The Drunkard's Walk

The Drunkard's Walk: How Randomness Rules Our Lives, written by Leonard Mlodinow, is one of those books that makes an arcane subject understandable. Mlodinow explains statistics and probability in very clear language, with many examples and counter examples.

He tracks the history of probability theory from when gamblers started analyzing the games they played in an effort to improve their chances. Different people analyzed dice and cards and came up with algorithms to predict different odds. One gambler analyzed the different roulette wheels at a casino and discovered one that landed on certain numbers more often than other numbers. He used his findings to place large bets and won big until the casino got rid of the offending machine.

There is a good discussion of the rules of large numbers, including a description of Benford's Law. Benford's Law is an observation about numbers in real life that says that smaller digits are more likely to occur than larger digits. There is also a long discussion of how difficult it is to estimate probabilities with small sample sizes. And some mention is made of the difference between statistics, which describes a set of measurements in the real world, and probability, which takes those measurements and tries to make predictions based on it. He also discusses the concept of randomness and whether it implies equal likelihood of the outcomes.

I learned a lot about probability (even though I think I'm already pretty educated about it) when Mlodinow explained some of the contradictions and counterintuitive results in probability. He explains the Monty Hall problem well enough that I think I actually understand it now (and believe it's true). He also explains related paradoxes such as the Two Daughters question by showing how to expand all the possibilities of the sample space. Some of the solutions can be shown not only by deductive logic but by looking at actual results in the population.

Mlodinow also discusses how our minds interpret randomness and make a sort of order out of it, whether correct or not. A long succession of heads for coin flips or a long hitting streak in baseball is not necessarily a non-random event. Given enough chances, a lot of different outcomes can be expected. The streak of a Wall Street analyst can be explained by showing that the population of analysts can be expected to produce at least one such winning streak over a long enough time period. However we see numbers and understand them differently for individual events that happen to us. A story with a lot of detail is more likely to be remembered than one without. Combinations of events can appear more likely than the events separately, which is impossible. I appreciated this psychological look at how numbers and chance are processed in the mind.

I also appreciated the explanation of false positives: how a test with small chance of a mistake doesn't necessarily mean that the results are certain. Indeed, after listening to this audiobook I have a much better understanding of certainty and chance. It is important to appreciate the vast numbers that are relevant to our lives. This book gives a great understanding to how numbers and randomness work in real life. I highly recommend it. A