Project 1: The Game of Hog

5-sided die

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


Important submission note: For full credit:

  • Submit with Phase 1 complete by Wednesday, October 30 (worth 1 pt).
  • Submit with Phases 2 and 3 complete by Sunday, November 3.

Although the checkpoint date is only a few days from the final due date, you should not put off completing Phase 1. We recommend starting and finishing Phase 1 as soon as possible to give yourself adequate time to complete Phases 2 and 3, which are can be more time consuming.

You do not have to wait until after the checkpoint date to start Phases 2 and 3.

Phase 1 is individual, Phases 2 and 3 can be completed with a partner.

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 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.

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

  • Pig Out. If any of the dice outcomes is a 1, the current player's score for the turn is 1.

    • 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 Pig Out did not occur, they score 12 points for the turn.
  • Free Bacon. A player who chooses to roll zero dice scores points equal to ten minus the minimum of the ones and tens digit of the opponent's score.

    • Example 1: The opponent has 13 points, and the current player chooses to roll zero dice. The minimum of 1 and 3 is 1, so the current player gains 10 - 1 = 9 points.
    • Example 2: The opponent has 85 points, and the current player chooses to roll zero dice. The minimum of 8 and 5 is 5, so the current player gains 10 - 5 = 5 points.
    • Example 3: The opponent has 7 points, and the current player chooses to roll zero dice. The minimum of 0 and 7 is 0, so the current player gains 10 - 0 = 10 points.
  • Feral Hogs. If the number of dice you roll is exactly 2 away (absolute difference) from the number of dice you rolled on the previous turn, you get 3 extra points for the turn. Treat the turn before the first turn as rolling 0 dice.

    • Example 1:

      • Both players start out at 0. (0, 0)
      • Player 0 rolls 3 dice and gets 1 point. (1, 0)
      • Player 1 rolls 4 dice and gets 1 point. (1, 1)
      • Player 0 rolls 5 dice and gets 1 point. 5 is 2 away from 3, so they get a bonus of 3. (5, 1)
      • Player 1 rolls 2 dice and gets 1 point. 2 is 2 away from 4, so they get a bonus of 3. (5, 5)
      • Player 0 rolls 7 dice and gets 1 point. 7 is 2 away from 5, so they get a bonus of 3. (9, 5)
      • Player 1 rolls 0 dice and gets 10 points. 0 is 2 away from 2, so they get a bonus of 3. (9, 18)
    • Example 2:

      • Both players start out at 0. (0, 0)
      • Player 0 rolls 2 dice and gets 3 points. 2 is 2 away from 0, so they get a bonus of 3. (6, 0)
  • Swine Swap. After points for the turn are added to the current player's score, if the first (leftmost) digit of the current player's score multiplied by the last (rightmost) digit of the current player's score are equal to the first (leftmost) digit of the other player's score multiplied by the last (rightmost) digit of the other player's score, then the two scores are swapped. (You can assume that all player scores have 3 digits or fewer.)

    • Example 1: At the end of a turn, the players have scores of 2 and 4. Since 2 * 2 != 4 * 4, the scores are not swapped.
    • Example 2: At the end of a turn, the players have scores of 22 and 4. Since 2 * 2 != 4 * 4, the scores are not swapped.
    • Example 3: At the end of a turn, the players have scores of 28 and 4. Since 2 * 8 == 4 * 4, the scores are swapped.
    • Example 4: At the end of a turn, the players have scores of 124 and 2. Since 1 * 4 == 2 * 2, the scores are swapped.
    • Example 5: At the end of a turn, the players have scores of 44 and 28. Since 4 * 4 == 2 * 8, the scores are swapped.
    • Example 6: At the end of a turn, the players have scores of 2 and 0. Since 2 * 2 != 0 * 0, the scores are not swapped.
    • Example 7: At the end of a turn, the players have scores of 10 and 0. Since 1 * 0 == 0 * 0, the scores are swapped.

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. However, you only have to make changes to

  • 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


The project is worth 25 points. 22 points are assigned for correctness, 1 point for submitting Part I by the checkpoint date, and 2 points for the overall composition.

You will turn in the following files:


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 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.

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, if you completed the optional Problem 12, you can play against the final strategy that you've created!

python3 -f

Phase 1: Simulator

Important submission note: For full credit:

  • submit with Phase 1 complete by Wednesday, October 30 (worth 1 pt).

All Phase 1 tests must pass in order to receive this point.

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. Example: 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, read over the file.

Problem 1 (2 pt)

Implement the roll_dice function in 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 (Pig Out).

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 Pig Out happens in the middle of rolling. In this way, you correctly simulate rolling all the dice together.

You can't implement the feral hogs rule in this problem, since roll_dice doesn't have the previous number of rolls as an argument. It will be implemented later.

You can observe the behavior of your function using Python directly. First, start the Python interpreter and load the file.

python3 -i

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 simiulating 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, dice=fixed_dice)

On most systems, you can evaluate the same expression again by pressing the up arrow, then pressing enter or return. If you want to get the second last, third last, etc., command you made, press up arrow repeatedly.

If you find a problem, you need to change your file, save it, quit Python, start it again, and then start evaluating expressions. Pressing the up arrow should give you access to your previous expressions, even after restarting Python.

Problem 2 (1 pt)

Implement the free_bacon helper function that returns the number of points scored by rolling 0 dice, based on the opponent's current score. You can assume that score is less than 100. For a score less than 10, assume that the first of the two digits is 0. Refer to the rules section for more information.

As noted above, you can also test free_bacon interactively by entering python3 -i in the terminal and then calling free_bacon 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.

You will need to implement the Free Bacon rule based on opponent_score, which you can assume is less than 100.

Your implementation of take_turn should call both roll_dice and free_bacon when possible.

Problem 4 (2 pt)

Implement is_swap, which returns whether or not the scores should be swapped, according to the Swine Swap rule.

The is_swap function takes two arguments: the players' scores. It returns a boolean value to indicate whether the Swine Swap condition is met.

Hint. Finding the leftmost digit is possible with a bunch of if statements but is simpler using a while loop.

Problem 5a (2 pt)

Implement the play function, which simulates a full game of Hog. Players alternate turns rolling dice until one of the players reaches the goal score.

You can ignore the Feral Hogs rule and feral_hogs argument for now; You'll implement it in Problem 5b.

To determine how much 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 wants to roll in the turn. Each strategy function should be called only once per turn. Don't worry about the details of implementing strategies yet. You will develop them in Phase 3.

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:

  • You should use the functions you have already written! You will need to call take_turn with all three arguments.
  • Only call take_turn once per turn.
  • Enforce all the special rules except for feral hogs
  • You can get the number of the other player (either 0 or 1) by calling the provided function other.
  • You can ignore the say argument to the play function for now. You will use it in Phase 2 of the project.

Problem 5b (1 pt)

Now, implement the Feral Hogs rule. When play is called and its feral_hogs argument is True, then this rule should be imposed. If feral_hogs is False, this rule should be ignored. (That way, test cases for 5a will still pass after you solve 5b.)

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.

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

Congratulations! You have finished Phase 1 of this project!

Phase 2: Commentary

You can work on and submit Phase 2 and 3 with a partner! Make sure one of you submits and then lists the other as a partner.

In the second phase, you will implement commentary functions that print remarks about the game after each turn, such as, "22 points! That's the biggest gain yet 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 possibly even previous scores. Since commentary can differ from turn to turn depending on the current point situation in the game, commentary functions return 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 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.

def announce_lead_changes(previous_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
            leader = None
        if leader != None and leader != previous_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.

    NOTE: the following game is not possible under the rules, it's just
    an example for the sake of the doctest

    >>> 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, 6)
    Player 0 now has 10 and Player 1 now has 6
    >>> h3 = h2(6, 17)
    Player 0 now has 6 and Player 1 now has 17
    Player 1 takes the lead by 11
    def say(score0, score1):
        return both(f(score0, score1), g(score0, score1))
    return say

Problem 6 (2 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.

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

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.

Note: The doctests for both/announce_highest in might describe a game that can't occur according to the rules. This shouldn't be an issue for commentary functions since they don't implement any of the rules of the game.

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 modifying/defining additional variables and instead using a built-in function to calculate your desired value when creating the new commentary function.

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


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!

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 fn as an argument. It returns another function that takes the same number of arguments as fn (the function originally passed into make_averaged). 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, you can write *args. To call another function using exactly those arguments, you 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
>>> printed_abs = printed(abs)
>>> printed_abs(-10)
Result: 10

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

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.

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(6) against the baseline strategy of always_roll(4).

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

Problem 10 (1 pt)

A strategy can try to 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.

Once you have implemented this strategy, change run_experiments to evaluate your new strategy against the baseline. Is it better than just rolling 4?

Problem 11 (2 pt)

A strategy can also take advantage of the Swine Swap rule. The swap strategy always rolls 0 if doing so triggers a beneficial swap and always avoids rolling 0 if doing so triggers a detrimental swap. In other cases, it rolls 0 if rolling 0 would give at least margin points. Otherwise, the strategy rolls num_rolls.

Hint: a tie is technically a "swap" (e.g., 43 being swapped with 43), but is considered neither detrimental nor beneficial for the purposes of this problem.

Once you have implemented this strategy, update run_experiments to evaluate your new strategy against the baseline. You should find that it gives a significant edge over always_roll(4).

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 always_roll(4) strategy. Some suggestions:

  • swap_strategy is a good default strategy to start with.
  • There's no point in scoring more than 100. Check whether you can win by rolling 0, 1 or 2 dice. If you are in the lead, you might take fewer risks.
  • Try to force a beneficial swap rolling more than 0 dice.
  • Choose the num_rolls and margin arguments carefully.

You can also check your exact final win rate by running


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 project! If you haven't already, relax and enjoy a few games of Hog with a friend.