Duelling Idiots and Other Probability Puzzlers
By addebook • Aug 18th, 2008 • Category: Mathematics •
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Duelling Idiots and Other Probability Puzzlers
Duelling Idiots and Other Probability Puzzlers
By Paul J. Nahin
Publisher: Princeton University Press
Number Of Pages: 256
Publication Date: 2000-10-15
ISBN-10 / ASIN: 0691009791
ISBN-13 / EAN: 9780691009797
Binding: Hardcover
What are your chances of dying on your next flight, being called for jury duty, or winning the lottery? We all encounter probability problems in our everyday lives. In this collection of twenty-one puzzles, Paul Nahin challenges us to think creatively about the laws of probability as they apply in playful, sometimes deceptive, ways to a fascinating array of speculative situations. Games of Russian roulette, problems involving the accumulation of insects on flypaper, and strategies for determining the odds of the underdog winning the World Series all reveal intriguing dimensions to the workings of probability. Over the years, Nahin, a veteran writer and teacher of the subject, has collected these and other favorite puzzles designed to instruct and entertain math enthusiasts of all backgrounds.
If idiots A and B alternately take aim at each other with a six-shot revolver containing one bullet, what is the probability idiot A will win? What are the chances it will snow on your birthday in any given year? How can researchers use coin flipping and the laws of probability to obtain honest answers to embarrassing survey questions? The solutions are presented here in detail, and many contain a profound element of surprise. And some puzzles are beautiful illustrations of basic mathematical concepts: “The Blind Spider and the Fly,” for example, is a clever variation of a “random walk” problem, and “Duelling Idiots” and “The Underdog and the World Series” are straightforward introductions to binomial distributions.
Written in an informal way and containing a plethora of interesting historical material, Duelling Idiots is ideal for those who are fascinated by mathematics and the role it plays in everyday life and in our imaginations.
Summary: Exactly who did the author have in mind?
Rating: 2
The best puzzle books start with problems that are interesting and non trivial, and offer unexpected solutions. They appeal to a crowd with different levels of education and offer a new idea or two to all. They will lead an unsuspecting layman to a new beautiful mathematical subject, and treat a pro with a lighthearted yet technically sound look at the concepts he is already familiar with.
“Dueling idiots” is none of that. To read it you must be more than familiar with probability theory, and at ease with going through rather tedious calculations and using mathlab. Yet all a sophisticated reader finds here is absence of fresh ideas and technical sloppiness.
I am giving it two stars rather than one because it could provide some probability theory buff with a nice set of “real life” applications — good as an auxiliary text book for an undergraduate probability class e.g. Apart from that, you will find a better puzzle book almost anywhere you look.
Summary: This Attempt Falls Short
Rating: 2
There is surely a need for a book like this but sadly this one doesn’t do the
job. The author clearly has no idea what’s really required. On p 20 he has
the results of five runs of 10,000 simulations to estimate the probability
P(A) of an event A. Now P(A) is known here, so these simulations are just an
ATTEMPT to verify that the program is working correctly. The author merely
notes that “the estimates for P(A) are a bit on the high side.” No kidding!
All five runs produced consistently high estimates, and combining the runs
there’s only one chance in 87 that the overall estimate would be so high
(ASSUMING the program were working properly). Of course, it’s POSSIBLE that
the procedure is correct, that such high estimates just happened by a long
shot, but my email suggesting that the simulations be rerun drew no reponse.
Given this failure to demonstrate that a KNOWN probability can be estimated
properly, goodness only knows how good/bad UNknown probability estimates are.
Little wonder so many bombs are missing their targets in Afghanistan.
Turning to how the random numbers were generated I promptly noticed the table
of autocorrelations on p 184. These are not only bad, the zero-lag
correlation (a variable with itself) is 1.023!!! Given that it should be
nothing but EXACTLY 1 I initially thought this was a social comment on the
age of the generator, but machines were NEVER THAT bad. Rather, you’ll find
the reason in the mishmash just above the table.
Indeed, in what little I read, statistical concepts are massacred. Further,
on p 27 there’s an expression for pi which is actually mathematical nonsense
(ie, it is incorrect). At that stage I quit reading, it’s so painful.
Nonetheless, I’ll give the author two stars for TRYING to fill a void. He
just needs someone to correct everything, which is obviously no small task.
Summary: Oddballs and urns
Rating: 5
Books on probability are often boring. (Remember all those tedious problems involving people obsessed with drawing balls from urns?). In “Duelling Idiots”, Nahin actually makes the subject fun by describing offbeat problems with unexpected solutions. If you like solving math puzzles, then this is a great book to look at. If you’re teaching a course and want to assign a book that students might actually read, then look no further.
Summary: Real world problems masked by somewhat frivolous statements
Rating: 4
Two areas where the results are often counter intuitive are quantum mechanics and probability. Even experienced mathematicians are often confused by results such as the birthday and Monty Hall problems. After years of expert analysis and commentary, the results are still disputed and disbelieved by many. While these problems are not covered in any detail here, others with sometimes unexpected results are extensively examined.
The title problem is a simple one where two individuals take turns spinning the chamber of a gun, pointing it at the other and pulling the trigger. While it is obvious that the first to go has the advantage it is surprising that the advantage is not greater than it is. Another problem of special interest during playoff season concerns the probability that the best team actually wins a seven game first with four wins series. It is a well-worn clich
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