Saturday, October 9, 2010

Book review: The Drunkard´s Walk

- How randomness rules our lives

Yesterday I finished reading the book 'The Drunkard's Walk' by Leonard Mlodinow. He is the co-author of the book The Grand Design with Stephen Hawking.

As the subtitle says the book is about randomness and how it controls our lives in ways we can not (or will not) understand. It was an utterly fascinating read.

Random is an inherently difficult topic to grasp even for people trained in fields were randomness is tackled everyday. Our perception of randomness is not in sync with how true randomness is observed and our understanding of random phenomenon is coloured by ideas of fairness, pattern matching, statistical significances, hot hand fallacies, false positives and a host of other logical and statistical fallacies.

True randomness is counter intuitive based on the experiences we've had and our wish to stay in control of events. To us true randomness is ever changing outcomes, sequences without patterns and a non-influencing average over time. Detecting randomness is extremely difficult. Truly random sequences does not have to appear random at every instance. With millions of cards being drawn everyday (at casinos world wide) someone is bound to get 10 blackjacks in a row and walk away with a ton of money. Or get two jackpots on the slot machines. Or many other things with large prizes involved.

But to each winner (and the people around them) these people will appear to have a system, to be able to beat the machine or have figured out the game. When in essence it's just randomness.

This book will help you understand the random world and avoid the fallacies that might otherwise cause you to make the wrong decisions.

Large data sets and patterns
With a large enough sample set pretty much everything has a measurable probability and will occur at some point. And with a large sample set the observed results will converge on the statistical average value (The law of large numbers).

This also means that even the most unlikely thing (someone winning the lottery for instance) is bound to happen regularly even though the odds of anyone specific winning is unbelievably small (*).

Additionally, over time patterns will emerge even though they do not exist. You'll see what appears to be a recurring event at some interval of time and react upon it, event hough it's nothing more than a random sequence in the data.

The book discusses the dangers of not understanding this when making decisions, unlikely things will occur now and then and we must be able to tell whether this is a skilled person, a rising trend, an emerging pattern or just random noise.

Fallacies and examples
Different fallacies and biases are also discussed in the book, how they arise what they mean and more importantly how to detect and avoid them. This includes fallacies such as the gambler's fallacy, hot hand fallacy, the prosecutor's fallacy and availability bias.

There are an enormous amount of examples in this book, which are aimed at making the reader understand a complex statistical situation. The examples are generally brilliant and makes reading the book, and understanding it, a lot easier. Common examples include the Monty Hall game show problem, illusions of patterns, normal distributions and many many more.

Consider the following two statements and determine which one you think is the most likely one to occur:

  1. It will be cold and rainy tomorrow.
  2. It will be rainy tomorrow.
The supporting argument of 'cold' will cause a lot of people to choose option 1 as the most likely one (It's usually cold when it's rainy). But the most likely one is option 2 as it also includes option 1.

The are many different possible temperatures while it rains but only some of the are allowed in option 1, decreasing the probability. Option 2 includes all possible rainy days.

A nice thing about this book is how Mlodinow takes the reader back in time to before the discovery of statistics and probability and then walks along the important historical characters as they lived their lives. You'll learn about Bernoulli, Pascal, Gauss, Laplace, Bayes and more, and how they all contributed to our understanding of probabilities today.

The book doesn't require a Master's in mathematics to understand, you'll get by with even basic math. This is about exemplifying statistics and explaining randomness, not about calculating odds or measuring outcomes of large test sequences.

If you've ever been interesting in understanding probability or statistics, or learning why the world appears to be unfair and non-random, why unlikely things happen or why you'll never beat the casino you really should read this book.

* The Danish national lottery has 36 possible numbers with seven winning numbers being drawn. This means that there are 8347680 different possible outcomes and each entry into the lottery has about 0.000012% chance of winning. This means that it will likely take thousands of years for you to win with seven correct numbers. Yet someone wins almost every week, which feeds the Gambler's fallacy (and other fallacies) in peoples minds. The reason someone wins is that a massive amount of lottery entries are played each week. With just 1 million entries there is a 88.7% chance that someone will win.