Duelling Idiots and Other Probability Puzzlers

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.

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 cliché that, "In a short series, anything can happen!" However, the mathematical analysis clearly supports this saying. The graph of the possible results shows that even if the probability of the stronger team winning any individual game 0.65, the weaker team still has a 20% chance of winning the series. Monte Carlo or statistical simulation methods are used to test and verify many of the results. The software package used to perform the tests is MATLAB and 63 pages of code listings is included at the end of the book. Solutions to all problems are included and many of them require a year or more of college calculus in order to understand the solution. Although many of the problems covered in this book have somewhat frivolous statements, they also are illustrative of situations encountered in the real world. Some in fact originated there and the statements were altered to make them more interesting to a general audience. This is a good book to use as a supplement in a course in applied probability theory.

This is yet another excellent contribution by professor Paul Nahin. The format of this book is different from his previous texts, but the high quality content is still there.The book is divided into three main parts. In the first part he presents the problems and elaborates on their history, if any, and provides hints or solves a related problem. In the second part, he provides complete solutions to the problems, both analytical and through computer simulation in most cases. Finally, in the third part, he includes all the programs (MATLAB version) used to obtain the solution to the puzzlers. The book also includes a chapter on random number generation, a key element of Montecarlo simulation.Some knowledge of basic probability and random variables is required to fully understand the problems and solutions. Also, knowledge of calculus is needed (particularly integral calculus). To understand the computer solutions the reader must know MATLAB. The computer simulations, however, can be rewritten using any languange. Personally, I prefer Perl and that is what I used to run some of the simulations.I believe that the computer programs could have been included in a CD or diskette, or a download site could have been used. Then, the 67 or so pages dedicated to these programs, could have been used to provide 5-10 additional problems!