Pre Calculus Probability group project A group of 2-3 students and a willingness to have fun and think outside of the box. Task: Your task is to use your knowledge of probability, expected outcomes/rate of returns and what is fun to you and come up with a carnival game of chance for our class. Your game needs to be based on probability, not skill. (no bean bag tosses etc.) It cannot be a game that already exists - you must create a unique game. The game should take a relatively short time to play, so it can be played several times in class. You must be able to explain the probability of your game so don’t make it too complicated. The goal is to create a fun game that your peers will want to play. You will want to come up with a game that has a positive expected value for the house (you) but one where the players feel like they can win too. You will decide how many tokens the game will cost. Prizes/payouts must be clearly visible so the participant knows what they could possibly win. You will be judged by your peers and the teacher. Carnival day is Thursday, March 29th. The Write-Up 1. Introduction - Provide an overview of your game. (1 Per Group) What type of game is it? Where would you play this type of game? How much does it cost to play? What are the prizes if you win? 2. Instructions - Step-by-Step instructions for how to play the game. (1 Per Group) 3. Game Description – What do you need to play the game? (1 Per Group) List all materials needed to play (dice, spinner, darts, ball, etc.) Draw picture of your game board, if necessary 4. Probability Analysis (1 Per Group) Create a probability chart for each possible outcome and compute the payoff. Show the mathematical calculations for the expected value of winning the game. Is the game fair? If the game is not fair, how could you change the game to make it fair? Write up the actual payoff that occurred during the carnival. Show the number of trials and what happened and compare that with the mathematically expected return of your game. Calculate what you would expect to make/lose if your game was played 100 times. 5. Reflection – Each student must write a 1-page reflection (1 Per Person) What were your overall feelings about this project? Did this project help you understand the probability any better? How did your group work together? Relevance: What have you learned about “Fair Games”? What is your opinion about Las Vegas and the gaming industry? Do you think it’s fair to have establishments designed for people to lose money? What is your opinion on the lottery? Would you advise your grandmother to play? What do you think about gaming casinos? Your responsibility as a carnival participant: 1. 2. 3. 4. Write down the name of the game you are playing. (you must try at least 5 different booths) How many times did you play the game? (1-5) What was the value of the prizes/money you walked away with? Or how much money did you lose? General impressions of the game. Your responsibility at the booth: 1. Write down every trial and the outcome of the trial. (you need to keep track of this while you man the booth). 2. Be friendly and encourage people to try your game. To turn in (April 3rd start of class): 1. The Write-Up [30 pts] 2. Packet of all members tally sheets. [5 pts] 3. Packet of all members actual payoff work that occurred while they were at the booths. [5 pts] Tally Sheets Name of the game: Number of times I played: Net result of the trials: Overall impressions of the game: Name of the game: Number of times I played: Net result of the trials: Overall impressions of the game: Name of the game: Number of times I played: Net result of the trials: Overall impressions of the game: Name of the game: Number of times I played: Net result of the trials: Overall impressions of the game: Name of the game: Number of times I played: Net result of the trials: Overall impressions of the game: Name of the game: Number of times I played: Net result of the trials: Overall impressions of the game: Grading Rubric: CATEGORY Game Instructions Group WriteUp Probability Analysis Individual Reflection Neatness and Organization 5 4 3 2 Students create a fully functioning game that students can play. They bring all of the game materials to class. Instructions are clear and easy to follow. The game can be played by others without referring to the game creators for help. Group has comprehensive writeup including: introduction, instructions, game description and probability analysis. The write-up has been thoughtfully prepared and provides insight into the actions of the group. Group provides accurate analysis of the math behind their game. The idea of a fair game is clearly explained in terms of their project and an alternative for making their game fair is presented. Students create a game that students can play. There may be slight oversights, but overall the game can be played. Instructions are somewhat clear and easy to follow. The game can be played by others with minimal interaction with creators of the game. Group has write-up including: introduction, instructions, game description and probability analysis. The write-up provides some insight into the actions of the group. Students create a game, but it cannot be played in class. Students have an idea for a game. Group has written instructions but they are unclear and a verbal description of the game is necessary. Group has an incomplete writeup including some of the following: introduction, instructions, game description and probability analysis. Instructions are incomplete. Group provides somewhat accurate analysis of the math behind their game. The idea of a fair game is explained in terms of their project. An attempt at providing an alternative for making their game fair is presented. Reflection attempts to explain students thought process during the project. The relevance of the project is described. Group provides some analysis of the math behind their game. The idea of fair game is mentioned. Group attempts some sort of analysis of their probability. Reflection attempts to explain students thought process during the project. Some attempt at a reflection is made. The work is presented in a neat and organized fashion that is usually easy to read. The work is presented in an organized fashion but may be hard to read at times. The work appears sloppy and unorganized. It is hard to know what information goes together. Reflection clearly explains students thought process during the project. The relevance of the project is clearly described. The work is presented in a neat, clear, organized fashion that is easy to read. An attempt at a writeup is made.