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 gamePlayability, appearance, interest

#2: the analysisParts 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 GAMEAnalysis 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 GAMESBy 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.

2 1/36

3 2/36

4 3/36

5 4/36

6 5/36

7 6/36

8 5/36

9 4/36

10 3/36

11 2/36

12 1/36

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 ScissorsOdds and EvensGiants Wizards ElvesCat and MouseThe Petersburg ParadoxMonty’s DilemnaThe Pancake ProblemSKUNK (the dice game)Count Down (dice game #2)HopperHappy Hopper #2BlinkoCard Game (invented)Perudo / Bluff / Dudo / Liar’s Dice

/ Pirates of the Caribbean

The Prisoner’s DilemnaHorse Race dice gameRouletteCrapsPokerSet (visual acuity, but

probability implied)Random number generators

and algorithmsJeopardylotterieshot streaksdice gamesBINGO

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 9th or 10th.