I know! I'll use my

Higher-order functions to

Order higher rolls.

- Introduction
- Logistics
- Graphical User Interface
- Testing
- Phase 1: Simulator
- Problem 0 (0 pt)
- Problem 1 (1 pt)
- Problem 2 (1 pt)
- Problem 3 (1 pt)
- Problem 4 (1 pt)
- Problem 5 (3 pt)
- Phase 2: Strategies

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:

**Free bacon**. A player who chooses to roll zero dice scores one more than the absolute difference in the digits of the opponent's two-digit score.*Examples:*if Player 1 has 42 points, Player 0 gains 1 + abs(4-2) = 3 points by rolling zero dice. If Player 1 has 48 points, Player 0 gains 1 + abs(4-8) = 5 points.**Hog wild**. If the sum of both players' total scores is a multiple of seven (e.g., 14, 21, 35), then the current player rolls four-sided dice instead of the usual six-sided dice.**Swine swap**. If at the end of a turn one of the player's total score is exactly double the other's, then the players swap total scores.*Example 1:*Player 0 has 20 points and Player 1 has 5; it is Player 1's turn. Player 1 scores 5 more, bringing the total to 10. The players swap scores: Player 0 now has 10 points and Player 1 has 20. It is now Player 0's turn.*Example 2*: Player 0 has 90 points and Player 1 has 50; it is Player 0's turn. Player 0 scores 10 more, for a total of 100. The players swap scores, and Player 1 wins the game 100 to 50.

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.

`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` |

`images` |
A directory of images used by `hog_gui.py` |

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 `hog.py`

. 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 `hog.py`

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).

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

`python3 hog_gui.py -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 @berkeley.edu
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.

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

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. 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.**

Implement the `roll_dice`

function in `hog.py`

. 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`

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
```

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
```

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:

- If the bids are equal, each player starts with
`goal`

points, resulting in an instant tie. It does not matter who rolls first. - 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.
- 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
```

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:

- Remember to enforce all the special rules! You should enforce the
*Hog wild*special rule here (by calling`select_dice`

), as well as the*Swine swap*special rule here. - You should use the
`take_turn`

function that you've already written. - You can get the value of the other player (either 0 or 1) by calling
the provided function
`other`

. - A
*strategy*is a function that determines how many dice a player wants to roll, depending on the scores of both players. A strategy function (such as`strategy0`

and`strategy1`

) takes two arguments: scores for the current player and opposing player. A strategy function returns the number of dice that the current player wants to roll in the turn. Don't worry about details of implementing strategies yet. You will develop them in Phase 2.

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 `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.

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!

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.

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
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
```

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 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(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.

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.

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

- Rolls 0 if it would cause a beneficial swap that gains points.
- Rolls
`num_rolls`

if rolling 0 would cause a harmful swap that loses points. - 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`

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.**

- Find a way to leave your opponent with four-sided dice more often.
- If you are in the lead, you might take fewer risks. If you are losing, you might take bigger risks to catch up.
- Vary your rolls based on whether you will be rolling four-sided or six-sided dice.
- Trigger a beneficial swine swap by trying to score only one point.

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 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!