Hints:

• You should call the functions you have implemented already.
• Call take_turn with four arguments (don’t forget to pass in the goal). Only call take_turn once per turn.
• Call hog_pile to determine if the current player will gain additional points due to Hog Pile, and if so, how many points.
• You can get the number of the next player (either 0 or 1) by calling the provided function next_player.
• You can ignore the say argument to the play function for now. You will use it in Phase 2 of the project.
• For the unlocking tests, hog.always_roll refers to the always_roll function defined in hog.py.

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

python3 ok -q 05 -u

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

python3 ok -q 05

Once you are finished, you will be able to play a graphical version of the game. We have provided a file called hog_gui.py that you can run from the terminal:

python3 hog_gui.py

Note: The GUI has been updated. See the announcement at the top of the page for instructions.

The GUI relies on your 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.

Make sure to submit your work so far to Canvas before the checkpoint deadline.

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

python3 ok --score

Congratulations! You have finished Phase 1 of this project!

👩🏽‍💻👨🏿‍💻 Pair programming? This would be a good time to switch roles. Switching roles makes sure that you both benefit from the learning experience of being in each role.

Phase 2: Commentary

In the second phase, you will implement commentary functions that print remarks about the game after each turn, such as: "22 point(s)! That's a record gain for Player 1!"

A commentary function takes two arguments, Player 0’s current score and Player 1’s current score. It can print out commentary based on either or both current scores and any other information in its parent environment. Since commentary can differ from turn to turn depending on the current point situation in the game, a commentary function always returns another commentary function to be called on the next turn. The only side effect of a commentary function should be to print.

Commentary examples

The function say_scores in hog.py is an example of a commentary function that simply announces both players’ scores. Note that say_scores returns itself, meaning that the same commentary function will be called each turn.

def say_scores(score0, score1):
    """A commentary function that announces the score for each player."""
    print("Player 0 now has", score0, "and Player 1 now has", score1)
    return say_scores

The function announce_lead_changes is an example of a higher-order function that returns a commentary function that tracks lead changes. A different commentary function will be called each turn.

def announce_lead_changes(last_leader=None):
    """Return a commentary function that announces lead changes.

    >>> f0 = announce_lead_changes()
    >>> f1 = f0(5, 0)
    Player 0 takes the lead by 5
    >>> f2 = f1(5, 12)
    Player 1 takes the lead by 7
    >>> f3 = f2(8, 12)
    >>> f4 = f3(8, 13)
    >>> f5 = f4(15, 13)
    Player 0 takes the lead by 2
    """
    def say(score0, score1):
        if score0 > score1:
            leader = 0
        elif score1 > score0:
            leader = 1
        else:
            leader = None
        if leader != None and leader != last_leader:
            print('Player', leader, 'takes the lead by', abs(score0 - score1))
        return announce_lead_changes(leader)
    return say

You should also understand the function both, which takes two commentary functions (f and g) and returns a new commentary function. This returned commentary function returns another commentary function which calls the functions returned by calling f and g, in that order.

def both(f, g):
    """Return a commentary function that says what f says, then what g says.

    >>> h0 = both(say_scores, announce_lead_changes())
    >>> h1 = h0(10, 0)
    Player 0 now has 10 and Player 1 now has 0
    Player 0 takes the lead by 10
    >>> h2 = h1(10, 8)
    Player 0 now has 10 and Player 1 now has 8
    >>> h3 = h2(10, 17)
    Player 0 now has 10 and Player 1 now has 17
    Player 1 takes the lead by 7
    """
    def say(score0, score1):
        return both(f(score0, score1), g(score0, score1))
    return say

Problem 6 (1 pt)

Update your play function so that a commentary function is called at the end of each turn. The return value of calling a commentary function gives you the commentary function to call on the next turn.

For example, say(score0, score1) should be called at the end of the first turn. Its return value (another commentary function) should be called at the end of the second turn. Each consecutive turn, call the function that was returned by the call to the previous turn’s commentary function.

Hint: For the unlocking tests for this problem, remember that when calling print with multiple arguments, Python will put a space between each of the arguments. For example:

>>> print(9, 12)
9 12

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

python3 ok -q 06 -u

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

python3 ok -q 06

Problem 7 (3 pt)

Implement the announce_highest function, which is a higher-order function that returns a commentary function. This commentary function announces whenever a particular player gains more points in a turn than ever before. For example, announce_highest(1) ignores Player 0 entirely and just prints information about Player 1. (So does its return value; another commentary function about only Player 1.)

To compute the gain, it must compare the score from last turn (last_score) to the score from this turn for the player of interest (designated by the who argument). This function must also keep track of the highest gain for the player so far, which is stored as running_high.

The way in which announce_highest announces is very specific, and your implementation should match the doctests provided. Don’t worry about singular versus plural when announcing point gains; you should simply use “point(s)” for both cases.

Hint: The announce_lead_changes function provided to you is an example of how to keep track of information using commentary functions. If you are stuck, first make sure you understand how announce_lead_changes works.

Hint: If you’re getting a local variable [var] reference before assignment error:

This happens because in Python, you aren’t normally allowed to modify variables defined in parent frames. Instead of reassigning [var], the interpreter thinks you’re trying to define a new variable within the current frame. We’ll learn about how to work around this in a future lecture, but it is not required for this problem.

To fix this, you have two options:

1) Rather than reassigning [var] to its new value, create a new variable to hold that new value. Use that new variable in future calculations.

2) For this problem specifically, avoid this issue entirely by not using assignment statements at all. Instead, pass new values in as arguments to a call to announce_highest.

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

python3 ok -q 07 -u

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

python3 ok -q 07

When you are done, you will see commentary in the GUI:

python3 hog_gui.py

Note: The GUI has been updated. See the announcement at the top of the page for instructions.

The commentary in the GUI is generated by passing the following function as the say argument to play.

both(announce_highest(0), both(announce_highest(1), announce_lead_changes()))

Great work! You just finished Phase 2 of the project!

👩🏽‍💻👨🏿‍💻 Pair programming? Celebrate, take a break, and switch roles!

Phase 3: Strategies

In the third phase, you will experiment with ways to improve upon the basic strategy of always rolling a fixed number of dice. First, you need to develop some tools to evaluate strategies.

Problem 8 (2 pt)

Implement the make_averaged function, 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 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 trials_count 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 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)
Result: 256
256
>>> printed_abs = printed(abs)
>>> printed_abs(-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.

Read the docstring for make_averaged carefully to understand how it is meant to work.

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

python3 ok -q 08 -u

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

python3 ok -q 08

Problem 9 (2 pt)

Implement the max_scoring_num_rolls function, 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, return 3.

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 starting from 10 to 1.

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

python3 ok -q 09 -u

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

python3 ok -q 09

Running experiments:

To run this experiment on randomized dice, call run_experiments using the -r option:

python3 hog.py -r

For the remainder of this project, you can change the implementation of run_experiments as you wish. The function includes calls to average_win_rate for evaluating various Hog strategies, but most of the calls are currently commented out. You can un-comment the calls to try out strategies, like to compare the win rate for always_roll(8) to the win rate for always_roll(6).

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.

👩🏽‍💻👨🏿‍💻 Pair programming? We suggest switching roles now, if you haven’t recently. Almost done!

Problem 10 (1 pt)

A strategy can try to take advantage of the Picky Piggy rule by rolling 0 when it is most beneficial to do so. Implement picky_piggy_strategy, which returns 0 whenever rolling 0 would give at least cutoff points and returns num_rolls otherwise.

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

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

python3 ok -q 10 -u

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

python3 ok -q 10

Once you have implemented this strategy, change run_experiments to evaluate your new strategy against the baseline. Is this strategy an improvement over the baseline?

Problem 11 (1 pt)

A strategy can also take advantage of the Hog Pile rules. The Hog Pile strategy always rolls 0 if doing so triggers the rule. In other cases, it rolls 0 if rolling 0 would give at least cutoff points. Otherwise, the strategy rolls num_rolls.

Hint: You can use the function picky_piggy_strategy you defined in Problem 10.

Hint: Remember that the hog_pile check should be done after the points from picky_piggy have been added to the score.

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

python3 ok -q 11 -u

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

python3 ok -q 11

Once you have implemented this strategy, update run_experiments to evaluate your new strategy against the baseline.

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:

• picky_piggy_strategy or hog_pile_strategy are default strategies you can start with.
• If you know the goal score (by default it is 100), there’s no point in 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.
• Choose the num_rolls and cutoff arguments carefully.
• Take the action that is most likely to win the game.

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

python3 ok -q 12

You can also play against your final strategy with the graphical user interface:

python3 hog_gui.py

Note: The GUI has been updated. See the announcement at the top of the page for instructions.

The GUI will alternate which player is controlled by you.

Project submission

At this point, run the entire autograder to see if there are any tests that don’t pass:

python3 ok

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

python3 ok --score

Once you are satisfied, submit to complete the project.

Submissions will be in Canvas.

Congratulations, you have reached the end of your first CS 111 project! If you haven’t already, relax and enjoy a few games of Hog with a friend.