You can work with a partner. Each of you should be familiar with all aspects of the game. This project has two components: #1: the game Playability, appearance, interest #2: the analysis Parts of the course that your game touches upon. The games are played at the end of the semester. A random draw is done to decide who presents their game on which day.

Different coloured destinations on the board correspond to different activities. Each activity is a separate mini-probability game. These could involve questions from the course. BOARD GAME APPROACH

A board game that utilizes concepts like Monty’s Dilemna, Hopper, and coin flipping elements.

GAME BOARD APPROACH Examples of analysis questions: Pose questions for yourself. e.g. What is the probability that you will land on a certain space on any turn? Do you roll again with doubles? Are there “chance cards”? e.g. If the destination is 12 squares away what is the probability that you will land on it on your next turn or on any turn? e.g. Are there connections to “Pascal-ish” types of route questions.

SPINNERS / DICE / COINS WHAT’S WRONG WITH THESE SPINNERS???

A football game with dice similar to the game of “Risk” whereby the offence rolls 3 dice and the defence rolls 2 dice. The offence advances different numbers of yards based on the outcomes of the die. Lots of probability opportunities here!

“Domination” An original game Players accumulate army stength, advance (upwards) on the board or attack their opponent’s army. This is based on drawing coloured dice from a bag (Hypergeometric probabilty distribution) and the results of the draw determines what options a player has. Each player may assume an offensive or defensive position. Advancing on the board followed a Fibinacci pattern and this was related to Pascal’s triangle.

CAT-MOUSE TYPE GAME Analysis could (should) include a flow chart or a tree diagram. Experimental and theortical probabilities possible, perhaps a simulation using MS Excel.

PLINKO GAMES Probabilities based on Pascal’s Triangle Consider a non- triangular shape and try to determine the best starting position This game includes betting on outcomes e.g. red / black / suit etc.

PASCAL’S TRIANGLE PROBABILITY GAMES By starting in one of the four corners, cards are drawn to determine advancement. Blocks (toothpicks) are placed on the board to hinder opponent’s advancement. Lots of “routes” type questions possible.

A “routes-type” racing game with players moving across the board and intercepting each other along the way. A spinner and dice determine the direction of travel and course of action.

POKER-LIKE GAMES: Warning… poker is well studied and difficult to do original work.

21/36 32/36 43/36 54/36 65/36 76/36 85/36 94/36 103/36 112/36 121/36 THIS IS NOT A SUFFICIENT PROBABILITY ANALYSIS

Remember: the goal of this project is to demonstrate your knowledge of probability Consider: Experimental and theoretical probaiblity Simple probabilities, independent and dependent events Conditional probability Permutations and Combinations Probability distributions (binomial? Hyper-geometric? Normal? Uniform? Expected value Pascal’s Triangle (number of routes…) tree diagrams (flow charts) using excel to run simulations. remember some of the games demonstrated in class and the probabilities discussed around them (e.g. Perudo, Cat and Mouse, Lovers and Lions, Skunk, Hoppers, …

To help get you started… take a look at these: Rock Paper Scissors Odds and Evens Giants Wizards Elves Cat and Mouse The Petersburg Paradox Monty’s Dilemna The Pancake Problem SKUNK (the dice game) Count Down (dice game #2) Hopper Happy Hopper #2 Blinko Card Game (invented) Perudo / Bluff / Dudo / Liar’s Dice / Pirates of the Caribbean The Prisoner’s Dilemna Horse Race dice game Roulette Craps Poker Set (visual acuity, but probability implied) Random number generators and algorithms Jeopardy lotteries hot streaks dice games BINGO

Please see your data management teacher for any clarification needed. As well, it is a good idea to check in with your teacher along the way so that (s)he can help you with ideas, suggestions, analysis, etc. Good luck. We look forward to playing your game on June 9 th or 10 th.