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Homework 2 - Shall We Play A Game?
June 25, 2019
General Notes
You will submit a minimum of three files, the core files must conform to the following naming conventions
(including capitalization and underscores). 123456789 is a placeholder, please replace these nine digits
with your nine-digit UID. The files you must submit are:
1. 123456789_stats102a_hw2.R An R script file containing all of the functions you wrote for the
homework. The first line of your .Rmd file, after loading libraries, should be sourcing this script.
2. 123456789_stats102a_hw2.Rmd Your markdown file which generates the output file of your
submission.
3. 123456789_stats102a_hw2.html/pdf Your output file, either a PDF or an HTML file depending
on the output you choose to generate.
4. included image files You may name these what you choose, but you must include all of the
image files you generated for your structured flowcharts, otherwise your file will not knit.
If you fail to submit any of the required core files you will receive ZERO points for the assignment.
If you submit any files which do not conform to the specified naming convention, you will receive (at
most) half credit for the assignment.
Your coding should adhere to the tidyverse style guide: https://style.tidyverse.org/
All flowcharts should be done on separate sheets of paper, but be included, inline as images, in your
final markdown document.
Any functions you write should be included in a separate functions file.
Your .Rmd file must knit. If your .Rmd file does not knit you will receive (at most) half credit for the
assignment.
The two most common reasons files fail to knit are because of workspace/directory structure issues and
because of missing include files. To remedy the first, ensure all of the file paths in your document are relative
paths pointing at the current working directory. To remedy the second, simply make sure you upload any
and all files you source or include in your .Rmd file.
NOTE: Everything you need to do this assignment is here, in your class notes, or was covered in discussion
or lecture.
DO NOT look for solutions online.
EVERYTHING you submit MUST be 100% your, original, work product. Any student suspected
of plagiarizing, in whole or in part, any portion of this assignment, will be immediately referred to
the Dean of Student’s office without warning, and you will get a zero for all parts of the tainted
homework.
YOU MAY collaborate on this assignment with a maximum of TWO other students.
– Each person must type up and submit their own files.
– Each person MUST include the name and UID of each collaborator at the top of their output file.
– You and your collaborators will receive the same grade though only one set of files will be scored.
Make sure you trust your collaborators!
– If you collaborate with another student and do not disclose it, it will be considered plagiarism.
1
Homework 2 Requirements
For each of the following problems you will:
a) Create a structured flowchart of the game and all functions/subroutines.
b) Write pseudocode sufficiently complete, clear, and concise enough to enable a person to accurately
implement the your design in any programming language they are adept with using.
c) You do not need to do complexity analysis of your game.
d) Finally, you must write the functions/subroutines which will allow your game to be played.
Chutes and Ladders
Rules
NOTE: The spinner has values 1-6.
2
(1) Create a representation of the game board.
Create an object in R to represent the default Chutes and Ladders game board, in whatever way you choose.
(2) Create a function to show the game board.
Your function should be named show_board() and take one argument board which is the internal represen?tation of the game board you have decided on.
The output of the function should be an image (i.e., a graphical representation of the game board) showing
the board with arrows representing the chutes and ladders. In keeping with the spirit of the original game,
make red arrows to represent the chutes and yellow arrows to represent the ladders.
(3) Write a function to simulate one game of Chutes and Ladders.
Your function should be named play_cl() and take the following arguments:
n_players The number of players. The original rules stipulate this is a game for 2-4 players, but your function
should accept an arbitrary integer value greater than zero. The default value should be 1.
spinner The number of values on the spinner or the individual values on the spinner. If spinner is a single
integer value (example: 6), your game will be played with a spinner that has 6 values on it: 1, 2, 3, 4, 5,
6. If, however, the value in spinner is a vector of integer values (example: c(1, 1, 3, 5, 7)), your game
will be played with a spinner with exactly those values.
The output of your function should be a list containing at least the following information:
winner An integer representing which player won the game.
turns A length-n_players integer vector containing the number of turns taken by each player.
chutes A length-n_players integer vector containing the number of times each player slid down a chute.
ladders A length-n_players integer vector containing the number of times each player climbed a ladder.
For some of the questions you will be answering, you may need to include additional information in the list
you return. Read through all of the question you will be asked to answer before you start programming.
3
Questions
A) Standard Game
1. Using the play_cl() function, simulate 10, 000 one-player games of Chutes and Ladders, immediately
before you simulate your data, set your random seed to your UID.
2. Using the play_cl() function, simulate 10, 000 two-player games of Chutes and Ladders, immediately
before you simulate your data, set your random seed to your UID with the digits in reverse order.
3. Using the play_cl() function, simulate 10, 000 three-player games of Chutes and Ladders, immediately
before you simulate your data, set your random seed to your UID then set the random seed to
sample(1e4, 1).
Answer the following questions for each of your simulations above:
a) What is the minimum number of turns needed to win the game? NOTE: This is the number of turns
all players took before the game ended.
b) What proportion of games are won by each player?
c) What proportion of games ended in the minimum number possible?
d) What proportion of games were "close?" For the purpose of this question, we will define a close game as
one where a player other than the winner would be capable of winning on their next turn.
e) What is the maximum number of turns needed to finish the game.
f) If a player has completed at least least 6 turns, what is the most likely square for that player to be on
at the end of their 6
th turn?
Also answer the following questions:
4. Plot the distribution of turns needed to finish each game setup (one, two, and three-player) on one set
of axes.
5. What proportion of three-player games ended in fewer total turns than the observed maximum number
of turns for one-player games
B) Custom Game
Write a function make_random_board() which, perhaps unsurprisingly, generates a random Chutes and
Ladders game board to play on. This function should take at least the following arguments:
n_rows The number of rows. The default value should be 10.
n_cols The number of columns. The default value should be 10.
n_chutes The number of chutes. The default value should be 10.
n_ladders The number of columns. The default value should be 9.
You are free to decide how the chutes and ladders are placed on your board, with the following caveats:
It must be possible to complete the game.
No chute or ladder may end or begin on the same square another chute or ladder begins or ends on.
You are free to add any additional optional arguments you want, though you are not required to do so. Some
ideas might include:
longest_chute Maybe you don’t want super long chutes which send a player from square 99 back to square 1.
shortest_ladder Maybe you don’t want pointless ladders which let a player move up only one square.
4
min_spacing Maybe you want to make sure you don’t have the starts of two chutes or the starts of two ladders right
next to each other. Otherwise, you could generate an impossible game (imagine a game with six chutes
in a row and no ladder bypassing them).
Once you have the function make_random_board() written, generate a 11 × 13 board with 13 chutes and 11
ladders. Show the board, and run the three simulations again with a spinner with the values 1, 2, 3, 5, 7, 11,
and 13 (with the same seed setting procedures) then answer all of the above questions again.
5
Homework 2 - Shall We Play A Game?
June 25, 2019
General Notes
You will submit a minimum of three files, the core files must conform to the following naming conventions
(including capitalization and underscores). 123456789 is a placeholder, please replace these nine digits
with your nine-digit UID. The files you must submit are:
1. 123456789_stats102a_hw2.R An R script file containing all of the functions you wrote for the
homework. The first line of your .Rmd file, after loading libraries, should be sourcing this script.
2. 123456789_stats102a_hw2.Rmd Your markdown file which generates the output file of your
submission.
3. 123456789_stats102a_hw2.html/pdf Your output file, either a PDF or an HTML file depending
on the output you choose to generate.
4. included image files You may name these what you choose, but you must include all of the
image files you generated for your structured flowcharts, otherwise your file will not knit.
If you fail to submit any of the required core files you will receive ZERO points for the assignment.
If you submit any files which do not conform to the specified naming convention, you will receive (at
most) half credit for the assignment.
Your coding should adhere to the tidyverse style guide: https://style.tidyverse.org/
All flowcharts should be done on separate sheets of paper, but be included, inline as images, in your
final markdown document.
Any functions you write should be included in a separate functions file.
Your .Rmd file must knit. If your .Rmd file does not knit you will receive (at most) half credit for the
assignment.
The two most common reasons files fail to knit are because of workspace/directory structure issues and
because of missing include files. To remedy the first, ensure all of the file paths in your document are relative
paths pointing at the current working directory. To remedy the second, simply make sure you upload any
and all files you source or include in your .Rmd file.
NOTE: Everything you need to do this assignment is here, in your class notes, or was covered in discussion
or lecture.
DO NOT look for solutions online.
EVERYTHING you submit MUST be 100% your, original, work product. Any student suspected
of plagiarizing, in whole or in part, any portion of this assignment, will be immediately referred to
the Dean of Student’s office without warning, and you will get a zero for all parts of the tainted
homework.
YOU MAY collaborate on this assignment with a maximum of TWO other students.
– Each person must type up and submit their own files.
– Each person MUST include the name and UID of each collaborator at the top of their output file.
– You and your collaborators will receive the same grade though only one set of files will be scored.
Make sure you trust your collaborators!
– If you collaborate with another student and do not disclose it, it will be considered plagiarism.
1
Homework 2 Requirements
For each of the following problems you will:
a) Create a structured flowchart of the game and all functions/subroutines.
b) Write pseudocode sufficiently complete, clear, and concise enough to enable a person to accurately
implement the your design in any programming language they are adept with using.
c) You do not need to do complexity analysis of your game.
d) Finally, you must write the functions/subroutines which will allow your game to be played.
Chutes and Ladders
Rules
NOTE: The spinner has values 1-6.
2
(1) Create a representation of the game board.
Create an object in R to represent the default Chutes and Ladders game board, in whatever way you choose.
(2) Create a function to show the game board.
Your function should be named show_board() and take one argument board which is the internal represen?tation of the game board you have decided on.
The output of the function should be an image (i.e., a graphical representation of the game board) showing
the board with arrows representing the chutes and ladders. In keeping with the spirit of the original game,
make red arrows to represent the chutes and yellow arrows to represent the ladders.
(3) Write a function to simulate one game of Chutes and Ladders.
Your function should be named play_cl() and take the following arguments:
n_players The number of players. The original rules stipulate this is a game for 2-4 players, but your function
should accept an arbitrary integer value greater than zero. The default value should be 1.
spinner The number of values on the spinner or the individual values on the spinner. If spinner is a single
integer value (example: 6), your game will be played with a spinner that has 6 values on it: 1, 2, 3, 4, 5,
6. If, however, the value in spinner is a vector of integer values (example: c(1, 1, 3, 5, 7)), your game
will be played with a spinner with exactly those values.
The output of your function should be a list containing at least the following information:
winner An integer representing which player won the game.
turns A length-n_players integer vector containing the number of turns taken by each player.
chutes A length-n_players integer vector containing the number of times each player slid down a chute.
ladders A length-n_players integer vector containing the number of times each player climbed a ladder.
For some of the questions you will be answering, you may need to include additional information in the list
you return. Read through all of the question you will be asked to answer before you start programming.
3
Questions
A) Standard Game
1. Using the play_cl() function, simulate 10, 000 one-player games of Chutes and Ladders, immediately
before you simulate your data, set your random seed to your UID.
2. Using the play_cl() function, simulate 10, 000 two-player games of Chutes and Ladders, immediately
before you simulate your data, set your random seed to your UID with the digits in reverse order.
3. Using the play_cl() function, simulate 10, 000 three-player games of Chutes and Ladders, immediately
before you simulate your data, set your random seed to your UID then set the random seed to
sample(1e4, 1).
Answer the following questions for each of your simulations above:
a) What is the minimum number of turns needed to win the game? NOTE: This is the number of turns
all players took before the game ended.
b) What proportion of games are won by each player?
c) What proportion of games ended in the minimum number possible?
d) What proportion of games were "close?" For the purpose of this question, we will define a close game as
one where a player other than the winner would be capable of winning on their next turn.
e) What is the maximum number of turns needed to finish the game.
f) If a player has completed at least least 6 turns, what is the most likely square for that player to be on
at the end of their 6
th turn?
Also answer the following questions:
4. Plot the distribution of turns needed to finish each game setup (one, two, and three-player) on one set
of axes.
5. What proportion of three-player games ended in fewer total turns than the observed maximum number
of turns for one-player games
B) Custom Game
Write a function make_random_board() which, perhaps unsurprisingly, generates a random Chutes and
Ladders game board to play on. This function should take at least the following arguments:
n_rows The number of rows. The default value should be 10.
n_cols The number of columns. The default value should be 10.
n_chutes The number of chutes. The default value should be 10.
n_ladders The number of columns. The default value should be 9.
You are free to decide how the chutes and ladders are placed on your board, with the following caveats:
It must be possible to complete the game.
No chute or ladder may end or begin on the same square another chute or ladder begins or ends on.
You are free to add any additional optional arguments you want, though you are not required to do so. Some
ideas might include:
longest_chute Maybe you don’t want super long chutes which send a player from square 99 back to square 1.
shortest_ladder Maybe you don’t want pointless ladders which let a player move up only one square.
4
min_spacing Maybe you want to make sure you don’t have the starts of two chutes or the starts of two ladders right
next to each other. Otherwise, you could generate an impossible game (imagine a game with six chutes
in a row and no ladder bypassing them).
Once you have the function make_random_board() written, generate a 11 × 13 board with 13 chutes and 11
ladders. Show the board, and run the three simulations again with a spinner with the values 1, 2, 3, 5, 7, 11,
and 13 (with the same seed setting procedures) then answer all of the above questions again.
5