Sunday, March 9, 2014

Game Design

Probability Project:
Design Your Own Game
In this assignment, you will be designing your own game in groups of 3-4 students.  The game should be the type of game that you would play at a carnival, amusement park or casino.   It cannot be a game that already exists— your group must create a unique game.  You must be able to explain the probability of your game, so don’t make it too complicated!
Final Products (due 3/21/14):
1.       Game – Include all game boards, playing pieces, cards, balls, etc. for your game.
2.       Instructions - You must create a set of written or typed instructions to clearly explain your game.  They must be easy to follow so that anyone can pick them up, read them and begin playing your game.
3.       Write-Up – See below.
Grading:
See rubric (next page).
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)
      Is the game fair?  Show the mathematical calculations for the expected value of winning the game. If the game is not fair, how could you change the game to make it fair?
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?
      Were there any group members that didn’t pull their weight?  Any group members who tried to boss the group around?
      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?
Grading Rubric:









CATEGORY
4
3
2
1
Game
Students create a fully functioning game that students can play. They bring all of the game materials to class.
Students create a game that students can play. There may be slight oversights, but overall the game can be played.
Students create a game, but it cannot be played in class.
Students have an idea for a game.
Instructions
Instructions are clear and easy to follow. The game can be played by others without referring to the game creators for help.
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 written instructions but they are unclear and a verbal description of the game is necessary.
Instructions are incomplete.
Group Write-
Up
Group has comprehensive write-up 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 has write-up including: introduction, instructions, game description and probability analysis. The write-up provides some insight into the actions of the group.
Group has an incomplete writeup including some of the following: introduction, instructions, game description and probability analysis.
An attempt at a writeup is made.
Probability Analysis
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.
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.
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.
Individual Reflection
Reflection clearly explains students thought process during the project. The relevance of the project is clearly described.
Reflection attempts to explain students thought process during the project. The relevance of the project is described.
Reflection attempts to explain students thought process during the project.
Some attempt at a reflection is made.
Neatness and Organization
The work is presented in a neat, clear, organized fashion that is easy to read.
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.

Saturday, February 8, 2014

Probability Challenge

Wild Tic-Tac-Toe
This game is the same as ordinary tic-tac-toe, except that on each turn a player can choose to play an X or an O. You win if you get three X’s in a row, or three O’s in a row.
What move or moves should the first player make so they always win? Show and explain your work to validate your answer.
wild-tic-tac-toe1
Related Game:
Same as the above game except that, after the first move, all placements must be made to a space beside the last space occupied. (If no such space exists, the game is a tie.) Example: the second player wins here:
wild-tic-tac-toe2
Is there a sure way for the first or second player to win? Show and explain your work to validate your answer.
The Math in This Problem: This variation of Tic-Tac-Toe allows the players to place either an X or an O onto the 3×3 grid. The winner is the first player to complete three X’s or three O’s in a row. This twist to the game really forces you to analyze the grid and your opponent’s potential moves, encouraging you to strategize more than you would have in the original version.

Probability Vocabulary

Complete the following vocabulary list by finding the definition of the words. Ensure that your completed list is printed and made available for grading. This assignment can be done individually or you can share the responsibility (approximately 5 words per student). Remember you also get credit for posting in the class blog for this unit.


Addition Rules
Combination
Combination
Combination Formula
Complement
Compound Event
Compound Events
Conditional Probability
Conditional Probability
Continuous
Counting Principle
Dependent Events
Discrete
Disjoint (or mutually exclusive)
Element or member
Empty Set
Event
Experimental Probability
Factorial
Fair Decision
Finite
Independent Events
Infinite
Intersection
Intersection Formula
Joint Probability
Marginal Probability
Modeling
Multiplication Rule
Odds Against
Odds in Favor
Outcome
Overlapping Events
Permutation
Permutation
Permutation Formula
Probability
Probability Distribution
Probability of Complement of an Event
Probability of Dependent Events
Probability of Independent Events
Random
Random Number Generator
Random number tables
Random Variable
Sample Space
Set
Set Theory
Simulation
Subjective Probability
Subset
Theoretical Probability
Tree Diagrams
Two-way Frequency Table
Uniform Probability Model
Union
Union Formula
Universal Set
Variability
Venn Diagram