The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern - Ebooks PDF Online

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The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern

Before the mid-seventeenth century, scholars generally agreed that it was impossible to predict something by calculating mathematical outcomes. One simply could not put a numerical value on the likelihood that a particular event would occur. Even the outcome of something as simple as a dice roll or the likelihood of showers instead of sunshine was thought to lie in the rea Before the mid-seventeenth century, scholars generally agreed that it was impossible to predict something by calculating mathematical outcomes. One simply could not put a numerical value on the likelihood that a particular event would occur. Even the outcome of something as simple as a dice roll or the likelihood of showers instead of sunshine was thought to lie in the realm of pure, unknowable chance.The issue remained intractable until Blaise Pascal wrote to Pierre de Fermat in 1654, outlining a solution to the “unfinished game” problem: how do you divide the pot when players are forced to end a game of dice before someone has won? The idea turned out to be far more seminal than Pascal realized. From it, the two men developed the method known today as probability theory. In The Unfinished Game, mathematician and NPR commentator Keith Devlin tells the story of this correspondence and its remarkable impact on the modern world: from insurance rates, to housing and job markets, to the safety of cars and planes, calculating probabilities allowed people, for the first time, to think rationally about how future events might unfold.

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Before the mid-seventeenth century, scholars generally agreed that it was impossible to predict something by calculating mathematical outcomes. One simply could not put a numerical value on the likelihood that a particular event would occur. Even the outcome of something as simple as a dice roll or the likelihood of showers instead of sunshine was thought to lie in the rea Before the mid-seventeenth century, scholars generally agreed that it was impossible to predict something by calculating mathematical outcomes. One simply could not put a numerical value on the likelihood that a particular event would occur. Even the outcome of something as simple as a dice roll or the likelihood of showers instead of sunshine was thought to lie in the realm of pure, unknowable chance.The issue remained intractable until Blaise Pascal wrote to Pierre de Fermat in 1654, outlining a solution to the “unfinished game” problem: how do you divide the pot when players are forced to end a game of dice before someone has won? The idea turned out to be far more seminal than Pascal realized. From it, the two men developed the method known today as probability theory. In The Unfinished Game, mathematician and NPR commentator Keith Devlin tells the story of this correspondence and its remarkable impact on the modern world: from insurance rates, to housing and job markets, to the safety of cars and planes, calculating probabilities allowed people, for the first time, to think rationally about how future events might unfold.

30 review for The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern

1. 5 out of 5

Ben

2. 4 out of 5

S.

The book illustrates the history of probability, not dense with equation's, in fact all of which are made easier to understand with all the examples and explanations that the author used. Why don't we go on learning maths this way, fun, simple and tightly related to the 'real' world ? The book illustrates the history of probability, not dense with equation's, in fact all of which are made easier to understand with all the examples and explanations that the author used. Why don't we go on learning maths this way, fun, simple and tightly related to the 'real' world ?

3. 4 out of 5

Valerie

Letter writing is most certainly a lost art. "I beg you to inform me how you would proceed in your research on this problem. I shall receive your reply with respect and joy, even if your opinion should be contrary to mine." contrasted with today's modern flame wars. Having just taken a class in decision quality at Stanford, I found the discussions of Baye's formula and assessing risk by using probability very interesting. It is difficult to imagine a time before probability mathematics. Letter writing is most certainly a lost art. "I beg you to inform me how you would proceed in your research on this problem. I shall receive your reply with respect and joy, even if your opinion should be contrary to mine." contrasted with today's modern flame wars. Having just taken a class in decision quality at Stanford, I found the discussions of Baye's formula and assessing risk by using probability very interesting. It is difficult to imagine a time before probability mathematics.

4. 4 out of 5

Marius Bancila

The title is a little bit misleading as the book is not entirely about the letters Pascal and Fermat have exchanged in 1654, but rather a history of the science of probabilities that started with the problem of the unfinished game. Devlin does focus on the letters of the two great French mathematicians but also shows how others have drawn inspiration from the methods Pascal and Fermat have established and how they developed and applied math to real world problems (not only gaming). The book is n The title is a little bit misleading as the book is not entirely about the letters Pascal and Fermat have exchanged in 1654, but rather a history of the science of probabilities that started with the problem of the unfinished game. Devlin does focus on the letters of the two great French mathematicians but also shows how others have drawn inspiration from the methods Pascal and Fermat have established and how they developed and applied math to real world problems (not only gaming). The book is nicely spiced with short biographies of many mathematicians. Overall Devlin makes a good case showing how hard it was for the great thinkers of 17th century to overstep what seemed rationale and develop correct mathematics for determining the chances of an event to occur.

5. 5 out of 5

William Schram

The Problem of Points taunted humanity for centuries. A letter between Blaise Pascal and Pierre de Fermat changed all of that forever. In "The Unfinished Game," Keith Devlin goes over the paradigm-shattering piece of correspondence that introduced the world to Probability Theory. Devlin explains the reasoning of each side and the points that each person made in previous letters. The game-changing idea was to predict what would happen if the game continued. People assumed that games of chance were The Problem of Points taunted humanity for centuries. A letter between Blaise Pascal and Pierre de Fermat changed all of that forever. In "The Unfinished Game," Keith Devlin goes over the paradigm-shattering piece of correspondence that introduced the world to Probability Theory. Devlin explains the reasoning of each side and the points that each person made in previous letters. The game-changing idea was to predict what would happen if the game continued. People assumed that games of chance were all up to the gods and did not realize that it was possible to predict events. Devlin discusses other aspects of Probability Theory as well. For example, in the same period as the correspondence, John Graunt developed a method to read statistics from raw data. Graunt was surprisingly accurate for the time and used for decades to make actuarial predictions. We can't discuss this era without some mention of the Bernoulli family, and we get that too. Finally, Devlin talks a bit about Bayes' Rule. Conditional Probability was far too tedious before computers were widespread. Devlin does not include too many equations in the book. He mainly discusses the methods employed.

6. 5 out of 5

Vishal Katariya

Nice history of probability theory.

7. 5 out of 5

Kelly Vincent

This book tells the story of the origins of probability, which emerged more recently than you would expect for such a fundamental field. It's somewhat famous among certain types of nerds that probability theory came from a handful of mathematicians pondering certain types of gambling. Specifically, the real origins are documented in a series of letters between Blaise Pascal and Pierre de Fermat. So this book includes selections from the (extant) letters and explains and discusses them, giving th This book tells the story of the origins of probability, which emerged more recently than you would expect for such a fundamental field. It's somewhat famous among certain types of nerds that probability theory came from a handful of mathematicians pondering certain types of gambling. Specifically, the real origins are documented in a series of letters between Blaise Pascal and Pierre de Fermat. So this book includes selections from the (extant) letters and explains and discusses them, giving the historical context and then continuing on to what the letters inspired. It's an interesting book, and it's always cool to actually see the primary sources that history books are relying on. It's also a fairly slim book. The math isn't extremely difficult to follow (this is no "calculus-based probability and statistics" textbook) and I don't think a full understanding of all of it is critical to an appreciation of the book, anyway. Prior to the events kicked off by the exchange of letters, virtually everyone thought the future was impossible to predict (well, in a secular sense, anyway). So while some avid gamblers tried to pay attention to the behavior of the games they played to figure out how to best bet, it seemed rather pointless. The late-fifteenth century mathematician Pacioli published a book that included the "problem of the unfinished game" (also called the "problem of the points"), which asks what the fair way to distribute the money when a game has to be aborted before its intended conclusion. For instance, if two players decide to play the best of 7 but have to stop after only 4 games, with 1 player with 1 win and the other with 3, how much of the pot should each walk away with? The only really obvious scenario is when they are exactly tied. All others seemed unknowable. The Chevalier de Mere was good enough at calculating odds that he used the modern casino long haul strategy of identifying games with probability just slightly in his favor (i.e., around 51% for him) and just playing a whole bunch of times. He contacted Pascal with several questions relating to games of chance, including the problem of the unfinished game. Pascal tried to solve it and then wrote to Fermat to get a second opinion on his solution. Thus, the exchange. Devlin walks us through the letters, Pascal's solution, Fermat's superior solution, and Fermat's patient attempts to explain the revolutionary ideas embedded in his solution to Pascal, who struggled to grasp it. I found this pretty interesting, because Pascal is one of the Greats, yet he just could not wrap his head around what Fermat was proposing. Sometimes math is hard, even when you're good at it. This certainly fits with my own experience of trying to learn probability theory--it is probably (heh) as counter-intuitive as any accurate idea can be. The most novel part of Fermat's approach, the one Pascal had so much trouble accepting because it seemed illogical, is the idea that when you are calculating probabilities on a game of say, best of 7, you have to calculate the odds based on 7 plays--not just 5 if one player would have won and the game would have finished. So with the unfinished game problem, if one player is leading after 3 plays, you still have to calculate the odds on 7 plays to get the right answers. Devlin goes on to discuss what happened with the new ideas. This includes (among other things): the first real instance of applied statistics (a 1662 pamphlet analyzing mortality rates in London), the landmark text that Huygens wrote on probability theory (starting with Fermat and Pascal but adding his own), the (amazing and numerous) Bernoullis, psychology and risk, probability in courts, the Normal distribution, annuities and insurance, Bayes, Site Profiler (the DoD system that predicted the events of 9/11, along with many other incidents that didn't happen), DNA profiling, and financial derivatives.

8. 5 out of 5

Claudia

It will never cease to amaze me how few hundred years ago, when relying almost exclusively on their minds, people where able to develop and discover such things. This book details how the theory of probabilities emerged from the question on how the pot should be divided between two players, when one of them leads with 2 to 1 and they stop playing. Keith Devlin, professor of mathematics at Stanford University, dissects the correspondence between Blaise Pascal and Pierre de Fermat and explains, in It will never cease to amaze me how few hundred years ago, when relying almost exclusively on their minds, people where able to develop and discover such things. This book details how the theory of probabilities emerged from the question on how the pot should be divided between two players, when one of them leads with 2 to 1 and they stop playing. Keith Devlin, professor of mathematics at Stanford University, dissects the correspondence between Blaise Pascal and Pierre de Fermat and explains, in a very simple and understandable way, all the thinking and connections which led to that discovery and, later on, to statistics, risk management and many other predictions used today, from financial trends to terrorist’s attacks. He also reviews the roles others had in this matter, which are not as famous as these two, but had, nonetheless, a major contribution to this particular field. And the letter between the two is just a piece of art… too bad these days we resume ourselves to electronic succinct messages. A highly enjoyable and interesting book.

9. 4 out of 5

Kelly Jackson

I do have a math background for disclosure purposes. I found the subject matter and historical context interesting. The writing style was a little grating. There was a lot of condescension in the prose. It's OK if you don't understand it... I do have a math background for disclosure purposes. I found the subject matter and historical context interesting. The writing style was a little grating. There was a lot of condescension in the prose. It's OK if you don't understand it...

10. 5 out of 5

Elizabeth

Not as entertaining or efficiently informative as The Man of Numbers. Felt a bit disjointed and speculative at times, as though Devlin thought, "Oh, yes, one other thing while I'm at it" many times throughout. Not as entertaining or efficiently informative as The Man of Numbers. Felt a bit disjointed and speculative at times, as though Devlin thought, "Oh, yes, one other thing while I'm at it" many times throughout.

11. 5 out of 5

John Landis

A complete waste of my time. I would rather they chose either the math or the people involved to concentrate on instead of focusing on both and failing twice.

12. 5 out of 5

Fred Cheyunski

13. 4 out of 5

Ed Terrell

Mathematics is anything but boring. Knights gambling over pots of gold combined with intrigue and suspense, where what seems obviously to be true just isn't so. It's not that we are irrational, its just that we don't know how to ask the right questions. "The Unfinished Game" is a quest to calculate how the pot or winnings should be divided if the game was not able to be played to completion. The key insight provide by Fermat was to focus on future rather than past outcomes. Along the way, he and Mathematics is anything but boring. Knights gambling over pots of gold combined with intrigue and suspense, where what seems obviously to be true just isn't so. It's not that we are irrational, its just that we don't know how to ask the right questions. "The Unfinished Game" is a quest to calculate how the pot or winnings should be divided if the game was not able to be played to completion. The key insight provide by Fermat was to focus on future rather than past outcomes. Along the way, he and Pascal created a new branch of mathematics: probability and statistics. Devlin casts a wide net to ensure that we get introduced to a consortium of mathematical wizards such as the Bernoullis, Huygens and Bayes. The book ties in the historical development of ideas with clear and concise mathematical explanations. It is worth reading for his discussion of Bayes rule alone. Clearly five stars.

14. 5 out of 5

Xin

15. 5 out of 5

Jeroen

An easy to read book on the origin of probability theory. The theory is explained well and established based on a letter between Pascal and Fermat. Easy to read for people that don't already know some of the probability theory basics and interesting background reading for those who do. Main drawback of the book is the easy way the author uses historic dates to set context of developments after the start by Fermat/Pascal. Those dates sometimes feel a bit chaotic and unstructured. An easy to read book on the origin of probability theory. The theory is explained well and established based on a letter between Pascal and Fermat. Easy to read for people that don't already know some of the probability theory basics and interesting background reading for those who do. Main drawback of the book is the easy way the author uses historic dates to set context of developments after the start by Fermat/Pascal. Those dates sometimes feel a bit chaotic and unstructured.

16. 4 out of 5

Sonya Mann

Pretty good Moderately entertaining and fairly informative. But not exceptionally written. I know a little more about the origins and anatomy of probability theory, so that makes me happy.

17. 4 out of 5

Kiora Nield

Super quick read with introductions to a lot of mathematicians that influenced probability theory. My favorite part was how he delved into the thinking they had to overcome to get to the breakthrough.

18. 4 out of 5

Nikos Koukis

This review has been hidden because it contains spoilers. To view it, click here. Meh, not really interesting. The only fact worth knowing is that Fermat and Pascal developed the modern theory of probabilities in 1654 via a series of mail correspondences. There you go. I saved you from going through 200 boring pages

19. 5 out of 5

Brett

Pascal and Fermat are two fascinating characters in the history of math. However, I simply wasn't interested in the story here. Pascal and Fermat are two fascinating characters in the history of math. However, I simply wasn't interested in the story here.

20. 5 out of 5

Lars Guthrie

21. 4 out of 5

Eric

I’ve got a dirty secret - I’m mathematically challenged, and it has always been so. I’ve had to work extra hard to be extra average at math. Secretly, I’d like to be good at math, and understand some of the advanced compression, encryption, and other algorithms that kick around the interwebs. Every now and then, I’ll pick up a math-oriented book, and I usually put it down in despair. Not so The Unfinished Game, which is as much about history as it is about probability. In a nutshell, the book des I’ve got a dirty secret - I’m mathematically challenged, and it has always been so. I’ve had to work extra hard to be extra average at math. Secretly, I’d like to be good at math, and understand some of the advanced compression, encryption, and other algorithms that kick around the interwebs. Every now and then, I’ll pick up a math-oriented book, and I usually put it down in despair. Not so The Unfinished Game, which is as much about history as it is about probability. In a nutshell, the book describes a snail mail conversation - an ancient form of collaboartion - between Pascal and Fermat regarding the correct way to devise the payment of a wager on an unfinished game of dice. The narrative weaves mathematical explanations between discussion of the time, place, and personalities of the story. A quick and compelling read, you’ll come out of it feeling that you’ve learned something truly important, borne of a discovery that took ages by modern standards. It is striking to consider how quickly we are able to use the social Web to iterate over interestin ideas, in comparison to the pen and paper ways of old. Strongly recommended.

22. 4 out of 5

Gary Fixler

Can one ever really finish "The Unfinished Game?" I admit, I did not read the full correspondence between Fermat and Pascal at the end of the book; I got much of it in pieces throughout. I'll save the 10 or so pages for a rainy day. I am impressed—and admittedly puzzled—by the praise each heaps upon the other in his letters. Modern teenagers in love fail to reach such heights of extended, floral flattery. Perhaps, owing to the slowness of communication-by-post, such admiration was delivered in b Can one ever really finish "The Unfinished Game?" I admit, I did not read the full correspondence between Fermat and Pascal at the end of the book; I got much of it in pieces throughout. I'll save the 10 or so pages for a rainy day. I am impressed—and admittedly puzzled—by the praise each heaps upon the other in his letters. Modern teenagers in love fail to reach such heights of extended, floral flattery. Perhaps, owing to the slowness of communication-by-post, such admiration was delivered in bulk, and metered out in doses by the recipient over the course of the following weeks. I can't say. What I can say is that this was a very fun read, and a nice peek into the lives behind a good number of names I've known for years. I really enjoyed following the connections back, from things I've known (and math I've [albeit indirectly] used) to the life and times of the 17th century. Math is timeless.

23. 5 out of 5

Doug

I loved this book. Pascal and Fermat never met in person but their exchange of letters started a revolution in terms of how mankind sees the world - in terms of risk management. Devlin documents the exchange and highlights significant topics in the discussion. I think his characterization of the problem of points, Pascal's probabilistic argument for believing in God, and his numerous examples of how Baye's theorem is used (especially in health care) are some of the best I've seen. And, he does a I loved this book. Pascal and Fermat never met in person but their exchange of letters started a revolution in terms of how mankind sees the world - in terms of risk management. Devlin documents the exchange and highlights significant topics in the discussion. I think his characterization of the problem of points, Pascal's probabilistic argument for believing in God, and his numerous examples of how Baye's theorem is used (especially in health care) are some of the best I've seen. And, he does a good job of identifying a priori and a posteriori probability, and the different ways that distinction is used. If you're interested in history and how our modern world has been shaped, pick up and read. You don't have to be mathematically inclined to enjoy it.

24. 4 out of 5

mandy

While this is book is meant to appeal to "regular" people, and not mathematicians, I found that the math that is included was at times hard to grasp. Luckily, Devlin has a knack for explaining the principles behind the formulas with real world examples, which helped a great deal. We also find out a lot of history about various 17th century mathematicians, so history buffs might enjoy this as well. Overall an interesting read. While this is book is meant to appeal to "regular" people, and not mathematicians, I found that the math that is included was at times hard to grasp. Luckily, Devlin has a knack for explaining the principles behind the formulas with real world examples, which helped a great deal. We also find out a lot of history about various 17th century mathematicians, so history buffs might enjoy this as well. Overall an interesting read.

25. 5 out of 5

David Robertus

A generally well done look at the origins of probability theory, the implications for the insurance industry and so on. The author takes a very interesting look at the mindset (or lack thereof) of people prior to the wide spread use of statistics and probability theory in modern every day life. This is intriguing to me in two ways- first,what life is like without it, and two, how frequently misused it is today (which is also addressed albeit briefly).

26. 5 out of 5

Kathy

Probability is such a part of modern life that it is hard to believe it wasn't until the 17th century that it started to be studied. The book is written in a way that can be understood by someone who has forgotten high school math. There are mathematical formulas in the book but the author lets you know you can skip them without losing the flow of the book. For someone with more mathematical background it lets you see how the familiar statistical formulas came about. Probability is such a part of modern life that it is hard to believe it wasn't until the 17th century that it started to be studied. The book is written in a way that can be understood by someone who has forgotten high school math. There are mathematical formulas in the book but the author lets you know you can skip them without losing the flow of the book. For someone with more mathematical background it lets you see how the familiar statistical formulas came about.

27. 4 out of 5

Thom

I appreciate the import of this idea, and the math behind it. I mostly liked the presentation - bits of the letters and the history behind them. Something about the writing - the style perhaps - didn't sit right with me. Will read some of Devlin's online column to see if I can narrow it down sometime. I appreciate the import of this idea, and the math behind it. I mostly liked the presentation - bits of the letters and the history behind them. Something about the writing - the style perhaps - didn't sit right with me. Will read some of Devlin's online column to see if I can narrow it down sometime.

28. 4 out of 5

Michael Artin

So far...the book is compelling simply because of the subject matter. But Devlin's style is so smug and sensationalistic that it gets in the way of digging into the interesting history. He spends so much time telling you "this was really important" and assuring you, "Don't worry if you don't get this...they didn't either!" Speaks down to the reader. So far...the book is compelling simply because of the subject matter. But Devlin's style is so smug and sensationalistic that it gets in the way of digging into the interesting history. He spends so much time telling you "this was really important" and assuring you, "Don't worry if you don't get this...they didn't either!" Speaks down to the reader.

29. 5 out of 5

Lauren Hutchinson

I really like statistics so I may be a bit biased. At times the book did get into some complex but the examples helped to convey the complex math that was being discussed. It was nice getting to learn a bit more about Pascal and Fermat, plus a whole lot of other characters. I'm not sure this book would be that enjoyable for anyone without an appreciation for vague mathematics. I really like statistics so I may be a bit biased. At times the book did get into some complex but the examples helped to convey the complex math that was being discussed. It was nice getting to learn a bit more about Pascal and Fermat, plus a whole lot of other characters. I'm not sure this book would be that enjoyable for anyone without an appreciation for vague mathematics.

30. 4 out of 5

Fraser Sherman

An interesting story about how the great mathematical thinkers Pascal and Fermat tackled an old problem (the Unfinished Game problem of the title) and developed the concept of probability to solve it. Devlin traces the growth of probability and statistics from that breakthrough (though a lot of independent ideas contributed too) through to the present age. Fascinating.