Monopoly Mathematics
Jonathan Garcia
I was playing a game of monopoly the other day, and in the course of strategizing I came up with the idea that how 'safe' you were in the game was a matter of what your expected income/outcome was as you went around the board. I figured it would be a fun project to make a helper program that would compute these values based on a given board configuration, but I found that the statistics got too complicated for me.
I was wondering if anybody more skilled with statistics could give me a hand with this - what is the expected value of your costs in traversing the monopoly board? I intended on ignoring chance and community chest and being sent to jail, as those seemed to overcomplicate the model, but if somebody can incorporate those effects I'd be interested in seeing them.
As mentioned in my first post and in my profile, I am a lover of math, probability, game theory, computer programming, and pretty much everything in between. Some people believe that doing any sort of analysis of a board game takes the fun out of it, but for me (and perhaps for you too), the analysis is the fun of it!
** Note: This website is non-commercial in nature, free to use, and intended solely for studying Monopoly strategy and related probability / mathematics. HASBRO, PARKER BROTHERS, the MONOPOLY name and logo, the distinctive design of the game board, the four corner squares, the MR. MONOPOLY name and character, as well as each of the distinctive elements of the board and playing pieces are trademarks of Hasbro for its property trading game and game equipment. 2012 Hasbro. All Rights Reserved. Used without Permission.
In an era where mathematical skills are becoming increasingly important, there is an innovative approach to teaching mathematical concepts to the public, especially children. Education in exclusive games based on mathematical concepts has emerged as an innovative solution to introduce and understand mathematical concepts in a fun and interactive way. This moved Diponegoro University TIM II KKN students to introduce a monopoly game based on mathematical concepts.
Through this relaxed but fun game, players, especially children, have new tools in the learning process. The extension of the monopoly game based on mathematical concepts has proven that learning does not always have to be done in a formal environment. So this modification of the monopoly game can have a positive impact in the form of increasing interest in mathematics, increasing self-confidence in calculating and increasing mathematical literacy.
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When I was a kid, my family's hobby was collecting Monopoly sets. Still in the cupboard of the old house, you can find the traditional monopoly, as well as British, French, Chinese editions, and I remember not what else.
In recent years, though, there have been bazillions of Monopoly editions produced. Deluxe, Mega, Here-And-Now, Star Wars, Pixar, Nintendo, Transformers, Spiderman... Evidently the owners of the Monopoly brand are onto a real cash cow. We've abandoned our hobby - it doesn't seem so meaningful any more.
Then, my son received a Junior Monopoly set for Christmas. Naturally, I wondered...
- Will this "Junior" Monopoly be a fun game for my kid?
- Could it even help him, say, learn a bit of money math?
- Or is this just a money spinner for Parker Brothers?
Junior Monopoly is not just a different edition of Monopoly. It's simplified to a level that kids can relate to (Parker Brothers recommends it for Ages 5 to 8)
- Instead of a property market, the game takes place in an amusement park.
- Instead of building houses and collecting rent, players build ticket booths and charge admission.
- Players don't trade to form sets. Instead, there are chance cards that allow you to take ticket booths off other players.
- Instead of being forced to Go to Jail, players Catch the Bus to the Cafe.
- Instead of $200 salary, players collect $2 pocket money as they pass Go.
For kids aged 5 to 8 - well, for mine at least - a game isn't fun if he doesn't win, at least sometimes. Chess isn't fun, unless I let him win. One piece of good news about Junior Monopoly is that it's almost a game of chance.
- Sometimes, a player has to make a "strategic" decision. Should I knock down mom's, or dad's ticket booth? or Should I build on the Magic Show or the Puppet Show?
- However, mostly, it's just Roll the die, move, and do what the rules say.
- This means "junior" has as much chance as anyone else of winning.
If a player owns all the booths in a set, the ticket price is doubled. Here is an opportunity to teach your child the two times tables - at least up to 2x5=10... Just make sure you ask your child what is owed when someone lands there!
Junior Monopoly is a good fun game for kids aged 5 to 8. It's more complex than, say, Snakes and Ladders, so adults won't be completely bored. On the other hand, the children still have as much chance of winning as the grown-ups.
It's not very educational, but there are opportunities for kids to learn about money, about giving change, about simple addition and subtraction, and the first half of the two times tables.
One of my favorite parts of mathematics is that there is always more to learn! For this reason, I have a wide array of interests within the field of mathematics, ranging from topology and probability to big data and the use of technology in mathematics. These varied interests have led to a variety of projects with my students, including using topology to plan the motion of an automated guided vehicle in a factory, using MATLAB software to simulate the game of euchre to try to develop winning strategies for that game, and analyzing huge datasets from hospitals around the nation to determine trends in health care.
Yes! The actuarial science major at Franklin College is an interdisciplinary major consisting of coursework in mathematics, statistics and business that will help students develop the quantitative skills needed to assess and manage risk, especially in a financial setting. In addition to developing these key quantitative skills, actuarial science majors will take courses designed to prepare them for the first two preliminary actuarial exams (Exam 1/P Probability and Exam 2/FM Financial Mathematics). Our long-standing degrees in Quantitative Analysis and Applied Mathematics provide additional options for students interested in applying their quantitative skills to a variety of settings, providing more career flexibility for those who decide not to become an actuary.
I have actually taken a special interest in students who are thinking about an actuarial career recently. While I am very happy in my current career as a math professor, I have prepared for the first two actuarial exams in probability and financial mathematics so that I can give future students interested in taking the exams some first-hand advice from my own experiences.
There are many routes to becoming an actuary, but if you know that you want to become one, then the faculty in the math department (like myself) would be happy to help you do whatever it takes to reach that goal.
Studies of the Math Wars present sharp disagreements over their characterizations and consequences. Nonetheless, they offer two important lessons. First, technologies that replace mental skills may demand educational reforms. Second, educational reforms tend to be complicated and controversial processes.
The second wave of Math Wars began in the 1980s, triggered by growing pressures to focus math education on applied concepts rather than technical procedures. Reform proponents urged their peers to embrace calculators as a tool to shift toward applied mathematics. Opponents warned that the incorporation of calculators in math education would create unhealthy technological dependency, impede the development of mental skills, and exacerbate inequalities given the steep prices of new technologies.
While developing its ecosystem, TI released a steady flow of new graphing calculator models. However, it learned that the cost to educators of adopting new models created a strong preference against technological innovation. In 2004, TI cemented its dominance in the market for educational graphing calculators with the release of the TI-84 graphing calculator series, which incorporated some of the features of the calculators the company introduced after 1990. TI locked in its monopoly and, thus, had no reason to develop new models. Math teachers preferred it this way. Over the past 20 years, TI has introduced several new versions of TI-84 calculators, but the innovations were mostly cosmetic.
Marcus du Sautoy, a professor of mathematics at the University of Oxford believes playing as Mrs Peacock, the character that starts off closest to the most rooms on the board, maximises the chance of success.
This square is more likely to be landed on than any other on the board as players can land on it, draw a card sending them directly to jail, or be punished by being sent to jail after throwing three doubles.
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