Customer Reviews

Chances Are: Adventures in Probability

5 star:		(21)
4 star:		(3)
3 star:		(3)
2 star:		(1)
1 star:		(4)

 

 

I loved this book! It's a quick read and received high praise by the New York Times and the New Yorker, so my humble comments only echo those. This book weaves a rare combination of entertaining stories with precise lessons of how risk and randomness affect our daily lives. One can tell the authors' depth of experience and love of teaching the interplay of mathematics, philosophy and the human condition. The mother and son authors chose a wide variety of historical vignettes and modern life dilemmas, making the discussions very accessible and entertaining. I enjoyed Steven Levitt's Freakonomics for its mix of illuminating stories, but I felt like this book explored a richer set of classic historical examples and many more lessons on risk that I can apply to my real-life decisions.

This is a truly phenomenal book! As a mathematician and a mathematics educator I have certainly studied and taught the mathematics of probability theory and statistics. I have always worked to convey to my students the story of the subject (mathematical story that is) and the intellectual context of the work, as well as convey a sense of the overall structure of its historical development. But I am a tad embarrassed to admit that I did not truly appreciate the *human context* of this subject until I read CHANCES ARE ....

Ellen Kaplan and Michael Kaplan have pieced together, clearly after a phenomenal amount of archival research, the picture of man's struggle to harness chaos and randomness in his life. The story they tell is compelling and richly human. Divided into 11 chapters, each section of text deals with the story of one particular aspect of the unpredictable - understanding the spread of disease and the effectiveness of vaccines, for instance, the role of the uncertainty in the courtroom, the effects of the unpredictable in political interactions and warfare, all connected to the innate human desire to master the unknown. Ellen and Michael not only explore factual details related to describing, accepting, and, in some cases, conquering uncertainty, but also discuss and reveal the psychological impact randomness induces at every stage of its contemplation. Reading their work becomes a personal experience: we see that the struggles encountered by a society are the personal struggles we each experience. This book is revealing on a multitude of levels.

Written with humor and eloquence, the book is a delight to read. Although mathematical formulae are kept to a minimum, mathematical richness of ideas is not denied. As an educator, I hope this book will become required reading for all students of probability and statistics. But this, of course, is not the only audience of readers. CHANCES ARE ... is an important book, absolutely relevant and accessible to all who are human. It is fundamentally a book about us.

This is a very special book. Michael and Ellen Kaplan put forth an intriguing thesis. We are taught deductive reasoning in geometry and logic classes, inductive reasoning in science. This book is about the great valley in between where we spend most of our lives: probability. They throw us some fun problems at the start to show that many of us (e.g. me) may not grasp probability intuitively. The "Blue Cab/Green Cab Problem" is an eye opener. If 85 percent of the cabs in a city are green, 15 percent blue, and a witness with 80 percent accuracy spots a blue cab, is it likely to actually be blue or green? The answer is surprising. People focus on the 80 percent accuracy, but the key is the 15 percent of blue cabs. This is more than a fun math problem. It can help you judge medical tests. A less-than-perfect diagnostic test of a rare condition is likely to be misleading. (Don't depend on your doctor; the Kaplans show that MDs are not good at probabilities.) There is a wonderful chapter on gambling and some new insights into Pascal's Wager. Pascal says to bet on the existence of God; the Kaplans, after doing the math, are not so sure. Again, this is more than just an academic exercise. A band of Evangelical Christians are currently going around our community using Pascal's Wager as an argument for converting young people to their fundamentalist Christianity. The authors also address the Monty Hall problem: whether a contestant on "Let's Make a Deal" should switch doors when Monty reveals what's behind one of them. Everybody knows by now, if they've read about the problem in USA Today or the NY Times, that one always swtiches. But the Kaplans are the first to explain the theoretical underpinnings of the problem, comparing it to the Principle of Restricted Choice in bridge. There's more. Philosopher David Hume said that the fact the sun has risen every morning is no proof that it will rise tomorrow. But the Kaplans show that Bayesian probability offers math that is not proof per se, but evidence of probability. My psychotherapist suggested I use Bayesian probability to help deal with my great variety of unrealistic anxieties. I am terrified, for example, of having to go to the bathroom on a long bike ride with no restroom nearby. Actually calculating the probability of this happening, using past experience, has relieved this nervousness. The best thing about the book, though, is its tone. Most math-book authors are making one point: they are smart and everybody else is dumb. The Kaplans are not arrogant, and explain why it's natural that we make the mistakes we do. They poke fun at the "geniuses" at the RAND Corporation who got annoyed when people refused to act like RAND mathematical diagrams predicted they would act. The RAND folks tried to convince two presidents to make a preemptive nuclear strike at the Soviet Union, but thankfully dumber but more experienced men prevailed (Truman and Eisenhower). An excellent book. There is a 100 percent chance that you will enjoy it.

Imagine traveling through a wormhole, at high speed, constantly twisting and turning; you want to stop and admire a beautiful pattern, see it in depth, but you are whipped away to the next turn. There are glimpses of beautiful ideas in this book, but to pursue them you will need to read more elsewhere.

This book touches on an impressive number of topics related to probability and game theory, and the authors weave in a number of interesting bits of history. Sadly, they touch on many topics very lightly and incompletely.

There are the makings of at least 4 or 5 really good books here, if the topics are properly covered. Overall this is worth reading, as the research behind this book is stunning in scope even if none of the ideas are adequately explicated.

This book is fun to read, with lots of great stories. The idea that much of how our minds work is based on rough probability estimates was new to me. The Kaplans describe many mental problems such as autism, as well as the strange behavior of psychopaths, as essentially disorders of a poor sense of probability in human social relations. Fascinating.

I liked the chapter on healing best. The Kaplans point out that depending on the way you report the results, the exact same study can make a drug's effect look enormous or trivial: "Program A reduced the death rate by 34 percent" and "Program C increased the patients' survival rate from 99.82 percent to 99.88 percent" makes Program A look good, but these numbers describe exactly the same program. Exaggeration of this type is all too frequent in today's medical research, and even many doctors often don't realize when they are being bamboozled. I am not kidding when I say that if more people understood what the Kaplans are getting at here, our health care system would save billions of dollars and a lot of grief. For more on this, see Hadler's book "The Last Well Person," which describes how the popularity of many expensive treatments, such as the cardiac bypass, is due to precisely this type of misleading statistics.

The book does have some equations, but they are not essential to understanding it. Feel free to skip them.

The Kaplans discuss economic growth in terms of gambling, and describe the gains from the sun each year as providing enough energy to justify between 1.5% and 2% economic growth. The Kaplans don't say where they got this figure. Economic growth being an interest of mine, I tend to disagree. Certainly economic growth figures of about this magnitude are common. However, "economic growth" is conventionally measured by GDP, a figure so inaccurate as to be almost laughable. GDP makes no adjustment for the costs of pollution, drawdown of natural resources, population growth, or reduction in quality of life, among other difficulties. More accurate economic measures, such as the Index of Sustainable Economic Welfare (ISEW) or the Genuine Progress Indicator (GPI), show that there has been little or no economic growth in the U.S. since the 1970s. Several other countries with healthy-looking GDP figures are basket cases when more accurate measures are considered. For more on this, see Herman Daly's book "Beyond Growth," or Brian Czech's book "Shoveling Fuel for a Runaway Train."

Overall, though, "Chances Are" is a highly recommended book.

This is an especially informative and entertaining book. It makes a great read. In fact it is worth putting by for re-reading. There is plenty to mull over. It draws humour from the gap between what is possible and what actually happens. Statistics and probability shimmer here, like Jeeves, ever ready to be consulted. What are the chances of my ship coming home without being sunk in a storm? Should I hedge my bets? As the authors see it, if uncertainty is our lot, then probability is the science of getting on with life. They reveal just what a human interest story and an absorbing study it is.

And also deep: some of the results go well beyond intuition, and some are actually counter-intuitive and likely to make the reader very curious to hear the theory behind them. Basic principles are explained over the course of the book. The reader with leisure can easily test some things at first hand. We are shown why calculation is necessary, even if it forces our minds first to acknowledge a gap that we are often more keen to leap. Even if the necessity for numbers is something we regret, I think most of us will find it yielding easily enough to the authors' pleasant and humorous approach.

The pace is fast: I felt I was listening to rapid double fire from the authors, mother and son, now playing a couple of comedians, now professors. We glimpse Aristotle's ideas of science and of ethics, Descartes' knowledge revolution, Pascal's approach to salvation, the spirit of Laplace, as the authors take us through the historical development of the notion of Chance. In medieval times apparently this notion just could not be taken for granted and much was ascribed to God's will. It took a while to establish probability as a ratio between one possibility and many. Imagine a range of possibilities where each is as likely as any other but just one will happen. If an event we are interested in can be represented as one such possibility or as the selection of several as an "each way" bet, then the ratio between the selection total and the grand total is the probability of the event.

Almost axiomatic, you'd think? Yes, but there may be trouble ahead! In the meantime, we find this approach allows for interesting tricks and techniques and solutions to betting problems and more besides. Here also to admire are Pascal's triangle and the bell curve, de Moivre's brilliant standard deviation idea and, if we toss a coin, say, 3600 times, we have a way of calculating how likely we are to arrive within a given range of deviation from perfectly even totals.

As for that trouble ahead, the authors draw attention to the problem that cards and coins can be biased and can be the stuff of cheating, and maybe perfect dice are impossible to make anyway. More generally, how could we ever know that we had truly analysed a practical problem exhaustively into exclusive, independent, and equal possibilities, or that an event in which we are interested could really be defined as a selection of them? Can probability ever get off the theoretical ground and be of reliable use?

So another idea of probability emerges as a measure of observed frequency of occurrence over a sufficiently large number of tests (provided the figures tend to a definite ratio). With all these ideas in an elegant suitcase we are now transported to Monte Carlo, where we soon find ourselves soaking up the psychology of gambling and investment (what's the difference?) and mulling over risk-taking strategies illustrated by funny, sad, and intriguing stories of people and of events.

Further chapters take us behind the scenes in insurance, medicine, law, the forecasting of weather and climate, military thinking, a whole variety of pursuits, as we learn about the wide application of statistics and probability, theory and techniques. Two and half centuries ago Reverend Bayes showed us how to adjust the strength of an opinion numerically according to the probability of relevant evidence but, in the USA at least, use of the technique is excluded from the courts. Alarming examples are presented of invalid numerical reasoning about probability, in court cases and medicine especially. Then with military and police matters pressing, the game theory of the well-known prisoners' dilemma is presented. Personally, I'd hesitate to rule out serving a ten-year sentence if the conventional wisdom of squealing left me vulnerable to my accomplice's friends. When is a game really over? Presidents Truman and Eisenhower probably wisely asked themselves the same question, the authors recall, and didn't nuke the Russians. The authors also quote a view of terrorism that seems very plausible to at least one reader.

There is much more, all arising from the notion of Chance and our attempts to cope with it. I found the book absorbing and enjoyable, and at the same time educational. It is done in conversational style, with humour, and respecting the intelligence of the reader. On the penultimate page we even find a possible moral for the whole story, incorporating a plausible notion of soul as distinct from body. Chances are you'll like it.

I enjoyed the parts related to probability and randomness but I personally got bored through extended portions. Readers with more of an appreciation for the humanities might find this more satisfying. If you can relate to sections that include material such as, "One person who saw the inevitable coming with the impatient joy of the dawn watcher was Marie-Jean-Antoine-Nicolas de Caritat, Marquis de Condorcet. A model of impulsive, heartfelt humanity, with the face of a sensitive boxer under his peruke, Condorcet had abandoned Christianity but retained its force of emotion and desire for certainty." then you should love this book. But these parts are not what you would expect by reading the dust cover of this book.

I really enjoyed the parts on weather forecasting and chaos, and medical research. Where the book ventured into areas that I am somewhat knowledgeable about it proved to be quite accurate.

Overall a good book and for those more erudite than I am, possible a very good one.

Talk about unlikely! What is the probability that if one of the authors of the book Chances Are had the last name of Kaplan, that the other one - who (based on the brief author bios) doesn't seem to be a relative - would also be a Kaplan? The book actually never discusses the issue, but that does not keep it from being an engaging read.

Michael and Ellen Kaplan's book deals with the history and applications of the mathematical field of probability and its sister discipline, statistics. Written for the math layman, this 300-page work tells of the development of probability and statistics from mere guesswork into a sophisticated way of looking at the world.

Of course, when one thinks of probability, the likely first topic one will think about is gambling. All those big shining buildings in Las Vegas (and elsewhere) are built by those who know how to win in the long run and those ill-fated people who are certain that they have a winning system. Since in most events, the house edge is small, the second advantage is the idea of gambler's ruin: namely, that the player with the most money (and the casino has much more than almost any player) will win out in the long run.

But these rules also apply in other areas as well. After all, one of the reasons the U.S. won the Cold War was gambler's ruin; the Soviet Union just couldn't afford to stay in the game. Within Chances Are shows how probability and statistics play a key role in areas as varied as health care, the justice system, war and weather prediction. But as important as how probability and statistics are used is how they are misused, either purposely or accidentally (a topic also discussed in the best-selling Freakonomics).

As an example, the Kaplan's discuss a court case where two children died of natural causes within months of each other and the mother was accused of murder. Bad math wound up making it seem like the odds of this happening naturally were one in 73 million, a calculation that help lead to the woman's conviction. Unfortunately, this calculation was almost worthless and should not have been used (or abused) in this case.

The Kaplans write in a breezy, if somewhat meandering, manner. If a particular subject doesn't interest you, don't worry; they'll be off to the next topic in a couple pages. The quality of this book goes beyond its style, though: by understanding how probability and statistics work, you can better understand their implications in the real world. And if you're well-informed, you can make better, more educated decisions.

A fine review of the history of understanding of chance and probability, and very well written to boot. Highly recommended to poker players and stock market players (if those are two different classes of readers).

I had high hopes for this book, which promised to be an interesting discourse on one of my favorite topics. I enjoyed parts of the book, but overall it left me disappointed. The writing was dry and tedious quite often, and I often had the impression that people who didn't already understand probability and statistics would probably not understand the brief technical explanations or equations provided. (For example, the discussion of Bayes Theorem.) But for those who do know P&S, these explanations were not very enlightening.

Still, I admire the attempt, and the authors certainly present a good deal of historical information related to P&S in some ways.