Is there much in life that we can actually influence? How much of what we accomplish can we attribute to our abilities? Can we know what will happen in the future? In what form will this happen, if at all?

The Drunkard’s Walk by Leonard Mlodinow explores these and related questions, discussing the importance of chance in our daily lives, the development of modern statistical research, and introducing some basic mathematical concepts that will help you better understand statistics. In short, you will gain insight into the extent to which luck may have affected your life.

You may be wondering if you should read the book. This book summary will tell you what important lessons you can learn from this book so you can decide if it is worth your time.

At the end of this book summary, I’ll also tell you the best way to get rich by reading and writing.

Without further ado, let’s get started.

## The Drunkard’s Walk Book Summary

**Lesson 1: **With the help of the law of large numbers it is possible to estimate the probability of certain events.

Suppose you decide to record your dice rolls. Do you think that the results will be completely random? If that were the case, each number would appear only once in six rolls. Most likely, though, that will not happen. What does that say about the nature of randomness?

However, there is no such thing as complete randomness in nature.

In 1873, a gambler named Joseph Jagger came to this realization. He used six roulette wheels to keep track of the results of his Russian roulette game. In one of the kettles, he noticed that the number nine appeared more frequently. As a result, he and his friends began placing bets on these numbers, eventually collecting around $5 million.

This raises the interesting question: How likely is it that certain numbers will recur in the future if they have already appeared several times?

One of the first mathematicians to address this problem was Jakob Bernoulli in the late seventeenth century. The Golden Theorem, also known as the Law of Large Numbers, is the result of his twenty years of effort.

To illustrate, imagine 5,000 pebbles in a jar, 60% of which are white and 40% of which are black. There is a chance that out of one hundred pebbles, sixty will be white and forty will be black, but it is also possible to get fifty white and fifty black, or some other combination that does not deviate too far from chance.

On the other hand, if one draws a thousand or two thousand pebbles, the ratio of white to black will approach 60:40. Because of the law of large numbers, the larger the sample, the more accurate the percentage will be.

Bernoulli used the law of large numbers to determine the probability of drawing between 58 and 62 white pebbles from a given pool of pebbles.

Jacob Jagger’s profit could have been even greater if he had known Bernoulli’s theory.

**Lesson 2: **A person’s understanding of probability can change drastically depending on the nature of the problem.

If you were tested for HIV and the result was positive, what steps would you take? In this situation, it is understandable that most people freak out. However, mathematics can shed some fascinating light on this situation.

The likelihood that your HIV test will come back positive is greater than you think. Writer Leonard Mlodinow had a positive HIV test result himself. Mlodinow then inquired about the likelihood of a test coming back positive when his doctor had found a negative result. Once in 1,000 HIV tests, he said.

In any case, he said, this possibility is not really significant. Mlodinov had asked about the probability of a positive result if there is no positive test subject. This is very different from the probability that a person is HIV-negative if the test is positive.

The shocking answer is that the vast majority of false-positive HIV test results are actually false-negatives. Only one in eleven tests can reliably determine whether or not a person has HIV. Therefore, despite a positive HIV test, there is more than a 90 percent chance that you do not have HIV.

Conditional probability is an important concept. Statistical probability analysis looks at how likely something is to occur after another event has already occurred. In our case, we had already received a positive result for HIV. For this reason, we had to calculate the probability that the person was actually pessimistic.

As another example, it is not uncommon for people with Ebola to complain of headaches. However, headaches are not always indicative of Ebola. Depending on the order of these two conditions, the situation is very different.

So the next time you come across a statistical report, be sure to check the assumptions it makes. You can increase a probability from 1% to 90%!

**Lesson 3: **Statistics are prone to random errors and fluctuations.

Is it unusual for two statistical measurements of the same phenomenon to disagree? Both deliberate manipulation of statistics to further particular goals and random human error are possible.

Inaccuracies in numbers or records can have far-reaching effects.

According to the Bureau of Labor Statistics, the unemployment rate in the U.S. fell from 4.8% the previous year to 4.7% in 2006, and in response, the New York Times published an article titled “Jobs and Wages Increased Modestly Last Month.” But unfortunately, that wasn’t the whole truth.

It’s possible that the reported 4.7% to 4.8% increase was a mistake. And it was, unfortunately for the New York Times: we call that a fluke.

It’s possible that someone in this case was simply reporting a problem. A small number of misreported cities could still affect the national average.

Subjective ratings, like those of wines, are particularly prone to random error. Typically, critics use a scale of 1 to 100 to rate wines. But how accurate are these ratings, really? If three wine experts give the same wine a rating of 80, we can assume that it’s quite good. However, let’s say the ratings are 60, 80 and 100. Again, the average score is 80, but not all critics were thrilled with the wine.

Mathematicians have developed the concept of sample standard deviation to quantify the spread of results in a given sample, which is useful to illustrate the diversity of such statistics.

If all wine critics gave the same score of 80, the standard deviation would be zero. The higher standard deviation (20) in the second scenario would better illustrate the diversity of wines and help consumers understand the scores.

Consequently, seemingly insignificant shifts or errors can have far-reaching consequences. Paying attention to them will help you better interpret the data and draw conclusions.

**Lesson 4: **The bell curve is a common result of using accurate data.

What would a graph of the heights of your friends and family look like? In statistics, a normal distribution or bell curve is found with many different types of data, including height measurements.

This bell-shaped distribution has two characteristic features:

One is where its mean lies. Mean is short for “average” (60, 80, and 100 have a mean of 80). The mean is the most common value in a normal distribution. So the mean value of the male height could be 1.8 m. On the bell curve, 1.8 is at the upper end and 1.79 and 1.81 are at the lower end.

The second distinguishing feature is the wide variety of their statistics. The farther you get from the center, the fewer data points there are to represent the data. If we use height as an indicator, we find that there are more men who are 5’8″ than those who are 5’81”, but there are also more men who are 5’81” than those who are 5’01”.

Therefore, if we can see the characteristics of a bell curve, the data is probably accurate.

Let us assume that the average height of a man in the United States is 1.8 meters. The average height of men at U.S. colleges and universities is somewhere between 1.78 and 1.81 m, but it would be difficult to find a data set with an average height of 1.7 m, given how far below the national average it is. Therefore, a sample may not be fully representative of the national average, but it is often quite close to it, such as the average height of men at a particular college.

This form of distribution is common in data sets and can be used to draw inferences about the data. In many cases, the results of a larger data set can be predicted from a smaller data set. This method is used to make reasonably accurate predictions about things like upcoming elections.

### Lesson 5: Linking seemingly unrelated records reveals useful connections.

Centimetre or foot? Your parents’ height, please. Are you able to see a connection between these two factors? If so, how can you put this connection into words?

Francis Galton, a mathematician and distant cousin of Charles Darwin, studied this phenomenon and developed the correlation coefficient.

Galton had a keen interest in statistical analysis. He took a precise mental measurement of all the people he saw, from the size of their heads and noses to the attractiveness of the girls he saw on the street (for him, the girls from London were the most attractive and those from Aberdeen the least attractive).

In addition, he began to extrapolate information about a child’s height from his parents’ measurements. He superimposed a chart of parental height on a chart of offspring height and found that there was a correlation between the two. In this way, he discovered the basic idea of correlation in statistics.

How strongly two variables are related is quantified by their correlation coefficient. In this case, we are interested in the relationship between the size of the parents and the size of the offspring, and we find a positive correlation between the two, indicating that this relationship increases with the size of the parents.

If a person’s height consistently follows a formula determined by the height of the parents, then the highest possible correlation exists between these factors. The average height of a person’s parents could be an accurate prediction of their own height. Although there is no perfect correlation between height and success, a positive correlation can be found.

For example, a positive correlation could exist between eating McDonald’s food and being overweight. In the highly unlikely event that eating McDonald’s food is inversely correlated with weight loss, eating more would result in a lower body mass index.

For this reason, we use the correlation coefficient to explain relationships between variables. The correlation coefficient is one of the most fundamental ideas in statistics and is a method of establishing a mathematical link between two variables.

**The Drunkard’s Walk Book Review**

The Drunkard’s Walk is a great book I’d like to recommend to anyone who is interested in personal development. If you spend some time digesting the ideas, it might make a positive impact on your life.

Many of us vastly underestimate (or would like to believe) the importance of chance. Realize that many events in life are random and therefore patterns cannot be looked for. There are some events that cannot be influenced and are instead purely random.

You should carefully examine any statistics you come across, as they may have been manipulated to support an unwelcome cause. What do you think of the current circumstances? Can random errors occur? Is the correlation expressed correctly? When you learn to examine statistics closely, you are less likely to be fooled by distorted information.

Although successful people usually have a lot of talent, they also benefit from a healthy dose of luck. So stop thinking less of yourself just because other people are more successful than you. It may simply be that they have benefited from more favorable circumstances.

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