Math 131

Spring 04

Paper 5: Probability Game

 

            For this paper you will invent and analyze a probability game.  Your game can be a variation (even slight) of one of the games discussed in class.  Your analysis will include both computer simulations and theoretical portions (although the proportions of these two will depend on the game itself).

            Your game should meet the following criteria:

 

            1.  Involves an element of chance, generally by using dice, spinners, tiles in a bag, etc.

            2.  Involves some kind of decision, i.e. whether to be player A or player B, when to stop rolling a die, etc.

            3.  Computer simulation can be used to analyze at least some aspect of the game.  Some games are straightforward to simulate on a computer, whereas others (such as Pig) are more difficult to simulate, but simulation can still be used to analyze strategies. 

            4.  Fun!  Often the games that are more fun and/or more interesting mathematically are more difficult to analyze, but it’s fine to choose a more challenging game and do analysis that is less complete.

 

            You can write your paper in many different ways.  You can address an audience of teachers, discussing your game and how it can help children learn math.  You can address a future player of the game.  You can write the story of how you learned to play your game well.

 

Your paper must include the following (in any order):

 

1.  A clear description of your game that is easy to follow for someone who has never seen it before.

2.  Some theoretical discussion of strategy for the game  appropriate for the specific game you’ve devised (you can ask for help with determining the appropriate level here and in the next part).   Some games will be easier to analyze theoretically than others.

3.  Discussion of the results of your computer simulations, once again, appropriate to your game.  For games that yield a complete theoretical analysis and don’t have much strategy, your discussion will primarily compare theoretical and experimental results.  For games that are more complicated, your simulations will give you insight into strategy.  For example, for the game Pig, you might do a simulation to compare several strategies for playing the game, checking how many points you would receive on a typical turn using each strategy.

 

Copyright 2005, Debra K. Borkovitz.  You may copy or edit this material for non-profit, educational use only.

 

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Name ____________________________

 

 

Using the scoring guide below, what score do you think you deserve on your paper, and why?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Scoring Guide for Paper 5

 

Level 5  -- Goes beyond Level 4, in scope, depth, and/or quality of writing. 

           

Level 4  Analysis is accurate and insightful.  Shows clear understanding of both the theoretical and experimental aspects of the analysis, and the analysis is appropriate to the difficulty of the game.  Game is clearly described.  Writing is clear and representations enhance communication in meaningful ways.   The paper can also go beyond the assignment in a significant way that makes up for deficiencies in the listed criteria.

 

Level 3  Includes much good analysis.  Shows understanding of most of the theoretical and experimental aspects of the analysis.  Perhaps analysis is not quite appropriate for the game.  Game is clearly described.  Writing is mostly clear and representations enhance communication in meaningful ways.

 

Level 2   Includes some good analysis.  Shows some understanding but some misconceptions or analysis is much less than appropriate for the game.  Writing is sometimes clear, sometimes not, and representations are sometimes used well, sometimes not.

 

Level 1  Does some part of the assignment reasonably well, but much is missing or incorrect.