## Chance: A Guide to Gambling, Love, The Stock Market & About Everything Else

Popular science books are an interesting category: On the one hand they have to be light on the academic details, and written in an entertaining fashion. On the other hand they attempt to educate the reader, if only a little bit. The book *Chance: A Guide to Gambling, Love, The Stock Market & About Everything Else* written by *Amir D. Aczel* is a basic introduction to probability theory.

The topics touched in the books after a gentle introduction into what probabilities: basic combinatorics, the concept of runs tests, the inspection paradox, the birthday problem, the secretary problem, Bayes theorem and the normal curve. The book concludes with a lengthy appendix written by *Brad Johnson* on probabilities in casino games.

In this review I want to discus a chapter I enjoyed and a chapter that I didn't like.

The chapter discussing the secretary problem, chapter 13, is called *How to Succeed in Love (Find the Best Apartment, or Adopt the Best Puppy)* is my least favorite chapter. Because it tries to make a common problem into something sensationalist, making unwarranted assumptions, basically rendering the conclusion useless. The same actually happened in a Dutch TV show (Eureka by the KRO) a while back.

The secretary problem is the question when to stop in a series of options is which you cannot go back to earlier options after you dismiss them. The same holds for the choice in life partner of course. When the amount of possible options is known the optimal strategy is to test the first 1/e = 36.8% of the possible options, and then settle for the first one that outperforms the ones you saw before. My problem with the chapter is that it assumes that the amount of possible options is known. It does not tell you what is the optimal strategy when the amount of possible options is unknown, as it is with dating in real life. It appears then that this 36.8% is a useless number. This chapter is in contrast to the rest of the book, where such silly assumptions are not made.

Chapter 10 is called The Inspection Paradox, and discusses exactly that paradox. This chapter is was my most favorite while reading, because the paradox was new to me, and the explanation is so simple.

The paradox is simple: If a bus service is scheduled to run every 10 minutes on average, you might be inclined to think that your average wait will be about 5 minutes, since you will arrive in between buses on average. The funny thing is is that your average wait will be longer than that. The illustration above beautifully shows that there is a higher probability you will end up in a long interval between buses. This means that, on average, you will wait longer then you would think.