This book brings together a variety of probability applications through entertaining stories that will appeal to a broad readership. What are the best stopping rules for the dating problem? What can Bayes’ formula tell us about the chances of a Champions League draw for soccer teams being rigged? How could syndicates win millions of lottery dollars by buying a multitude of tickets at the right time? What’s the best way to manage your betting bankroll in a game in which you have an edge? How to use probability to debunk quacks and psychic mediums? How can the Monte Carlo simulation be used to solve a wide variety of probability problems? Are seven riffle shuffles of a standard deck of 52 playing cards enough for randomness?
- Provides seventeen engaging stories that illustrate ideas in probability.
- Written so as to be suitable for those with minimal mathematical background.
- Stories can be read independently.
- Can be used as examples and exercises for teaching introductory probability.
These questions and many more are addressed in seventeen short chapters that can be read independently. The engaging stories are instructive and demonstrate valuable probabilistic ideas. They offer students material that they most likely don’t learn in class, and offer teachers a new way of teaching their subject.
Table of Contents
What is Casino Credit Worth?
One Hundred Prisoners: Freedom or Death
Birthday Surprises and 500 Oldsmobiles
Was the Champions League Rigged?
Benford Goes to the Casino
Surprising Card Games, or, It's All in the Cards
The Lost Boarding Pass and the Seven Dwarfs
Monte Carlo Simulation and Probability: The Interface
Lotto Nonsense: the World is Asking to be Deceived
March Madness Grips the USA
Coincidences and Impossibilities
Euler's Number e is Everywhere
The 10 Most Beautiful Formulas in Probability
Beating the Odds on the Lottery
Investing and Gambling with Kelly
To Stop or Not to Stop? That is the Question
Henk Tijms is a Dutch Emeritus Professor of Applied Mathematics. He taught applied probability and stochastic optimization for more than 30 years, and has written several widely used textbooks on these subjects, including the 2017 text “Probability: A Lively Introduction”.
"Henk Tijms is well known for seeking to make the ideas of probability accessible to the lay reader. Here, a typical chapter considers some setting where chance plays a role, and, with minimal use of mathematical formulae, Tijms shows how to reach a sensible conclusion. Not surprisingly, several of the book’s 17 short stories feature lotteries and/or casinos. Some chapters offer instances where the probability in question is much larger than would frequently be supposed; others give examples of extremely rare events. … Do read a copy – you will surely enjoy it."
—John Haigh in Significance, June 2019
"The author mentions that the book can be useful for teachers and, indeed, this is a collection of surprising probability results—surprising in the sense that the numerical probabilities are not necessarily intuitive. …. All in all, this small book is a nice if unsurprising database for illustrations and possibly for exercises in elementary probability courses … . It makes for nice reading, especially while traveling. I hope some fellow traveler will pick up the book from where I left it in the Mexico City airport."
—Christian Robert in Chance, April 2019
"Surprises in Probability – Seventeen Short Stories" is another gem by international award-winning probability expert Henk Tijms. This superb collection of real-life probability stories ranges from 17th century gamblers’ discoveries to 21st century lotteries, sports betting, and investment strategies. Each story draws the reader in, and then enlightens them with both basic and subtle probability principles that illuminate and explain the apparent paradoxes. Perfect for the college student trying to get a feel for probability, for the instructor looking for examples to enliven their classes, for experts looking for just the right examples to share with their friends, and for weekend scientists not afraid to scratch their heads and smile, waiting for the Aha! moment that always appears. Analytical insights, theoretical principles, counterintuitive conclusions are all presented in Professor Tijms' patented lively style. —Ted Hill, author of Pushing Limits
"In a world full of uncertainty, you can't know enough about the laws of chance. Henk Tijms is a master at explaining how they work, showing why they so often catch us out in everyday life. Chances are you'll be amazed by his insights."
—Robert Matthews, author of Chancing It
"A challenge, when teaching introductory statistics, can be to motivate what seem to be at times very abstract concepts. This short book grew out of a series of popular science articles written for magazines or blogs. It comprises seventeen independent chapters (described by the author as short stories), able to be read in any order, with each examining an engaging real-world problem, or set of problems. ... The chapters are self-contained and begin by motivating the real-world problem, before building up the mathematical theory required to tackle it. ... This book works equally well as general interest reading or for finding teaching examples. With each chapter being around ten pages long, it is a quick read, and is easy to dip into and out of. While overall the material is not challenging, there were a few results presented that I found novel and interesting."
- Mary Fortune in ISCB, June 2019
"…a really fun book. It is a compendium of (surprise) seventeen probability problems…These are all explained with words, a very few equations, some pictures and lots of appeal to intuition. But the fun is really after the 'standard' version of the problem when the author explains variations and extensions, many of which I was not previously aware of (and my degree is in probability)!...I could easily imagine a teacher using it to enrich the standard problems in a probability course. A skilled undergraduate could turn the prose into mathematics as an independent reading course, or extend the results as an undergraduate thesis. And of course, anybody who loves probability."
-Peter Rabinovitch, MAA Reviews, October 2019
"Tijms’s whimsical style and playful colloquialisms offer an amusing, if cursory, review of the content one might find scattered throughout the exercise sections of a classic probability text (but the benefit of collecting several such examples in one place cannot be downplayed!). The text does not delve deeply into any one topic, often providing just enough context to silhouette an interesting problem without illuminating it in full. But for the inquisitive and sophisticated reader, Surprises in Probability offers an enticing bread crumb trail into a fascinating world."
- Jonathan M. Wells, The American Satistician, Vol 74