Stats 102A - Homework 4 Instructions: Monopoly
Homework questions and instructions copyright Miles Chen, Do not post, share, or distribute without permission.
Homework 4 Requirements
You will submit three files.
The files you submit will be:
1. 102a_hw_04_script_First_Last.R Your R script file containing the functions you write for the homework
assignment. Write comments as necessary.
2. 102a_hw_04_output_First_Last.Rmd Take the provided R Markdown file and make the necessary edits so
that it generates the requested output. The first line of your .Rmd file should be to source the R script file you
wrote.
3. 102a_hw_04_output_First_Last.pdf Your output PDF file. This is the primary file that will be graded. Make
sure all requested output is visible in the output file.
Failure to submit all files will result in an automatic 40 point penalty.
Academic Integrity
At the top of your R markdown file, be sure to include the following statement after modifying it with your name.
“By including this statement, I, Joe Bruin, declare that all of the work in this assignment is my own original work.
At no time did I look at the code of other students nor did I search for code solutions online. I understand that
plagiarism on any single part of this assignment will result in a 0 for the entire assignment and that I will be referred
to the dean of students.”
If you collaborated verbally with other students, please also include the following line to credit them.
“I did discuss ideas related to the homework with Josephine Bruin for parts 2 and 3, with John Wooden for part 2,
and with Gene Block for part 5. At no point did I show another student my code, nor did I look at another student’s
code.”
Recommended Reading:
a. S3 (not necessary for this HW): https://adv-r.hadley.nz/s3.html
b. R6: https://adv-r.hadley.nz/r6.html
Monopoly Board game simulation
For this homework assignment, you will create a simulation of the classic board game,
Monopoly. The goal is to find out which spaces on the board get landed on the most.
You will not simulate the entire game. You will simulate only the movement of pieces, and will keep track of which
squares the pieces land on.
You can familiarize yourself with the game board. (Taken from Amazon’s product page.)
http://ecx.images-amazon.com/images/I/81oC5pYhh2L._SL1500_.jpg
Official rules https://www.hasbro.com/common/instruct/monins.pdf
1
Rules for movement
The Monopoly Board is effectively a circle with 40 spaces on which a player can land. Players move from space to
space around the board in a circle (square).
The number of spaces a player moves is determined by the roll of 2 dice. Most often, the player will roll the dice, land
on a space, and end his turn there. If this were the entire game, the spaces would have a uniform distribution after
many turns.
There are, however, several exceptions which provide the primary source of variation in space landing.
Go to Jail
One space, “Go to Jail” sends players directly to jail (there is a jail space on the board). This space never counts as
having been ‘landed upon.’ As soon as the player ‘lands’ here, he is immediately sent to jail, and the jail space gets
counted as landed upon. This is the only space on the game board that moves a player’s piece. The count of how
often this space is landed on will always be 0.
Rolling Doubles
If a player rolls doubles (two of the same number), the player moves his piece, and then gets to roll the dice again for
another move. However, if a player rolls doubles three times in a row, he is sent directly to jail. (The third space that
the player would have ‘landed on’ does not count, but the jail space gets counted as landed on.)
Card Decks: Chance and Community Chest
A player can land on a “Chance” or “Community Chest” space. When a player lands on these spaces, he draws a
card from the respective deck and follows its instructions. The instructions will sometimes give money to or take
money from the player with no change in the player’s position on the board. Other times, the card will instruct the
player to move to another space on the board. The list of cards that can be drawn from each deck is provided.
There are nine cards in the Chance deck that move the player’s token. There are two cards in the Community Chest
deck that move the player’s token. All other cards do not move the player’s token. For the sake of this simulation,
you only need to program actions for the cards that move the tokens. There is no need to do anything for ‘get out of
jail’ or any of the other cards.
A card may say ‘move to the nearest railroad’ or ‘move to the nearest utility’ or even ‘go to property . . . ’. In these
cases, the player always moves forward. So if a player is on ‘Oriental Avenue,’ the nearest railroad is ‘Pennsylvania
Railroad’ and NOT ‘Reading Railroad.’
For the sake of this simulation, the Chance and Community Chest get counted as landed on when the player
lands on the Chance or Community Chest space. The player may also generate another count if the card moves the
player to another space on the board. In those cases, a tally is counted for the Chance/Community Chest space, the
token is moved, and then a tally is counted for the space where the player ends his turn.
Jail
Jail is the most complicated aspect of this simulation.
If a player lands on space 11 (Jail) simply from rolling the dice, he is not in Jail. He is ‘just visiting’ jail. He generates
a tally for landing on jail, and his play continues on as normal.
A player can be sent to jail in several ways:
• he rolls doubles three times in a row;
• he lands on the “go to jail” space;
• he draws a card that sends hims to jail.
As soon as the player is sent to jail, his token moves to jail (space 11), he generates a count for landing on jail, and
his turn ends immediately.
2
On the next turn, the player begins in jail and the player will roll the dice. If he rolls doubles on the dice, he gets out
of jail and moves the number of spaces the dice show. However, even though he rolled doubles, he does NOT roll
again. He takes his move out of jail and his turn ends. If he does not roll doubles, he stays in jail.
A player cannot stay in jail for more than three turns. On the third turn he begins in jail, he rolls the dice and moves
the number of spaces the dice show no matter what.
Play then continues as normal.
For this simulation, each time a player ends his turn in Jail, a tally will be counted as having been ‘landed upon.’
There are more rules on jail that include paying a fee to get out early, or using a get out of jail free card. We will not
implement those rules. We will simply simulate a ‘long stay’ strategy for Jail. This means that the player will never
pay the fee to get out jail early. He will roll the dice and only leave jail if he gets doubles or it is his third turn in jail.
The Assignment
Your assignment is to implement the rules of Monopoly movement.
You must use R6 to create an object class Player which will be used to keep track of a player.
Part 1
You will first demonstrate that you have coded the rules by showing the output of the first 20 turns using the preset
dice. Your output for this section should match the published results exactly.
The output should be very verbose. It should announce the player roles, where the player moves, what spaces get
tallies, if they rolled doubles, etc.
Part 2
The next part is to run 1,000 simulations of a two-player game that lasts 150 turns. This is a total of over 3 hundred
thousand tosses of the dice - 1000 games x 150 turns x 2 players + additional rolls if the player gets doubles.
Your task is to keep track of where the players land. We ultimately want to build a distribution showing which
spaces are most likely to be landed upon. Advance the tokens around the board according to the rules. Keep in mind
the special situations involving the cards, jail, and rolling doubles. After 150 turns, reset the game and start over.
Simulate 1000 games.
Your final output will be two tables of the spaces on the board and their frequencies. Each table will show the space
name, how many times the space was landed upon, and the relative frequency of landing on that space.
The first table is arranged in descending order of frequency of landing. (Jail should be #1, Go to jail should be last.)
The second table is arrange in the order of the spaces on the board. (Go will be #1, Boardwalk will be last.)
Also print a bargraph showing the frequency of how often each space is landed on.
You do not have to simulate or track money at all in this simulation.
Starter Code
For your convenience, I have created the necessary data frames for the game board, and the two decks of cards.
I have also created several helper R6 classes for you:
• PresetDice: You will use this for Part 1: showing the movement of the player for 20 turns
• RandomDice: You will use this for Part 2: the simulation of 1000 games.
• CardDeck: For creating the Chance and Community Chest decks. This reference class ‘shuffles’ the deck, and
each time a player draws a card, it shows the next card drawn. When all the cards in the deck have been used,
it ‘shuffles’ the deck again.
Please take the time to read through these R6 class definitions. Understanding the definitions, and what the methods
do will be helpful in completing the assignment.
3
Tips
At first blush, the task may seem overwhelming.
• Break the task into smaller manageable parts.
• Start with a simulation that moves pieces around the board and keeps track of where they land. (I’ve done this
part for you in my example code.)
• Then add complexity one part at a time. Each time you add something, thoroughly test it to make sure it
behaves the way you want it to.
• The PresetDice reference class will be very helpful in your testing. For example, you can intentionally create
some dice rolls to test certain situations. What to test if Chance is working correctly? Set your dice to cause
the player to land on Chance. Want to test if doubles is working correctly? Set the PresetDice to produce
doubles. If you had purely random dice, you might have to wait for the computer to produce many many
random outcomes before you see three doubles in a row.
My recommendation in terms of adding complexity:
• Add code so landing on “Go to jail” sends the player to jail.
• Add code that draws from the Chance and Community Chest decks and moves the player accordingly. Keep in
mind that some cards have no effect on player movement, while other cards do.
• Add code to allow players to move again after doubles.
• Add code to implement the rules for Jail. You’ll need to keep track of whether the player is actually in jail or
not, how many turns the player has been in jail, and the rules for getting out.
Grading
1. Do NOT print the verbose version for all of 1000 games.
2. We will not run your code. The simulation will take time to run, and we do not have the luxury of running the
entire simulation for all students.
3. We will check the output of the 20 preset turns.
These are the point values of each turn. I also specify the rule implementation that we are looking for in each of these
turns.
• Turn 4 (8 pts) Roll three sets of doubles, third doubles sends player to jail, also drawing community chest
• Turn 6 (4 pts) Rolling doubles exits jail
• Turn 8 (4 pts) Go to jail space sends player to jail
• Turn 11 (4 pts) Third turn. No doubles roll. Player exits jail.
• Turn 14 (4 pts) Chance card advances to nearest railroad. Take a ride on Reading Railroad.
• Turn 15 (4 pts) Chance card that doesn’t move and rolling doubles.
• Turn 16 (4 pts) Chance card that sends player to jail.
• Turn 19 (4 pts) Rolled doubles on third turn in jail. Gets out of jail.
• The other 12 turns are worth 2 points each.
That is 60 points.
4. We will check the final output of counts in the results tables.
Things we are looking for in the results tables (5 points each):
• Jail should be the most frequent space landed on.
• Jail should have a frequency between 10 and 13%.
• Spots 2 and 3 should be Illinois Ave and Go (possibly switched)
• New York Ave. and Tennessee Ave. should be in the top 10.
• Reading Railroad and B&O Railroad should be in the top 10.
• Mediterranean Ave and Baltic Ave should be in the bottom 5.
• Park Place should be very infrequent. Bottom 10.
• Go to jail should be landed on 0 times.
5. If your 20 turn output and table output matches what we are looking for, you will get full credit.
4
6. If your outputs do not match, We will skim your code to see if certain functions or chunks of code exist to see if
you can recover some (up to half) of the points you lost.
We will check for the following sections. Because your code will be quite long, it is VERY IMPORTANT you
CLEARLY mark these sections for the grader if you want to recover points.
a. drawing chance card
b. drawing community chest card
c. landing on “go to jail”
d. roll again for rolling doubles
e. going to jail for rolling three doubles
f. jail functionality
You can ‘hard code’ the functions that handle the decks. In other words, you can write something along the lines of
## for chance deck
...
if(carddrawn == 1)
code changes player position to space 1 # advance to go
if(carddrawn == 2)
code changes player position to space 25 # advance to Illinois avenue
# etc.
...
Good luck!
I know this is a tough assignment. Like everything else in life, sometimes you have to prioritize other things (eg.
health, sleep, sanity, etc.) over the task at hand.
If you are unable to implement all parts of the solution, that is also okay. I cannot give you full credit, but please
indicate what you were able to implement and what you were not able to implement. You will be graded on what you
were able to complete.
You are encouraged to talk with other students currently enrolled in Stats 102A.
Best wishes!