Project 1: The Game of Hog
I know! I'll use my
Higher-order functions to
Order higher rolls.
Introduction
Important submission note: For full credit:
- Submit with Phase 1 complete by Wednesday, July 3 (worth 1 pt).
- Submit with Phases 2 and 3 complete by Monday, July 8.
Please note that 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 harder and more time consuming. There will also be limited, if any, office hour support on Thursday due to the July 4 holiday. 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.
Rules
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 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.
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 and the last (rightmost) digit of the opponent player's score are equal, then the two scores are swapped.
- Example 1: The current player has a total score of 31 and the opponent has 83. The current player rolls one dice with value 5. The player's new score is 36, and the opponent's score is 83. The leftmost digit of the current player's score and the rightmost digit of the opponent's score are both 3, so the scores are swapped.
- Example 2: The current player has a total score of 1 and the opponent has 2. The current player rolls one dice with value 6. The player's new score is 7, and the opponent's score is 2. The leftmost digit of the current player's score is 7, and the rightmost digit of the opponent's score is 2. The scores are not swapped.
- Example 3: The current player has a total score of 99 and the opponent has 21. The current player rolls three dice that total 8. The player's new score is 107, and the opponent's score is 21. The leftmost digit of the player's score is and the rightmost digit of the opponent's score are both 1, so the scores are swapped.
- Example 4: The current player has a total score of 35 and the opponent has 25. The current player rolls two dice that total 10. The player's new score is 45, and the opponent's score is 25. The leftmost digit of the player's score is not equal to the rightmost digit of the opponent's score, so the scores are not swapped.
Download starter files
To get started, download all of the project code as a zip archive.
You only have to make changes to hog.py
.
hog.py
: A starter implementation of Hogdice.py
: Functions for rolling dicehog_gui.py
: A graphical user interface for Hogucb.py
: Utility functions for CS 61Aok
: CS 61A autogradertests
: A directory of tests used byok
images
: A directory of images used byhog_gui.py
Logistics
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:
hog.py
You do not need to modify or turn in any other files to complete the project. To submit the project, run the following command:
python3 ok --submit
You will be able to view your submissions on the Ok dashboard.
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. 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.
We recommend that you submit after you finish each problem. Only your last submission will be graded. It is also useful for us to have more backups of your code in case you run into a submission issue.
If you do not want us to record a backup of your work or information about your progress, you can run
python3 ok --localWith this option, no information will be sent to our course servers. If you want to test your code interactively, you can run
python3 ok -q [question number] -iwith 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 debug printing 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!
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:
python3 hog_gui.py
Once you complete the project, if you completed the optional Problem 12, you can play against the final strategy that you've created!
python3 hog_gui.py -f
Phase 1: Simulator
Important submission note: For full credit:
- submit with Phase 1 complete by Wednesday, July 3 (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 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:
- 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 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 v1.5.2
=====================================================================
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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()
(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 (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 (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, we correctly simulate rolling all the dice together.
Understand the problem:
Before writing any code, unlock the tests to verify your understanding of the 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
Debugging your code interactively:
If the tests don't pass, it's time to debug. You can observe the behavior of
your function using Python directly. First, start the Python interpreter and
load the hog.py
file.
python3 -i hog.py
Note: to start the interpreter after the failing test is complete, try running
python3 ok -q 01 -i
instead. This will open an interpreter and then run the test until the first doctest that fails.
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)
7
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
hog.py
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.
Continue debugging your code and running the ok
tests until they all pass. You
should follow this same procedure of understanding the problem, implementing a
solution, testing, and debugging for all the problems on this project.
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.
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
As noted above, you can also test free_bacon
interactively by entering
python3 -i hog.py
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.
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
Problem 4 (2 pt)
Implement is_swap
, which returns whether or not the scores should be
swapped, according to the rules.
The is_swap
function takes two arguments: the players' scores. It returns a
boolean value to indicate whether the Swine Swap condition is met.
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 (3 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.
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.
- 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 theplay
function for now. You will use it in Phase 2 of the project.
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
The last test for Question 5 is a fuzz test, which checks that your
play
function works for a large number of different inputs. Failing this test means something is wrong, but you should look at other tests to see where the problem might be.
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
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.
Windows users (June 2019): If you see
No module named '_tkinter'
and you used our automated installer, you need to go back to lab 0 and follow the steps to cleanly uninstall and reinstall Python and Git-Bash using the alternate method.
Unfortunately we did not realize that the version of Python that our installer installed did not include the required Tkinter modules. This will be resolved in a later version of the automated installer.
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 by the earlier deadline using the following command
python3 ok --submit
Congratulations! You have finished Phase 1 of this project!
Phase 2: Commentary
Important submission note: For full credit:
- submit with Phase 2 and 3 complete by Monday, July 8.
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 on okpy.org
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 hog.py
is an example of a commentary function that
simply announces both players' scores. Note that say_scores
returns a reference
to 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
else:
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.
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. 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 howannounce_lead_changes
works.
Note: The doctests for
both
/announce_highest
in hog.py might describe a game that may be impossible. 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 can either:
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.
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, if play the game again, you will see the commentary.
python3 hog_gui.py
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, 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
256
>>> printed_abs = printed(abs)
>>> printed_abs(-10)
Result: 10
10
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.
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
To run this experiment on randomized dice, call run_experiments
using
the -r
option:
python3 hog.py -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)
. You should
find that it wins slightly more often than it loses, giving a win rate around
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 10 (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.
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. You should find that it wins more than
half of the time.
Problem 11 (2 pt)
A strategy can also take advantage of the Swine Swap rule. The
swap_strategy
rolls 0 if it would cause a beneficial swap. It also returns 0
if rolling 0 would give at least margin
points, unless this would cause
a non-beneficial swap. Otherwise, the strategy rolls num_rolls
.
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. 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.
- Choose the
num_rolls
andmargin
arguments carefully.
You can check that your final strategy is valid by running Ok.
python3 ok -q 12
You can also check your exact final winrate by running
python3 calc.py
At this point, run the entire autograder to see if there are any tests that don't pass.
python3 ok
Once you are satisfied, submit to Ok to complete the project.
python3 ok --submit
If you have a partner, make sure to add them to the submission on okpy.org.
You can also play against your final strategy with the graphical user interface:
python3 hog_gui.py -f
The GUI will alternate which player is controlled by you.
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.