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Lady Luck: The Theory of Probability
"Should I take my umbrella?" "Should I buy insurance?" "Which horse should I bet on?" Every day ― in business, in love affairs, in forecasting the weather or the stock market questions arise which cannot be answered by a simple "yes" or "no." Many of these questions involve probability. Probabilistic thinking is as crucially important in ordinary affairs as it is in the most abstruse realms of science.
This book is the best nontechnical introduction to probability ever written. Its author, the late Dr. Warren Weaver, was a professor of mathematics, active in the Rockefeller and Sloan foundations , an authority on communications and probability, and distinguished for his work at bridging the gap between science and the average citizen. In accessible language and drawing upon the widely diverse writings of thinkers like Kurt Godel, Susanne K. Langer, and Nicholas Bernoulli, Dr. Weaver explains such concepts as permutations, independent events, mathematical expectation, the law of averages, Chebychev's theorem, the law of large numbers, and probability distributions. He uses a probabilistic viewpoint to illuminate such matters as rare events and coincidences, and also devotes space to the relations of probability and statistics, gambling, and modern scientific research. Dr. Weaver writes with wit, charm and exceptional clarity. His mathematics is elementary, grasp of the subject profound, and examples fascinating. They are complemented by 49 delightful drawings by Peg Hosford. 13 tables. 49 drawings. Foreword. Index.
This book is the best nontechnical introduction to probability ever written. Its author, the late Dr. Warren Weaver, was a professor of mathematics, active in the Rockefeller and Sloan foundations , an authority on communications and probability, and distinguished for his work at bridging the gap between science and the average citizen. In accessible language and drawing upon the widely diverse writings of thinkers like Kurt Godel, Susanne K. Langer, and Nicholas Bernoulli, Dr. Weaver explains such concepts as permutations, independent events, mathematical expectation, the law of averages, Chebychev's theorem, the law of large numbers, and probability distributions. He uses a probabilistic viewpoint to illuminate such matters as rare events and coincidences, and also devotes space to the relations of probability and statistics, gambling, and modern scientific research. Dr. Weaver writes with wit, charm and exceptional clarity. His mathematics is elementary, grasp of the subject profound, and examples fascinating. They are complemented by 49 delightful drawings by Peg Hosford. 13 tables. 49 drawings. Foreword. Index.
400 pages, Paperback
First published August 1, 1982
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Displaying 1 - 11 of 11 reviews
July 26, 2007
The main strength of Mr. Weaver's "Lady Luck" lies in its sheer readability. Mr. Weaver is very careful about presenting his arguments so that they may have maximum intuitive appeal, while at the same time refusing to compromise the mathematical rigor that is necessary to construct any serious theory of rudimentary probability. What is most important about the work is that it provides the reader an extremely entertaining and well written framework for thinking about questions of probability. A concept such as "independent random variable" which a mediocre statistics textbook may quickly skip is a surprisingly philosophically complicated idea, and has troubled academicians, let alone lay people. Mr. Weaver's work, far from being in any sense "slow," deals with how we are to take into account this very basic ideas that form the starting point to this particular area of the mathematical sciences. Finally, Mr. Weaver's references to distinctively late 50s early 60s phenomenon provide an entertaining look at the thoughts of the time.
June 12, 2020
As a famous song goes, Luck be a Lady tonight. Warren Weaver wrote Lady Luck back in the 1960s with the hope that this book would be read by the layman. It starts easily enough, going through the storied history of Probability and discussing the reasons for its founding. In contrast to other fields of inquiry, we can trace the birth of Probability to gentlemen such as; Cardano, Pascal, Fermat, and others. Initially, Probability was intended to find solutions to Gambling problems. Eventually, these applications became more widespread, culminating in our modern treatment of it.
The book is eminently readable. As I mentioned in the opening paragraph of this review, Weaver wanted this book to be read by the layman. His intent was for people to become enamored of Probability Theory and become mathematicians, or at least, to become people that used Probability in their everyday lives. It starts with the history and moves on to famous problems and their solutions. For example, Weaver discusses the Problem of Points; where a game is called off in the middle and we have to decide how to fairly distribute the pot. This leads to the idea of the expected value. Weaver writes about the Gambler’s Ruin and the Gambler’s Fallacy.
Throughout the book, Weaver discusses all sorts of different ideas. He goes into the story of how Benford’s Law was discovered. He writes about various theorems and oddities that result from pure chance. This makes the book very entertaining as well as informative. Weaver writes of massive numbers; numbers beyond the comprehension of man. He writes about the Tower of Hanoi puzzle with 64 pieces. He writes about an enormous block of matter, one million times harder than a diamond, worn down by the touch of a wise man.
Weaver does not use formal equations or terminology too often, but he does make mention of things like Sample Spaces. He mentions these things so that you won’t be out of the loop. I enjoyed going through this book.
The book is eminently readable. As I mentioned in the opening paragraph of this review, Weaver wanted this book to be read by the layman. His intent was for people to become enamored of Probability Theory and become mathematicians, or at least, to become people that used Probability in their everyday lives. It starts with the history and moves on to famous problems and their solutions. For example, Weaver discusses the Problem of Points; where a game is called off in the middle and we have to decide how to fairly distribute the pot. This leads to the idea of the expected value. Weaver writes about the Gambler’s Ruin and the Gambler’s Fallacy.
Throughout the book, Weaver discusses all sorts of different ideas. He goes into the story of how Benford’s Law was discovered. He writes about various theorems and oddities that result from pure chance. This makes the book very entertaining as well as informative. Weaver writes of massive numbers; numbers beyond the comprehension of man. He writes about the Tower of Hanoi puzzle with 64 pieces. He writes about an enormous block of matter, one million times harder than a diamond, worn down by the touch of a wise man.
Weaver does not use formal equations or terminology too often, but he does make mention of things like Sample Spaces. He mentions these things so that you won’t be out of the loop. I enjoyed going through this book.
August 12, 2008
The number of permutations of n objects taken r at a time is n!/(n-r)!. I expect I was forced to memorize this at one point in my high school career and promptly forgot it. _Lady Luck_ takes 87 pages to get to this point, going far out of its way not to startle, bore, or frighten the reader into abandoning the text. The approach is quaint (perhaps annoyingly so, but this was an old-fashioned book even in 1963), but it works. I'm still reading, and more important, I'm learning.
July 15, 2012
What a great book.
This isn't a *comprehensive* introduction to probability and statistics, but it's a good book to get your feet wet and stretch your brain.
It doesn't treat you like an idiot and it moves fast, but if you're willing to slow down and reread a few of the chapters you'll be rewarded with that awesome "click" where everything slides into place.
Plus it's got that cute cold war retro vibe that can only come from a time where "everyone nukes everyone else" was not a statistical outlier.
This isn't a *comprehensive* introduction to probability and statistics, but it's a good book to get your feet wet and stretch your brain.
It doesn't treat you like an idiot and it moves fast, but if you're willing to slow down and reread a few of the chapters you'll be rewarded with that awesome "click" where everything slides into place.
Plus it's got that cute cold war retro vibe that can only come from a time where "everyone nukes everyone else" was not a statistical outlier.
October 23, 2021
This is a very well-written introductory book on probability. Some developments in mathematics and other sciences author describes may be outdated, but that's because book was written decades ago.
September 2, 2019
A classic and one of my favorite books
Some years ago I got the idea that I could, by studying probability and statistics, work out a way to beat the Las Vegas bookies by betting on baseball games.
Hmm..., one might say. Well, I was young and while not exactly foolish, I was adventurous and liked challenges.
Anyway, I knew a little mathematics and a little probability, but it was only when I picked up this absolutely charming book and began to read it that I realized with a kind of glee and something akin to a thrill that I was about to learn something of great value.
Warren Weaver, a good friend, by the way, of Claude Shannon, the great information theory pioneer, has a wonderful gift for expression and an equally wonderful gift for explaining things clearly and making his subject matter exciting. And the engaging illustrations by Peg Hosford do nothing but add to the excitement.
From the very first words in the book, "This book is, in one sense, about thinking. About a certain way of thinking, that is...," I knew immediately what he meant and that I had stumbled upon exactly the sort of book I was looking for.
Weaver begins literally with "Thoughts about Thinking" and illustrates how probabilistic reasoning, as he calls it, is the only kind of reasoning that can help us answer certain kinds of questions, questions such as will it rain today? or is Alex Rodriguez, who hasn't had a hit in five at bats, due for a hit this time up? or "if I have my left lung removed, what is the chance that the cancer will really be cured?" (p. 28) He follows this with a most interesting short chapter on the history of probability, "The Birth of Lady Luck." And then he explains "The Concept of Mathematic Probability." His exposition was so clear and such a pleasure to read that I can still recall the delight I experienced in reading it for the first time.
In the chapter on "The Counting of Cases," Weaver gets down to the basics of compound events and the difference between combinations and permutations--knowledge that is necessary, for example, in order to analyze a game of chance, especially games involving dice or playing cards..
The next chapter covers independent events, and then there are some famous problems including the one involving dice throwing that the Chevalier de Mere presented to the celebrated French mathematician Blaise Pascal. Weaver had mentioned it earlier, noting that this historical problem from 1654 actually marked the above mentioned "birth of Lady Luck."
In other chapters Weaver introduces us to the law of large numbers and explains the "maturity of chances" fallacy and some other fallacies. He explains in a particularly clear and utterly convincing manner why the so-called Martingale system and other "doubling up" systems yield no advantage to the bettor, and why, if any given independent event is disadvantageous for the bettor, no system of betting on such events will ever lead to an advantage for the gambler. In the case of doubling your bet after each loss, Weaver shows that every time you win, you will be one unit ahead no matter how many times you double up--except for one very deadly proviso: Sooner or later you will run into a streak of losses that will wipe you out--or, run you up against the betting limit of the casino or whomever you are betting against, and you will have to eat your losses. It is simply a matter of the observing the powers of two: 2,4,8,16,32,64,128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536.
In other words, if your betting unit is $100 and you decide to bet on National Football League games, betting $100 the first week, and if you lose doubling your bet to $200 the next week, and then to $400, the following week, etc., until you either win or the season ends, you will gain $100 for each time you win. Should you however run into a bad streak, say losing every week, you would lose $65,536 after the 16th game! (I have simplified this of course since, due to the bookie's vigorish, you actually have to wager $110 to win $100.)
If you double up on something like the throw of the dice at a casino where the odds of winning the bet are less than fifty-fifty, your chance of a ruinous streak is (markedly) increased.
A very interesting chapter is number XIII, "Rare Events, Coincidences, and Surprising Occurrences" where Weaver presents some of the coincidences he has experienced and collected over the years. He goes on to explain the nature of such rare events and gives a very interesting look at them from a mathematical point of view. One of the events is about a guy in Las Vegas who made an amazing 28 passes in a row at a dice table at the Desert Inn. He, cautious bettor that he was, made only about $750, while the side bettors made $150,000. Another event was thirteen spades having been dealt to a bridge player. Weaver discusses whether we should believe that this and some other very, very rare events could happen by chance.
Since reading this book, I have read a number of other popular books on probability, statistics and gambling, but I can say, as good as some of them were, none were nearly as exciting nor half as interesting as this book. As far as I am concerned Lady Luck is a classic of the genre, and more or less timeless.
As for the baseball betting...well, that's another story, but suffice it to say it ain't easy beating the line.
--Dennis Littrell, author of “The World Is Not as We Think It Is”
Some years ago I got the idea that I could, by studying probability and statistics, work out a way to beat the Las Vegas bookies by betting on baseball games.
Hmm..., one might say. Well, I was young and while not exactly foolish, I was adventurous and liked challenges.
Anyway, I knew a little mathematics and a little probability, but it was only when I picked up this absolutely charming book and began to read it that I realized with a kind of glee and something akin to a thrill that I was about to learn something of great value.
Warren Weaver, a good friend, by the way, of Claude Shannon, the great information theory pioneer, has a wonderful gift for expression and an equally wonderful gift for explaining things clearly and making his subject matter exciting. And the engaging illustrations by Peg Hosford do nothing but add to the excitement.
From the very first words in the book, "This book is, in one sense, about thinking. About a certain way of thinking, that is...," I knew immediately what he meant and that I had stumbled upon exactly the sort of book I was looking for.
Weaver begins literally with "Thoughts about Thinking" and illustrates how probabilistic reasoning, as he calls it, is the only kind of reasoning that can help us answer certain kinds of questions, questions such as will it rain today? or is Alex Rodriguez, who hasn't had a hit in five at bats, due for a hit this time up? or "if I have my left lung removed, what is the chance that the cancer will really be cured?" (p. 28) He follows this with a most interesting short chapter on the history of probability, "The Birth of Lady Luck." And then he explains "The Concept of Mathematic Probability." His exposition was so clear and such a pleasure to read that I can still recall the delight I experienced in reading it for the first time.
In the chapter on "The Counting of Cases," Weaver gets down to the basics of compound events and the difference between combinations and permutations--knowledge that is necessary, for example, in order to analyze a game of chance, especially games involving dice or playing cards..
The next chapter covers independent events, and then there are some famous problems including the one involving dice throwing that the Chevalier de Mere presented to the celebrated French mathematician Blaise Pascal. Weaver had mentioned it earlier, noting that this historical problem from 1654 actually marked the above mentioned "birth of Lady Luck."
In other chapters Weaver introduces us to the law of large numbers and explains the "maturity of chances" fallacy and some other fallacies. He explains in a particularly clear and utterly convincing manner why the so-called Martingale system and other "doubling up" systems yield no advantage to the bettor, and why, if any given independent event is disadvantageous for the bettor, no system of betting on such events will ever lead to an advantage for the gambler. In the case of doubling your bet after each loss, Weaver shows that every time you win, you will be one unit ahead no matter how many times you double up--except for one very deadly proviso: Sooner or later you will run into a streak of losses that will wipe you out--or, run you up against the betting limit of the casino or whomever you are betting against, and you will have to eat your losses. It is simply a matter of the observing the powers of two: 2,4,8,16,32,64,128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536.
In other words, if your betting unit is $100 and you decide to bet on National Football League games, betting $100 the first week, and if you lose doubling your bet to $200 the next week, and then to $400, the following week, etc., until you either win or the season ends, you will gain $100 for each time you win. Should you however run into a bad streak, say losing every week, you would lose $65,536 after the 16th game! (I have simplified this of course since, due to the bookie's vigorish, you actually have to wager $110 to win $100.)
If you double up on something like the throw of the dice at a casino where the odds of winning the bet are less than fifty-fifty, your chance of a ruinous streak is (markedly) increased.
A very interesting chapter is number XIII, "Rare Events, Coincidences, and Surprising Occurrences" where Weaver presents some of the coincidences he has experienced and collected over the years. He goes on to explain the nature of such rare events and gives a very interesting look at them from a mathematical point of view. One of the events is about a guy in Las Vegas who made an amazing 28 passes in a row at a dice table at the Desert Inn. He, cautious bettor that he was, made only about $750, while the side bettors made $150,000. Another event was thirteen spades having been dealt to a bridge player. Weaver discusses whether we should believe that this and some other very, very rare events could happen by chance.
Since reading this book, I have read a number of other popular books on probability, statistics and gambling, but I can say, as good as some of them were, none were nearly as exciting nor half as interesting as this book. As far as I am concerned Lady Luck is a classic of the genre, and more or less timeless.
As for the baseball betting...well, that's another story, but suffice it to say it ain't easy beating the line.
--Dennis Littrell, author of “The World Is Not as We Think It Is”
January 2, 2010
Interesting at first .... especially with the cold war comments ... but I quickly tired of it and have now set this book aside. If you have no background in probability this is probably a good starting point for an easy read.
May 31, 2015
Fine primer for a non-mathematician who is not afraid to do a little algebra. Dated references give the book a hokey charm.
February 4, 2021
Мостеллер Ф., Рурке Р., Томас Дж. "Вероятность" е много по добро въведение
January 2, 2022
Libro de divulgación acerca de probabilidad: historia y aplicaciones a paradojas y juegos de azar. El libro es entretenido pero obviamente no es algo que te haga un experto después de leerlo.
March 25, 2025
a fun read, nothing to call home about. boy oh boy is it hard to put down and start again
Displaying 1 - 11 of 11 reviews