# Csci assignment 4: game of pig – monte carlo method

CSCI Assignment 4: Game of Pig – Monte Carlo Method

Collaboration Policy

We encourage collaboration on various activities such as lab, codelab, and textbook exercises. However, no collaboration between students is allowed on the programming assignments. Please be sure to read and understand our full policy at:

Student will demo their assignment to me for feedback and grading.

Assignment Specifications

We are going to use the Monte Carlo Method to determine the probability of scoring outcomes of a single turn in a game called Pig.

For this assignment you will simulate a given number of hold-at-N turns of a game called Pig, and report the estimated probabilities of the possible scoring outcomes. You are NOT implementing the game of Pig, only a single turn of this game. The value of N will be acquired via user input, as will the number of repetitions.

What is Pig?

Pig is a folk dice game with simple rules: Two players race to reach 100 points. In each turn, a player repeatedly rolls a die until either the player holds and is credited with the sum of the rolls so far (i.e. the current turn score) or rolls a 1 (“pig”), in which case the turn score is 0.

So at every point during a turn, the player is faced with a choice between two moves:

roll (again) – a roll of the die occurs

2 – 6: the number is added to the current turn score; the  turn continues

1: the player loses all points accumulated in the turn (i.e. scores a 0); turn ends

hold – The turn ends as the the hold option is invoked for one reason or another.

You can play the game yourself a few times before you start to think about the assignment. It can be useful to visualize and understand how a turn works. Play the game here.

Hold-at-N Turn Strategy

A good strategy to help decide when to hold and when to roll is the “hold-at-N strategy”:
the player chooses a number, N, that will hopefully both maximize their turn score while minimizing their chances of losing that score by rolling a 1; as soon as their current turn score reaches (or passes) N, the player holds.

We are going to test this strategy for different values of N, which will be supplied by user input, by simulating a number of turns (which will also be supplied by user input). Obviously, the larger the number of simulations, the better the estimate of probabilities.

For instance, suppose the user asks the program to test the strategy for N = 20.
We throw the die for a turn (“simulate a turn”), and get the following rolls:

Roll 1: 2 – current turn score = 2
Roll 2: 5 – current turn score = 7
Roll 3: 6 – current turn score = 13
Roll 4: 2 – current turn score = 15
Roll 5: 4 – current turn score = 19
Roll 6: 3 – current turn score = 22

At this point we end the turn by holding, since we have a score of 22 (which is at least our N).

Of course, if we simulate the same turn again, we might get:

Roll 1: 6 – current turn score = 6
Roll 2: 5 – current turn score = 11
Roll 3: 5 – current turn score = 16
Roll 4: 3 – current turn score = 19
Roll 5: 1 – current turn score = 0

We rolled a 1 which according to the rules ends the turn and grants a turn score of 0.

Question: for N = 20, what range of scores are possible? How many variables will you need to hold the probability estimates for those scores? What if we choose another number for N?

Again, remember that you are only implementing one turn of this game and then simulating it many times to estimate the probability of each scoring outcome of this turn strategy.

Random Seed Requirement

You will of course, be using the C++ cstdlib library function rand(), which you will “prime” with a seed value using the function srand(int).

As you know, if you want to get different random values every time you run a program using the rand function, you should seed it with srand(time(0));

When you are testing your program, however, you will want to directly compare your program’s output with the sample runs below, so you will want to work with the exact same random values that are used in our solution. To do this you have to seed rand with 333: srand(333);

If you are not working on Cloud 9 then your values may differ from the sample results, even using the seed 333, due to differing implementations of rand() on different operating systems.

Input Requirements

Enter a single positive integer indicating the number at which to hold.

Enter a single positive integer indicating the number of turns to be simulated.

Larger numbers will tend to yield better estimations but take longer to execute.

We test with both small and large numbers, so testing may take some time.

Output Requirements

Prompt the user with: “What value should we hold at? “

Prompt for number of simulations: “Hold-at-N turn simulations? “

Output a blank line between the input prompt and table output.

On the next line, print “Score” and “Estimated Probability” separated by a tab (‘t’).

After the simulations, print a table line for each score outcome that occurred, in increasing order of score.

For each score outcome, print the score, a tab, and the fraction of turn simulations that yielded that score rounded to six digits after the decimal place.

Print the table to a file named “output.txt”

Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

## Calculate the price of your order

Total price:
\$0.00

How it works?

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

## Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.