A Review of The Drunkard’s Walk: How to View the World More Accurately and Guarantee Success in Life

“For even a coin weighted toward failure will sometimes land on success.” — Leonard Mlodinow in The Drunkard’s Walk: How Randomness Rules Our Lives

In The Drunkard’s Walk: How Randomness Rules Our Lives, Leonard Mlodinow presents compelling evidence on how lacking we are when it comes to understanding real life probability and randomness. While probability may seem simple enough on the surface, the complex world that we live in is a web of randomness that could never be fully untangled.

If you want to gain a better understanding of the world around us, this book is required reading. While there are plenty of lessons to be learned, I came away with three major takeaways, which I explore in detail below. Additionally, I highlighted and took notes as I went through this book. At the end of this post, I’ve included my Quotes & Notes — Quotes being exact portions of the book that I highlighted, and Notes being the written bullet points that I took at the end of each chapter, summarizing my biggest takeaways from each chapter.

The Most Common (and Costly) Misconception

“…in no other branch of mathematics is it so easy for experts to blunder as in probability theory.” — Martin Gardner in Scientific American

There are lots of concepts in life that are often misunderstood — physics, health science, and psychology, to name a few. While these are vast topics that impact each of us everyday, there’s one subject matter that trumps all else in its impact on us all: randomness. Unfortunately, we are inherently bad at understanding randomness. Sure, we generally understand that a series of ten fair coin flips won’t always result in exactly five heads and five tails. Sometimes we’ll get six heads, and other times we might get three. As it turns out though, life is a bit more complex than series of simple coin flips. Doubly unfortunate is the fact that the impacts of misunderstanding the effects of randomness are wide-ranging, potentially catastrophic, and difficult to detect.

The human population incorrectly believed that the earth was flat for thousands of years. While discovery and progress likely would have occurred more rapidly if the earth’s roundness was discovered sooner, believing that the earth was flat didn’t impact everyday decision-making. If you misunderstood the roundness of the earth years ago, this had zero bearing on your ability to run a successful business or take care of your family. However, misunderstanding randomness and probability would have negatively effected your ability to do these things well. This is because randomness and probability are inherent in every single decision we make, whether we realize it or not.

For most of us who don’t major in a math-related field, our entire understanding of probability comes from a few measly chapters of math textbooks that we haven’t thought about since high school or college. Even the smartest among us — doctors, lawyers, Supreme Court justices, and those with a PhD in statistics — often have a fuzzy understanding at best.

Mlodinow deploys various examples in the book, but my personal favorite is has to do with the Monty Hall problem — a counter-intuitive probability problem based on the popular Let’s Make a Deal game show. In September of 1990, this question was posed in a popular newspaper column (verbiage slightly altered by Mlodinow):

“Suppose the contestants on a game show are given the choice of three doors: Behind one door is a car; behind the others, goats. After a contestant picks a door, the host, who knows what’s behind all the doors, opens one of the unchosen doors, which reveals a goat. He then says to the contestant, ‘Do you want to switch to the other unopened door?” Is it to the contestant’s advantage to make the switch?’”

The seemingly obvious answer is that you have a 50/50 chance either way. However, the columnist answered that it is actually better to switch, causing an uproar in responses to the column. According to the book, 92% of people disagreed with the columnist. One mathematics professor wrote a particularly scathing letter. My favorite part:

“As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and, in the future, being more careful.”

As it turns out, the columnist was right (and thousands of professional mathematicians who weighed in were wrong). The contestant does indeed increase their chance of picking the car simply by switching doors. (For a full explanation of the Monty Hall problem, check out this explainer video).

The fact that the most highly trained mathematicians among us were so confident, yet so wrong, serves as a red flag to us all. Plus, this was a neatly crafted game with defined rules. Every day life is much more complex than the Monty Hall problem. The Monty Hall problem example leads to two major conclusions:

1. Accurately assessing probability and randomness in everyday life is incredibly difficult (and impossible to do with 100% accuracy); and
2. Those who develop an above average understanding of this topic will have a leg up in all situations, since probability and randomness are inherent in every part of life.

Of course, the Monty Hall problem is just one example. Throughout the book, Mlodinow gives real world examples of how misunderstanding probability can lead to devastating consequences — from incorrect verdicts in the court system to choosing the wrong leaders for some of the world’s most important organizations. Here are two more of the most common errors we make in day-to-day life that majorly impact our rate of success:

1. Extrapolating from small sample sizes. A small sample doesn’t necessarily mean that the data is irrelevant, but it also doesn’t mean that the data should be extrapolated without further investigation.
2. Building false narratives. Mlodinow explains that by math and probability alone, we should expect 10% of Fortune 500 CEOs to perform either above or below average for five straight years. Yet, it is a near certainty that all CEOs who perform above average for five straight years will be praised as business savants, even though some of these CEOs achieved their success through sheer luck.
3. Conditional probability. Problems of conditional probability are the most difficult to understand and can result in massively inaccurate information when solved incorrectly. A powerful example from the book is as follows: assume that 1 out of every 10,000 men are actually infected with HIV, and the false positive rate is 1 in 1,000 (i.e. for every 1,000 tests, 1 incorrectly identifies someone as having HIV, even though they do not actually have HIV). Mlodinow explains that he actually tested positive for HIV at one point. His doctor somberly told him that the odds of a false positive were just 1 in 1,000. Yet, in reality, Mlodinow had over a 90% chance of not actually being infected. The probability that a completely random man actually has HIV is 1 in 10,000. However, the probability that a man who has tested positive for HIV actually has HIV is 1 in 11. How does this math out? If you test 10,000 random men, 10 will test positive but NOT actually have HIV (1 in 1,000 false positive rate). One will test positive and actually have HIV. This leaves us with 11 people who tested positive for HIV — 1 who actually has HIV, and 10 false positives.

Shoot Your Shot (Again and Again and Again)

“For in a complex undertaking, no matter how many times we fail, if we keep trying, there is often a good chance we will eventually succeed.” — Leonard Mlodinow in The Drunkard’s Walk: How Randomness Rules Our Lives

In today’s world, you can become an expert in just about anything. Whether it’s YouTube tutorials, a cheap (or free) online course, or another method, knowledge has never been so widely available. This accessible information is a blessing and a curse — a blessing because we can legitimately learn about anything we want to; a curse because there are so many different things vying for our limited attention span. This often leads us to start a new project, only to get distracted by the next shiny project and leave the old one in the dust.

While raw intelligence is an important factor in being successful, Mlodinow convincingly argues that there’s another factor that’s more vital (and in our control): number of attempts. In other words, there’s a distinct mathematical edge in life for those who keep tinkering, refuse to give up, and never stop shooting their shot. For example, let’s compare two hypothetical people’s odds of success: Smart Stevie and Persistent Pam.

Stevie is a smart guy— on average, any venture that he attempts has a 30% chance of success. Pam, on the other hand, is of average intelligence. Her ventures have only a 10% chance of success. Stevie took a highly-sought-after corporate job out of college and has little time for anything outside of work. Let’s say Stevie tries to start two different businesses over the course of his life. Even with his heightened intelligence, there’s a 49% chance that both of his ventures will fail. Pam has more free time on her hands, so she attempts to start ten different businesses over her lifetime. Even though Pam is much less likely to be successful on any single given venture when compared to Stevie, the fact that she took more chances is much more important. In this scenario, Pam has a 65% chance that at least one of her ventures will be successful. If Pam were to double her attempts to twenty, she would have an 88% chance of at least one successful venture. If she could get to fifty attempts over her entire life, she would have over a 99% chance of success.

Because randomness (i.e. luck) is a fact of life, there is no certainty of success in any endeavor. As a species, we hate randomness because it is completely out of our control. Lucky for us, there’s a profoundly important factor that we do control: the number of shots we take. We can’t control the baseline level of processing power we’re born with or the ultimate outcome of any single project. However, we can massively increase our odds of overall success by never ceasing to try new things. The math is clear— if we make enough attempts over a lifetime, our probability of finding success rounds up to 100%.

Don’t Judge a Pitcher by His Outcomes

“…we are all too easily fooled by the money someone earns.” — Leonard Mlodinow in The Drunkard’s Walk: How Randomness Rules Our Lives

For any mega-successful person, there was a point in time before they were known as a mega-successful person; before the general public knew about them. In 2003 (before the founding of Facebook), Mark Zuckerberg would have had similar odds of obtaining funding from outside investors as most other young entrepreneurs. Several years later, he could have found funding for any business idea under the sun. What changed? He was the same Mark Zuckerberg — intelligent, hardworking, and savvy. But, now he had a claim to fame — a real life, tangible success in Facebook.

What if control of Facebook had been wrested away from him in the early years by co-founder? What if government regulations would have come into effect that stunted Facebook’s initial growth? Or another competitor came into the market around the same time that cut their market share in half? In this scenario, Zuckerberg is still a high-performing individual who is capable of founding a successful company. However, he doesn’t have a tangible success yet, so he would have a much more difficult time obtaining funding for his next venture.

Mlodinow’s lesson is this: we overvalue results and undervalue process. We overweight someone’s track record and underweight their true ability. The world is a messy place, full of people who over or under-perform their actual abilities in the short-term. If we could observe a person’s track record over their entire life, we could feel pretty comfortable about judging a person solely by their track record. Unfortunately, we don’t get this luxury.

Let’s say there are 1,000 entrepreneurs seeking funding from a wealthy investor, who can afford to fund 500 of them. Each of these entrepreneurs have started exactly one business. 500 of them have failed, and 500 of them have succeeded (i.e. still exist and are growing). The wealthy investor would be making a grave mistake by choosing to simply invest in the 500 entrepreneurs who have found success so far. By doing so, the investor would almost certainly be passing on some incredibly lucrative opportunities (and investing in some bad ideas). This is not to say that the investor should completely ignore past successes or failures. However, they should be taken with a grain of salt, especially with such a small sample size.

Life happens. Mistakes are made. Unpredictable events occur. Over a large enough sample size, the outcomes of people’s decisions will equal their true abilities. But, we almost never get such a sample size, which means we must put in the work to identify people’s skills, qualities, and character over their previous track record.

Baseball is a perfect example of this phenomenon. A pitcher’s past success can be measured by their Earned Run Average (ERA) — the amount of runs that they allow per 9 innings pitched. In the long run, a pitcher’s ERA will match their true ability. In the short-term, however, an ERA can be quite misleading. Thanks to the sabermetric revolution, we now have statistics such as Expected Fielding Independent Pitching (xFIP) designed to measure ability instead of outcome. xFIP is designed to measure what a pitcher’s ERA should have been, based on other indicators of success (walk rate, strikeout rate, etc.). If, over his last five games, a pitcher has an ERA of 2.50 (good), but an xFIP of 5.50 (bad), he has almost certainly been getting lucky. Fifteen years ago (before xFIP was known) we would have seen the 2.50 ERA and assumed that the pitcher had found his groove. Today, we know that a short-term xFIP is much more predictive than a short-term ERA. Thus, we can be almost certain that this pitcher isn’t pitching exceptionally well — he’s just been very lucky over his last five games.

Of course, judging a pitcher by his recent outcomes, or an entrepreneur by his last business venture, is human nature. It’s a shortcut that, on average, will lead us in the right direction. However, if the goal is to make the best decisions possible, we must do the hard work of evaluating talent, hard work, and character just as much as we factor in past success or failure.

Because of the marketplace’s natural inclination to overvalue success and undervalue failure, we can be sure that arbitrage exists when viewing the world through this lens. On the one hand, there are plenty of “posers” whose success outweighs their actual talents. These people and organizations demand a price that is well in excess of their actual contributions. If we recognize these situations, we can save ourselves lots of wasted time and money by letting someone else overpay. On the other hand, diamonds in the rough — those whose actual talent exceeds their track record thus far — are out there waiting to be found. These are the pre-Facebook Mark Zuckerberg’s of the world. They are incredibly talented, yet undervalued by the marketplace because they haven’t broken through …yet. Identifying these types of people and organizations isn’t easy. We might have to put our reputation on the line to hire someone with a less-than-ideal track record. But, the rewards for identifying such mispriced talent will lead to massive success in the long-haul.

We can (and should) expand this concept to beyond the borders of investing and business. When we see someone down on their luck, it’s important to remember this potential for a mismatch in talent vs. outcome. There are people in “dead-end” jobs that, with a different series of fortunes, would be in a much better position. Likewise, there are successful people that, in a different set of circumstances outside of their control, would be much closer to a “dead-end” job. This isn’t to say that people have no influence over their outcomes. Rather, it’s an important reminder that the world is filled with infinite shades of gray instead of simple black and white outcomes.

Notes & Quotes

Below are my highlighted quotes from the book, along with my annotations I took as I read through it. The bolded quotes or notes are passages or thoughts that I found especially interesting upon reflection.

Prologue

“the human mind is built to identify for each event a definite cause and can therefore have a hard time accepting the influence of unrelated or random factors.”

Chapter 1: Peering through the Eyepiece of Randomness

“The outline of our lives, like the candle’s flame, is continuously coaxed in new directions by a variety of random events that, along with our responses to them, determine our fate.”

“Making wise assessments and choices in the face of uncertainty is a rare skill. But like any skill, it can be improved with experience.”

“There exists a vast gulf of randomness and uncertainty between the creation of a great novel — or a piece of jewelry or chocolate-chip cookie — and the presence of huge stacks of that novel — or jewelry or bags of cookies — at the front of thousands of retail outlets. That’s why successful people in every field are almost universally members of a certain set — the set of people who don’t give up.”

Notes:

• Pg. 8: regression to the mean discussion
• To be successful in most fields, one must wade through an ocean of randomness and uncertainty, which most people hate. This is why the common trait in successful people is that they don’t give up.
• Roger Maris may have just been a better player in 1961; or, he benefited from randomness in beating Ruth’s record.

Chapter 2: The Laws of Truths and Half-Truths

“What it takes to understand randomness and overcome our misconceptions is both experience and a lot of careful thinking.”

Notes:

• Availability bias: when recalling something, we overweight the importance of vivid memories (they are more easily “available”)
• Even smart people are generally bad with probability and randomness. See court case pg. 39.

Chapter 3: Finding Your Way through a Space of Possibilities

“The great American physicist Richard Feynman once told me never to think I understood a work in physics if all I had done was read someone else’s derivation. The only way to really understand a theory, he said, is to derive it yourself (or perhaps end up disproving it!)”

“…in no other branch of mathematics is it so easy for experts to blunder as in probability theory.” — Martin Gardner in Scientific American

Notes:

• When the solution to the Monty Hall problem went mainstream, there was public outcry — not just from average people, but from mathematicians and PhD’s harshly criticizing the solution and its author (pg. 44)
• Probability theory is one of the most common (if not the most common) fields where experts are fooled.
• Gerolamo Cardano — interesting character, one of the first to properly understand probability theory and “sample space”

Chapter 4: Tracking the Pathways to Success

“It is dangerous to judge ability by short-term results.”

Notes:

• Even in a 7 game series, there is a decent chance of the inferior team winning.
• We rarely get a statistically significant sample size before judging short-term results. This is dangerous and leads to constant noise-chasing.
• Just because you have a small sample doesn’t mean the results are random/meaningless, but you shouldn’t assume they are meaningful either.
• Pascal’s Triangle: the number of ways you can choose some number of objects from a collection with equal or greater number.

Chapter 5: The Dueling Laws of Large and Small Numbers

“It is more reliable to judge people by analyzing their abilities than by glancing at the scoreboard.”

Notes:

• Far too often, we assume a sampling of results is representative of the population/situation/person, when in reality the sample is far too small.
• Excellent example with Fortune 500 CEOs on pg. 100:
• By chance alone, we can expect 10% of these CEOs to have 5 straight winning or losing years. Yet, there will almost certainly be a narrative built around these successes/failures.
• The key when dealing with small samples such as these is to judge the people, abilities, and/or situations rather than the results (Process > Results in short-term).

Chapter 6: False Positives and Positive Fallacies

“Most of our life experiences are like that: we observe a relatively small sample of outcomes, from which we infer information and make judgments about the qualities that produces those outcomes.”

“The relevant number is not the probability that a man who batters his wife will go on to kill her (1 in 2,500) but rather the probability that a battered wife who was murdered was murdered by her abuser.”

Notes:

• This chapter is on conditional probability, which can seem nuanced, but the differences in probability can be drastic.
• Bayes’ Theorem/conditional probability is useful in real life situations — we observe a small sample and make inferences/judgements — but how should we make these inferences?
• A misunderstanding of conditional probabilities is far too common in medical testing and courtrooms (pg. 116 and pg. 120 examples)

Chapter 7: Measurement and the Law of Errors

“Although measurement always carries uncertainty, the uncertainty in measurement is rarely discussed when measurements are quoted.”

“When we observe a success or a failure, we are observing one data point, a sample from under the bell curve that represents the potentialities that previously existed. We cannot know whether our single observation represents the mean or an outlier, an event to bet on or a rare happening that is not likely to be reproduced. But at a minimum we ought to be aware that a sample point is just a sample point, and rather than accepting it simply as reality, we ought to see it in the context of the standard deviation or the spread of possibilities that produced it.”

Notes:

• We often view measurements as absolutely correct without understanding them in the context of uncertainty/randomness.
• While margin of error is cited in polls, we make judgments and decisions on minuscule sample sizes in daily life without considering the margin of error.
• When observing a success or failure, we must realize it is just one data point which could be the mean OR an outlier. Rather than judging based on a single outcome, the standard deviation or RANGE of outcomes will lead to much better judgments and decisions.

Chapter 8: The Order in Chaos

“…the ability to persist in the face of obstacles is at least as important a factor in success as talent.”

“…while our genetic makeup is out of our control, our degree of effort is up to us. And the effects of chance, too, can be controlled to the extent that by committing ourselves to repeated attempts, we can increase our odds of success.”

“…much of the order we perceive in nature belies an invisible underlying disorder and hence can be understood only through the rules of randomness.”

“…though in random variation there are orderly patterns, patterns are not always meaningful. And as important as it is to recognize the meaning when it is there, it is equally important not to extract meaning when it is not there.”

Notes:

• Things are often random (or seemingly so) at the micro level, yet quite orderly and predictable at the macro level.
• Not everything is normally distributed. Many fields follow the 80/20 rule, etc.
• While success is often random, we can control our effort and determination, which will give us more and more attempts and increases our odds of success.

Chapter 9: Illusions of Patterns and Patterns of Illusion

“…even with data significant at, say, the 3 percent level, if you test 100 nonpsychic people for psychic abilities — or 100 ineffective drugs for their effectiveness — you ought to expect a few people to show up as a psychic or a few ineffective drugs to show up as effective.”

“According to the mathematics of randomness, such runs are to be expected in 200 random tosses. Yet they surprise most people.”

“…if you look long enough, you’re bound to find someone who, through sheer luck, really has made startlingly successful predictions.”

“…if you had singled out Bill Miller in particular at the start of 1991 in particular and calculated the odds that by pure chance the specific person you selected would beat the market for precisely the next fifteen years, then those odds would indeed have been astronomically low.”

“So the relevant question is, if thousands of people are tossing coins once a year and have been doing so for decades, what are the chances that one of them, for some period of fifteen years or longer, will toss all heads?”

“I calculated the odds that by chance some manager in the last four decades would beat the market each year for some period of fifteen years or longer. That latitude increased the odds again, to the probability I quoted earlier, almost 3 out of 4.”

“…it is important in our own lives to take the long view and understand that streaks and other patterns that don’t appear random can indeed happen by pure chance. It is also important, when assessing others, to recognize that among a large group of people it would be very odd if one of them didn’t experience a long streak of successes or failures.”

“There is therefore a fundamental clash between our need to feel we are in control and our ability to recognize randomness.”

“While people may pay lip service to the concept of chance, they behave as though chance events are subject to control.” — Ellen Langer

“…very few find the answer the fast way — through the attempt to falsify their idea…”

“Finally, we should learn to spend as much time looking for evidence that we are wrong as we spend searching for reasons we are correct.”

Notes:

• When looking at a large enough population, we should expect to see extraordinary successes and failures through pure randomness. “Yet they surprise most people.” (pg. 176 quote)
• Stock picking success of one man was only a “success” because of the arbitrary calendar year timeline. There were plenty of 365 day periods where he was not successful (pg. 179–181).
• Our need to feel in control inhibits our ability to cope with randomness.
• We should seek out contradictory evidence rather than confirmatory evidence.

Chapter 10: The Drunkard’s Walk

“When we look back in detail on the major events of our lives, it is not uncommon to be able to identify such seemingly inconsequential random events that led to big changes.”

“It is easy, looking at the past, to construct such nice graphs and neat explanations, but this logical picture of events is just an illusion of hindsight with little relevance for predicting future events.”

“We can learn to view both explanations and prophecies with skepticism. We can focus on the ability to react to events rather than relying on the ability to predict them, on qualities like flexibility, confidence, courage, and perseverance. And we can place more importance on our direct impressions of people than on their well-trumpeted past accomplishments.”

“…in complex systems (among which I count our lives) we should expect that minor factors we can usually ignore will by chance sometimes cause major incidents.”

“For in a complex undertaking, no matter how many times we fail, if we keep trying, there is often a good chance we will eventually succeed.”

“A path punctuated by random impacts and unintended consequences is the path of many successful people, not only in their careers but also in their loves, hobbies, and friendships.”

“…we are all too easily fooled by the money someone earns.”

“…when they knew how much they each were getting paid, the higher-paid subjects exhibited more resistance to input from their partners than the lower-paid ones.”

“We unfortunately seem to be unconsciously biased against those in society who come out on the bottom.”

“many of life’s failures are people who did not realize how close they were to success when they gave up.” — Thomas Edison

“What I’ve learned, above all, is to keep marching forward because the best news is that since chance does play a role, one important factor in success is under our control: the number of at-bats, the number of chances taken, the number of opportunities seized. For even a coin weighted toward failure will sometimes land on success. Or as the IBM pioneer Thomas Watson said, ‘If you want to succeed, double your failure rate.’”

“We can seek to understand people’s qualities or the qualities of a situation quite apart from the results they attain, and we can learn to judge decisions by the spectrum of potential outcomes they might have produced rather than by the particular result that actually occurred.”

Notes:

• Fund manager graphs: pg. 198 & 200
• The clarity of events when viewed in hindsight is an illusion. If we start before and try to trace forward, there is no clarity.
• We should work on separating process from outcome in all aspects of life — this includes adaptability, perseverance, and judging people by their qualities rather than successes/failures.
• Bill Gates: example of impacts of random events on pg. 208
• We are easily fooled by how much (or little) money someone earns, including ourselves/our own sense of importance (pg. 211)
• Because randomness does play a role, one factor is always under our control: our number of attempts. Keep shooting your shot.
• Judge decisions by their quality at the time of decision and the range of possible outcomes, rather than judging solely based on results.