# 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
Monday, February 3(worth 1 pt).- Submit with Phases 2 and 3 complete by
Thursday, February 6.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.

You can get 1 extra credit point by submitting the entire project one day early on

Wednesday, February 5.

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.

### 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:

**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.

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

**Free Bacon**. A player who chooses to roll zero dice scores points equal to one more than the absolute alternating difference of the digits of the opponent's score cubed.

*Example 1*: The opponent has 4 points, and the current player chooses to roll zero dice.`4*4*4 = 64`

, so the current player gets`1 + |6 - 4| = 3`

points.*Example 2*: The opponent has 1 points, and the current player chooses to roll zero dice.`1*1*1 = 1`

, so the current player gets`1 + |1| = 2`

points.*Example 3*: The opponent has 20 points, and the current player chooses to roll zero dice.`20*20*20 = 8000`

, so the current player gets`1 + |8 - 0 + 0 - 0| = 9`

points.*Example 4*: The opponent has 45 points, and the current player chooses to roll zero dice.`45*45*45 = 91125`

, so the current player gets`1 + |9 - 1 + 1 - 2 + 5| = 13`

points.

**Feral Hogs**. If the number of dice you roll is exactly 2 away (absolute difference) from the number of points you scored on the previous turn, you get 3 extra points for the turn. Treat the turn before the first turn as scoring 0 points. Do**not**take into account any previous feral hog bonuses or swine swap (next rule) when calculating the number of points scored the previous turn.

*Example 1:*- Both players start out at 0. (0, 0)
- Player 0 rolls 3 dice and gets
**7**points. (7, 0) - Player 1 rolls 1 dice and gets
**4**points. (7, 4) - Player 0 rolls
**5**dice and gets**10**points.**5**is 2 away from**7**, so player 0 gets a bonus of 3. (20, 4) - Player 1 rolls
**2**dice and gets**8**points.**2**is 2 away from**4**, so player 1 gets a bonus of 3. (20, 15) - Player 0 rolls
**8**dice and gets 20 points.**8**is 2 away from**10**, so player 0 gets a bonus of 3. (43, 15) - Player 1 rolls
**6**dice and gets 1 point.**6**is 2 away from**8**, so player 1 gets a bonus of 3. (43, 19)

*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 player 0 gets a bonus of 3. (6, 0)

**Swine Swap**. Define the*excitement*of the game to be three to the power of the sum of the players' scores. After points for the turn are added to the current player's score, if the excitement's first digit and last digit are the same, the scores should be swapped.

*Example 1*: At the end of a turn, the players have scores of 2 and 4; 3^{2 + 4}= 729, and 7 != 9, the scores are not swapped.*Example 2*: At the end of a turn, the players have scores of 11 and 1; 3^{11 + 1}= 531441, and 5 != 1, the scores are not swapped.*Example 3*: At the end of a turn, the players have scores of 1 and 0; 3^{1 + 0}= 3, and 3 == 3, the scores are swapped.*Example 4*: At the end of a turn, the players have scores of 23 and 4; 3^{23 + 4}= 7625597484987, and 7 == 7, the scores are swapped.

## Final Product

Our staff solution to the project can be interacted with at hog.cs61a.org -- if you'd like, try it out now! When you finish the project, you'll have implemented a significant part of this game yourself!

## 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 `hog.py`

.

`hog.py`

: A starter implementation of Hog`dice.py`

: Functions for rolling dice`hog_gui.py`

: A graphical user interface for Hog`ucb.py`

: Utility functions for CS 61A`ok`

: CS 61A autograder`tests`

: A directory of tests used by`ok`

`gui_files`

: A directory of various things used by the web gui.

## 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!

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

`python3 hog_gui.py`

## Phase 1: Simulator

Important submission note:For full credit:

- submit with Phase 1 complete by
Monday, February 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 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()`

. **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*).

The Pig Out rule is reproduced below:

**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.

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.

**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`

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`

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 simulating 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.

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 test example that fails.

### 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.

The Free Bacon rule is reproduced below:

**Free Bacon**. A player who chooses to roll zero dice scores points equal to one more than the absolute alternating difference of the digits of the opponent's score cubed.*Example 1*: The opponent has 4 points, and the current player chooses to roll zero dice.`4*4*4 = 64`

, so the current player gets`1 + |6 - 4| = 3`

points.*Example 2*: The opponent has 1 points, and the current player chooses to roll zero dice.`1*1*1 = 1`

, so the current player gets`1 + |1| = 2`

points.*Example 3*: The opponent has 20 points, and the current player chooses to roll zero dice.`20*20*20 = 8000`

, so the current player gets`1 + |8 - 0 + 0 - 0| = 9`

points.*Example 4*: The opponent has 45 points, and the current player chooses to roll zero dice.`45*45*45 = 91125`

, so the current player gets`1 + |9 - 1 + 1 - 2 + 5| = 13`

points.

The built-in

`abs`

function returns the absolute value of its argument.

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 `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.

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.

The Swine Swap rule is reproduced below:

**Swine Swap**. Define the*excitement*of the game to be three to the power of the sum of the players' scores. After points for the turn are added to the current player's score, if the excitement's first digit and last digit are the same, the scores should be swapped.*Example 1*: At the end of a turn, the players have scores of 2 and 4; 3^{2 + 4}= 729, and 7 != 9, the scores are not swapped.*Example 2*: At the end of a turn, the players have scores of 11 and 1; 3^{11 + 1}= 531441, and 5 != 1, the scores are not swapped.*Example 3*: At the end of a turn, the players have scores of 1 and 0; 3^{1 + 0}= 3, and 3 == 3, the scores are swapped.*Example 4*: At the end of a turn, the players have scores of 23 and 4; 3^{23 + 4}= 7625597484987, and 7 == 7, the scores are swapped.

IMPORTANT NOTE: Do not import any external modules to accomplish this task,`python`

can handle arbitrarily large numbers automatically. For example,`>>> 2 ** 1000 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376`

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 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.

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

`python3 ok -q 05a -u`

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

`python3 ok -q 05a`

### 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.)

The Feral Hogs rule is reproduced below:

**Feral Hogs**. If the number of dice you roll is exactly 2 away (absolute difference) from the number of points you scored on the previous turn, you get 3 extra points for the turn. Treat the turn before the first turn as scoring 0 points. Do**not**take into account any previous feral hog bonuses or swine swap (next rule) when calculating the number of points scored the previous turn.*Example 1:*- Both players start out at 0. (0, 0)
- Player 0 rolls 3 dice and gets
**7**points. (7, 0) - Player 1 rolls 1 dice and gets
**4**points. (7, 4) - Player 0 rolls
**5**dice and gets**10**points.**5**is 2 away from**7**, so player 0 gets a bonus of 3. (20, 4) - Player 1 rolls
**2**dice and gets**8**points.**2**is 2 away from**4**, so player 1 gets a bonus of 3. (20, 15) - Player 0 rolls
**8**dice and gets 20 points.**8**is 2 away from**10**, so player 0 gets a bonus of 3. (43, 15) - Player 1 rolls
**6**dice and gets 1 point.**6**is 2 away from**8**, so player 1 gets a bonus of 3. (43, 19)

*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 player 0 gets a bonus of 3. (6, 0)

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

`python3 ok -q 05b -u`

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

`python3 ok -q 05b`

Also make sure to re-run the checks for 5a. If these don't pass anymore, perhaps
you're not using the `feral_hogs`

argument correctly.

`python3 ok -q 05a`

The last test for Question 5b 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 the issue could be caused by errors in your answers to previous problems.

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`

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 before the checkpoint deadline:

`python3 ok --submit`

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!

## Phase 2: Commentary

You can work on and submit Phase 2 and 3 with a partner! Make sure one of you submits and then adds 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 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(prev_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 != prev_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. E.g.,
`announce_highest(1)`

and its return value ignore Player 0 entirely and just
print information about Player 1. 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 hog.py 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 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`

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 `g`

as an argument. It returns another function that takes
the same number of arguments as `g`

(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 `g`

on the same arguments.
This function should call `g`

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(g):
... def print_and_return(*args):
... result = g(*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(8)`

against the baseline strategy of `always_roll(6)`

.

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.

Note it is impossible for strategies to know what number of points the current player earned on the previous turn, and thus we cannot predict feral hogs. For strategies, we do not take into account bonuses from feral hogs to calculate bonuses against the margin or whether a swap will occur

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 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`

.

Note it is impossible for strategies to know what number of points the current player earned on the previous turn, and thus we cannot predict feral hogs. For strategies, we do not take into account bonuses from feral hogs to calculate bonuses against the margin or whether a swap will occur

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.

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 rolling more than 0 dice.
- Choose the
`num_rolls`

and`margin`

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 check your exact final win rate by running

`python3 calc.py`

This should pop up a window asking for you to confirm your identity, and then
it will print out a win rate for your final strategy. If it doesn't and instead
hangs, please download a fresh calc.py from here and put
it in your `hog`

folder.

The old `calc.py`

technically worked but took over an hour to give a solution,
this version just sends your strategy to our server where we use a super-fast
implementation of hog to calculate your win rate.

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.

Check to make sure that you did all the problems by running

`python3 ok --score`

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

`python3 hog_gui.py`

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.

/proj/hog_contest

## Hog Strategy Contest

If you're interested, you can take your implementation of Hog one step further by participating in the Hog Contest, where you play your `final_strategy`

against those of other students. The winning strategies will receive extra credit and will be recognized in future semesters!

To see more, read the contest description. Or simply check out the leaderboard.