%set seed
ng('shuffle');
%initial values
trueState=["goat","goat","car"];
%randomize them
trueState=trueState(randperm(3));
%player doesn't know what's behind any door;
%set all values to NaN
playerState=["door","door","door"];
%query use
playerChoice = questdlg('Pick a Door, any Door!', ...
'Monty Hall', ...
'1','2','3','1');
%convert to numeric
playerChoice=str2double(playerChoice);
%mark the chosen doo
playerState(playerChoice)="choice";
%if player chose the car...
if find(playerState=="choice")==find(trueState=="car")
%host selects randomly between the other two doors
remainingDoors=find(trueState=="goat");
openedDoor=remainingDoors(randi(2));
playerState(openedDoor)="goat";
else %otherwise, select the other door with the goat
playerState(trueState=="goat" & playerState=="door")="goat";
end
%identify door opened
hostChoice=find(playerState=="goat");
%identify remaining doo
emainingDoor=find(playerState=="door");
%ask the player if they want to switch
textToAsk=['You selected Door ' num2str(playerChoice) ...
'. Monty Hall opens Door ' num2str(hostChoice) ...
' and reveals a goat. Do you want to switch to Door ' ...
num2str(remainingDoor) '?'];
switchChoice = questdlg(textToAsk, ...
'Monty Hall', ...
'Yes','No','No');
%if the player switches, change their choice in playerState
if switchChoice=="Yes"
playerState(remainingDoor)="choice";
playerState(playerChoice)="door";
end
%determine player's reward
if find(playerState=="choice")==find(trueState=="car")
waitfor(msgbox('Congratulations! You won a car!'));
else
waitfor(msgbox('Congratulations! You won a goat!'));
end
Project 3: Monty Hall
For the third project, you will modify the Monty Hall code provided in lecture (monty_hall.m,
Week 10 folder on CCLE) to run in the Command Window and in docked figure windows,
produce images representing the state of the game at each step, and allow the player to start a
new game after completing one. Save your script as pj3_
.m where, as
in previous assignments, is replaced by your 9-digit student ID number.
Background
Let’s Make a Deal was a popular game show which began in 1963; the host of the game show
was named Monty Hall. On this show, like most game shows, people played games to win
prizes. The Monty Hall probability puzzle, which draws its name from the game show, was never
played on the show and has little to do with the show, so I won’t be discussing the show further.
The Monty Hall probability puzzle first appeared in The American Statistician in 1975 but was
popularized by its appearance in a reader’s letter in a column called “Ask Marilyn” in Parade
magazine by Marilyn vos Savant, the woman with (at the time, at least) the highest IQ ever
measured. Below is the problem. The bolded text represents the problem as originally
presented in Parade (which, as discussed in lecture, is woefully underspecified), while the
emaining text was added by me to clarify the rules of the game:
Suppose you're on a game show, and you're given the choice of three doors: Behind one
door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who
knows what's behind the doors, opens another door, say No. 3, which has a goat. He
then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch
your choice? EXTRA RULES: The host must always open a door that was not picked by the
contestant. The host must always open a door to reveal a goat and never the car. The host
must always offer the chance to switch between the originally chosen door and the remaining
closed door. If the host has a choice of which door to open (that is, the player chose co
ectly
and the other two doors have goats), the host will open one of the two doors with goat at
andom.
The co
ect answer is that you are more likely to win the car if you switch. Specifically, if you do
not switch, the probability of winning is 1 in 3, because in that case the second “Do you want to
switch?” part of the game is completely ignored and the game reduces to picking the door that
was originally chosen; because the probability that there is a car behind one of the three doors
at the beginning of the game is 1 in 3, the probability of winning if you do not switch is 1 in 3.
If you do switch, the probability of winning is 2 in 3, which is counterintuitive at first. Most people
elieve the probability is the same as above (1 in 3) or equal for the two doors (1 in 2). Consider
that the car can be behind any of the doors at the start of the game, and the probability that the
car is behind the door the player originally chose is 1 in 3. Likewise, the probability that the car
is behind one of the other two doors is 2 in 3. If the car is behind the door that the player chose,
then the host will open a door at random and the player will always lose if they switch. If the car
is behind a door that the player did not choose, then the host is forced to open the remaining
door with the goat (not chosen by the player, not containing a car) and the player will always win
if they switch because they will always switch to the car. Thus, there is a 1 in 3 chance that
switching will always yield a goat (car is behind the player’s door) and a 2 in 3 chance that
switching will always yield a car (car is not behind the player’s door), resulting in a probability of
winning if you switch in general of 2 in 3.
If that was confusing, don’t wo
y, you don’t need to understand the solution at all to complete
the project. If you still don’t believe it, you can do Extra Credit Option 2 and prove it to yourself.
Part 1: Trying again (3 points)
Your first task is to allow the player to repeat the game if they wish. This requires two additions:
1. Put the entire game in a while loop (1 point). You may put the rng('shuffle');
command inside or outside of the loop, it makes no difference
2. Add an extra query to the end of the game (inside the loop) asking the player if they would
like to play again (2 points). If the player says “No”, the loop should exit (see details on input
format below. Although I don’t like using
eak myself, feel free to use it here.
Part 2. Adapting the game for MATLAB Online (5 points)
If you try running my example code in MATLAB Online, you’ll see that MATLAB Online’s
treatment of dialog boxes is very clunky and ugly. It also makes the displays harder to see.
Using the Command Window to input and output text is much sleeker and is fully compatible
with the online platforms. For Part 2, you’ll adapt the game to run through the Command
Window, using the input function to take in user input (don’t forget the extra ‘s’ argument to
store the result as a string) and disp, sprintf, or fprintf to display any extra output.
Specifically:
• Change dialog boxes to Command Window input & output (1 point)
• Add Type 1, 2, or 3, then press Enter to the text when choosing a door (1
point)
o Only the single characters 1, 2, or 3 should allow the experiment to continue
• Add Type Y for Yes or N for No, then press Enter when asking to switch
and when asking to play again (1 point each)
o Your code should be case insensitive, accepting y or Y, n or N
o Only the single characters y, Y, n, or N should allow the experiment to continue
(or terminate, if n or N is given at the end)
• If an invalid input is provided, create a new input prompt with the text Invalid input;
please try again. (1 point)
o After each valid input, clear the command window with clc
Technical point: You can still use desktop MATLAB for this project; it does not need to be done
in MATLAB Online. If you do use desktop MATLAB, use this command to dock figures within
MATLAB:
f=figure('WindowStyle','docked’);
Comment this line out when you submit your project; it’s not worth points, but it will make
grading easier.
Part 3: Adding pictures (4 points)
Your second task is to add pictures to the game. The pictures to be used are in the Week 10
folder on CCLE:
• doors.png: The doors in the game. The objects behind the doors (goat or car) will be
inserted into the doors.
• goat.png: The goat
• car.png: The car
The following outline describes the desired behavior, or “script” of the game. Pay close
attention to all steps and make sure that your code follows this script exactly!
1. The “Run” button is pressed and the game begins.
2. The image of the doors is displayed (1 point), and the player is asked which door they
would like to select.
3. The player makes their selection: 1, 2, or 3.
4. The image is updated by inserting a goat into the door that the host (played by the
computer) selects. The image should be resized to fit within the door; see the
Bowser and Luigi code at the end of the Image Manipulation lecture for an
example. See the Bond code in the same lecture for an example of inserting one
image into another. None of the blue inside of the door should be visible once the
image is inserted, and at least one pixel of the black outline of the door should
emain on the outside of the image after insertion.
5. The new image of the doors is displayed (1 point), showing the goat, and the player is
asked if they would like to switch.
6. The player makes their selection: Y or N.
7. The image is updated by inserting the prize behind the player’s chosen door: the original
door if the player did not switch, and the door the player switched to if they switched.
This image will either be the goat or the