CAS 109 - The Mathematics of Gaming
The Mathematics of Gaming is a Liberal Arts Mathematics course. Using the backdrop of traditional casino games and horse racing, students will investigate relevant concepts that involve applications of arithmetic, algebra, probability and statistics. The students will learn different ways to present and interpret numerical and statistical data. The students will investigate mathematical models and simulations along with their applications. The students will investigate gaming strategies involving mathematical reasoning and psychological components such as risk versus reward, wagering and bluffing. Students will also be required to read and discuss the short novel "The Gambler" by Fyodor Dostoyevsky.
Prerequisites: MAT 093 (4-credit) Integrated Arithmetic and Basic Algebra, MAT 091 Mathematical Literacy I, or equivalent
4 Class Hours
Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
1. Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics.
2. Represent mathematical information symbolically, visually, numerically and verbally.
3. Employ quantitative methods such as, arithmetic, algebra, geometry, or statistics to solve problems.
4. Estimate and check mathematical results for reasonableness.
5. Recognize the limitations of mathematical and statistical methods.
6. Define basic terms related to probability and statistics.
7. Calculate theoretical probabilities and odds.
8. Set up and solve simple proportions.
9. Generate and employ a set of random numbers for simulating probabilities.
10. Discern between events that are independent and dependent.
11. Develop models for various casino games using expected value.
12. Discern between a fair and an unfair game.
13. Create a tree diagram to represent a multistage experiment.
14. Collect, organize and display data using tables and charts.
15. Create a probability distribution for an experiment.
16. Calculate the mean and variance for a distribution of sample means.
17. Apply concepts of the distribution of sample means using z-scores and the normal distribution.
18. Utilize the optimization strategies in games of chance.
19. Describe and explain strategy for money management and wagering in games of chance.
20. Calculate permutations and combinations for probability applications.
21. Describe and play games involving strategy (NIM, TIC_TAC_TOE, ROCK-PAPER-SCISSORS) and bluffing (LIARS DICE, BLUFF).
22. Investigate the mathematics of streaks using descrete and continuous methods.
23. Describe the differences between theoretical and empirical probabilities.
24. Calculate the odd and payoffs in a horse race based upon the betting pool.
25. Describe non-mathematical factors that may influence the results of chance events.
26. Perform simple regression and factor analysis.
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