Project 1: The Game of Hog

5-sided die

I know! I'll use my
Higher-order functions to
Order higher rolls.

Table of Contents


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.

In Hog, two players alternate turns trying to reach 100 points first. 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, unless any of the dice comes up a 1, in which case the score for the turn is only 1 point (the Pig out rule).

To spice up the game, we will play with some special rules:

This project includes five files and two directories, but all of your changes will be made to the first file, and it is the only one you should need to read and understand. To get started, download all of the project code as a zip archive. A starter implementation of Hog Functions for rolling dice A graphical user interface for Hog Utility functions for CS 61A
ok CS 61A autograder
tests A directory of tests used by ok
images A directory of images used by


This is a one-week project. You may work with one other partner. You should not share your code with students who are not your partner.

Start early! The amount of time it takes to complete a project (or any program) is unpredictable.

You are not alone! Ask for help early and often — the TAs, readers, lab assistants, and your fellow students are here to help. Try attending office hours or posting on Piazza.

In the end, you will submit one project for both partners. The project is worth 20 points. 17 points are assigned for correctness, and 3 points for the overall composition of your program.

The only file that you are required to submit is You do not need to modify or turn in any other files to complete the project. To submit the project, change to the directory where is located and run submit proj1. Eventually, you will receive email confirmation of your submission, though perhaps not until two days before the deadline.

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).

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!

In order to render the graphics, make sure you have Tkinter, Python's main graphics library, installed on your computer. Once you've done that, you can run the GUI from your terminal:


Once you complete the project, you can play against the final strategy that you've created!

python3 -f


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.

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 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, but there is a catch. At first, the test cases are locked. To unlock tests, run the following command from your terminal:

python3 ok -u

This command will start an interactive prompt that looks like:

# Unlocking tests for proj1 #

At each "? ", type in what you would expect the output to be.
Type exit() to quit
Unlocking tests for q00

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

At the ?, you can type what you expect the output to be. If you are correct, then this test case will be available the next time you run the autograder.

The idea is to understand conceptually what your program should do first, before you start writing any code.

Once you have unlocked some tests and written some code, you can check the correctness of your program using the tests that you have unlocked:

python3 ok

To help with debugging, ok can also be run in interactive mode:

python3 ok -i

If an error occurs, the autograder will start an interactive Python session in the environment used for the test, so that you can explore the state of the environment.

Most of the time, you will want to focus on a particular question. Use the -q option as directed in the problems below.

The tests folder is used to store autograder tests, so make sure not to modify it. You may lose all your unlocking progress if you do. If you need to get a fresh copy, you can download the zip archive and copy it over, but you will need to start unlocking from scratch.

Phase 1: Simulator

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

Problem 0 (0 pt)

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

* Dice can be fair, meaning that they produce each possible outcome
  with equal probability. Examples: four_sided, six_sided.

* For testing functions that use dice, deterministic test dice
  always cycle through a fixed sequence of values that are passed
  as arguments to the make_test_dice function.

Before we start writing any code, let's understand the make_test_dice function by unlocking its tests.

python3 ok -q 0 -u

This should display a prompt that looks like this:

# Unlocking tests for proj1 #

At each "? ", type in what you would expect the output to be.
Type exit() to quit
Unlocking tests for q00

Case 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.

Once you successfully unlock all cases for this question, you can verify that the test dice work correctly by checking the tests:

python3 ok -q 0

Note: you can exit the unlocker by typing exit() (without quotes). Typing Ctrl-C on Windows to exit out of the unlocker has been known to cause problems, so avoid doing so.

Problem 1 (1 pt)

Implement the roll_dice function in It takes two arguments: the number of dice to roll and a dice function. It returns the number of points scored by rolling that number of dice: either the sum of the outcomes or 1 (pig out).

To obtain a single outcome of a dice roll, call dice(). Please call the dice function exactly the number of times specified by the first argument, even if a 1 is rolled. Otherwise, the GUI and tests won't work.

To test the correctness of your implementation, first unlock the tests for this problem:

python3 ok -q 1 -u

And then check that the tests pass:

python3 ok -q 1

Remmber that you can start an interactive Python session if an error occurs by adding a -i option to the end:

python3 ok -q 1 -i

Problem 2 (1 pt)

Implement the take_turn function, which returns the number of points scored for a turn. You will need to implement the Free bacon rule. You can assume that opponent_score is less than 100. For a score less than 10, assume that the first of two digits is 0. Your implementation should call roll_dice.

Test your implementation before moving on:

python3 ok -q 2 -u
python3 ok -q 2

Problem 3 (1 pt)

Implement the select_dice function, which helps enforce the Hog wild special rule. This function takes two arguments: the scores for the current and opposing players. It returns either four_sided or six_sided dice that will be used for the next turn.

Test your implementation before moving on:

python3 ok -q 3 -u
python3 ok -q 3

Problem 4 (1 pt)

When two players start a game of Hog, who rolls first? One way to determine the turn order is through an auction in which players bid points for the privilege of rolling first.

Each player chooses a bid greater than 0. The following three rules determine who rolls first and starting scores:

  1. If the bids are equal, each player starts with goal points, resulting in an instant tie. It does not matter who rolls first.
  2. If one bid is exactly 5 higher than the other, the higher bidder rolls first starting with 10 points, and the other player starts with 0. For example, if player 0 bids 2 and player 1 bids 7, player 1 would roll first starting with 10 points and player 0 would start with 0 points.
  3. Otherwise, the player with the higher bid rolls first. Each player starts with a number of points equal to her/his opponent's bid. For example, if player 0 bids 3 and player 1 bids 4, player 1 would roll first starting with 3 points and player 0 would start with 4 points.

The bid_for_start function attempts to implement these rules by returning three values: the starting scores of the players and which player rolls first (0 or 1).

However, there are mistakes in the implementation provided! Your job is to correct the errors. You can change the function however you wish, but the structure provided is a good place to start. You may find this debugging guide helpful.

Test and debug the given implementation before moving on:

python3 ok -q 4 -u
python3 ok -q 4

Problem 5 (3 pt)

Implement the play function, which simulates a full game of Hog. Players alternate turns, each using the strategy originally supplied, until one of the players reaches the goal score. When the game ends, play returns the final total scores of both players, with Player 0's score first, and Player 1's score second.

Here are some hints:

Test your implementation before moving on:

python3 ok -q 5 -u
python3 ok -q 5

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


If you don't already have Tkinter (Python's graphics library) installed, you'll need to install it first before you can run the GUI.

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.

Congratulations! You have finished Phase 1 of this project!

Phase 2: Strategies

In the second 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 6 (2 pt)

Implement the make_averaged function. This higher-order function takes a function fn as an argument. It returns another function that takes the same number of arguments as the original. This returned function differs from the input function in that it returns the average value of repeatedly calling fn on the same arguments. This function should call fn a total of num_samples times and return the average of the results.

To implement this function, you need a new piece of Python syntax! You must write a function that accepts an arbitrary number of arguments, then calls another function using exactly those arguments. Here's how it works.

Instead of listing formal parameters for a function, we write *args. To call another function using exactly those arguments, we call it again with *args. For example,

>>> def printed(fn):
...     def print_and_return(*args):
...         result = fn(*args)
...         print('Result:', result)
...         return result
...     return print_and_return
>>> printed_pow = printed(pow)
>>> printed_pow(2, 8)
Result: 256

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

Test your implementation before moving on:

python3 ok -q 6 -u
python3 ok -q 6

Problem 7 (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.

Note: 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.

Test your implementation before moving on:

python3 ok -q 7 -u
python3 ok -q 7

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

python3 -r

Running experiments For the remainder of this project, you can change the implementation of run_experiments as you wish. By calling average_win_rate, you can evaluate various Hog strategies. For example, change the first if False: to if True: in order to evaluate always_roll(8) against the baseline strategy of always_roll(5). You should find that it loses more often than it wins, giving a win rate below 0.5.

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

Problem 8 (1 pt)

A strategy can take advantage of the Free bacon rule by rolling 0 when it is most beneficial to do so. Implement bacon_strategy, which returns 0 whenever rolling 0 would give at least margin points and returns num_rolls otherwise.

Test your implementation before moving on:

python3 ok -q 8 -u
python3 ok -q 8

Once you have implemented this strategy, change run_experiments to evaluate your new strategy against the baseline. You should find that it wins more than half of the time.

Problem 9 (2 pt)

A strategy can also take advantage of the Swine swap rule. The swap_strategy

  1. Rolls 0 if it would cause a beneficial swap that gains points.
  2. Rolls num_rolls if rolling 0 would cause a harmful swap that loses points.
  3. If rolling 0 would not cause a swap, then do so if it would give at least margin points and roll num_rolls otherwise.

Test your implementation before moving on:

python3 ok -q 9 -u
python3 ok -q 9

Once you have implemented this strategy, update run_experiments to evaluate your new strategy against the baseline. You should find that it performs even better than bacon_strategy, on average.

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

python3 ok

Problem 10 (3 pt)

Implement final_strategy, which combines these ideas and any other ideas you have to achieve a win rate of at least 0.54 (for full credit) against the baseline always_roll(5) strategy. (At the very least, try to achieve a win rate above 0.53 for partial credit.) Some ideas:

NOTE: The win rates were changed to 0.54 for full credit and 0.53 for partial credit at 5:00pm Friday 9/12.

You may want to increase the number of samples to improve the approximation of your win rate. The course autograder will compute your exact average win rate (without sampling error) for you once you submit your project, and it will send it to you in an email.

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

python3 -f

The GUI will alternate which player is controlled by you.

Congratulations, you have reached the end of your first CS 61A project!