mathematics

The Mathematics of Games and Gambling

The Mathematics of Games and Gambling is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand The Mathematics of Games and Gambling rather than just read about it. In short: The Mathematics of Games and Gambling is a book on probability theory and its application to games of chance. It was written by Edward Packel, and published in 1981 by the Mathematical Association of America as volume 28 of their New Mathematical Library series, with a second edition in 2006.

Key takeaways

The Mathematics of Games and Gambling belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect The Mathematics of Games and Gambling to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of The Mathematics of Games and Gambling from memory before moving on to harder problems.

Reference excerpt

The Mathematics of Games and Gambling is a book on probability theory and its application to games of chance. It was written by Edward Packel, and published in 1981 by the Mathematical Association of America as volume 28 of their New Mathematical Library series, with a second edition in 2006.

Topics The book has seven chapters. Its first gives a survey of the history of gambling games in western culture, including brief biographies of two famous gamblers, Gerolamo Cardano and Fyodor Dostoevsky, and a review of the games of chance found in Dostoevsky's novel The Gambler. The next four chapters introduce the basic concepts of probability theory, including expectation, binomial distributions and compound distributions, and conditional probability, through games including roulette, keno, craps, chuck-a-luck, backgammon, and blackjack. The sixth chapter of the book moves from probability theory to game theory, including material on tic-tac-toe, matrix representations of zero-sum games, nonzero-sum games such as the prisoner's dilemma, the concept of a Nash equilibrium, game trees, and the minimax method used by computers to play two-player strategy games. A final chapter, "Odds and ends", includes analyses of bluffing in poker, horse racing, and lotteries. The second edition adds material on online gambling systems, casino poker machines, and Texas hold 'em poker. It also adds links to online versions of the games, and expands the material on game theory.

Audience and reception The book is aimed at students, written for a general audience, and does not require any background in mathematics beyond high school algebra. However, many of its chapters include exercises, making it suitable for teaching high school or undergraduate-level courses using it. It is also suitable for readers interested in recreational mathematics. Although it could also be used to improve readers' ability at games of chance, it is not intended for that, as its overall message is that gambling games are best avoided. Reviewer Sarah Boslaugh notes as a strength of a book the smooth interplay between its mathematical content and the context of the games it describes. Despite noting that the book's description of modern games is based on American practice, and doesn't address the way those games differ in Britain, reviewer Stephen Ainley calls the book "very enjoyable", adding that "it is hard to see how it could be done better or more readably". Reviewer J. Wade Davis calls it "accessible and very entertaining".

Recognition The Basic Library List Committee of the Mathematical Association of America has listed this book as essential for inclusion in undergraduate mathematics libraries. It was the 1986 winner of the Beckenbach Book Prize.

References

Worked examples

Example 1 — a first encounter with The Mathematics of Games and Gambling

Start with the simplest possible case. Write down what The Mathematics of Games and Gambling claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to The Mathematics of Games and Gambling before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about The Mathematics of Games and Gambling ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of The Mathematics of Games and Gambling

In research: The Mathematics of Games and Gambling appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses The Mathematics of Games and Gambling in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: The Mathematics of Games and Gambling is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1981 non-fiction books, 2006 non-fiction books, Games of chance, so understanding it makes those chapters shorter.
In everyday life: Look for The Mathematics of Games and Gambling outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study The Mathematics of Games and Gambling in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what The Mathematics of Games and Gambling means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain The Mathematics of Games and Gambling out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is The Mathematics of Games and Gambling in simple terms?

Why does The Mathematics of Games and Gambling matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study The Mathematics of Games and Gambling?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on The Mathematics of Games and Gambling.