The Drunkard’s Walk

The Drunkard's Walk After a taking a Random Walk Down Wall Street, I picked up a copy of The Drunkard’s Walk by Leonard Mlodinow from the local library. This isn’t an investment book per se, but as its subtitle, “How randomness rules our lives” suggests, it offers some insight into the confusing and often misunderstood world of randomness and chaos that surrounds us in both financial and everyday life.

The basic premise to the book is that we love to analyze and feel in control of situations, even when there’s little data to be certain. When a politician isn’t re-elected, when a movie flops or when a stock drops in price; people believe they know why and explain exactly why they’re correct. However, in many cases all of that “knowledge” is useless in predicting if a film will do well, if an election will be won or if a stock will drop in value in the future.

First though and just for fun, here are some questions for you to answer based on content in the book. Make a note of your answers and see how you did at the end of the post, or try the interactive version.

Question 1

What is greater:

A. The number of six-letter English words having “n” as their 5th letter?
B. The number of six-letter English words ending in “ing“?

Question 2

A perfect coin is flipped 20 times in a row and it resulted in the following sequence.
Is the next flip of the coin, more likely to be heads or tails?

A. Heads, we’re on a roll here!
B. Tails, it’s “time” for Tails to show up.
C. Equally Heads or Tails.

Question 3

You’re in a game show and have been given the choice of three doors – behind one door is a car, behind the other two doors there is nothing. You’re asked to pick a door and you’ll win whatever is behind it. Now, after you’ve picked a door, the game show host, who knows what is behind all three doors, opens one of the two unchosen doors to reveal nothing. He then asks you, “do you want to switch to the other unopened door?”

A. Stay with your original choice because you have more chance of winning.
B. Switch doors since you have more chance of winning.
C. The chances are 50:50 so it doesn’t matter if you switch or not.

Question 4

In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?

A. 1 in 2
B. 1 in 3
C. 1 in 4

Question 5

In a family with two children, what are the chances, if one of the children is a girl named Florida, that both children are girls?

A. 1 in 2
B. 1 in 3
C. 1 in 4

But what about the book already?

So in The Drunkard’s Walk, physicist Leonard Mlodinow takes us on a journey starting with the ancient Greeks and ending up in the 21st century. He uses many examples from history, sports, medicine, finance and business to illustrate points and show how we gradually evolved our understanding of calculating probability; from the Greeks who didn’t get it at all to the Insurance companies of today who have got it all figured out.

I am a self-confessed numbers geek so I’m biased towards the book. But the writing is very accessible, there isn’t any detailed mathematics (although the book contains many references to look up the details if interested), and the examples are explained well in a conversational and entertaining style.

He discusses some business cases such as Sherry Lansing’s tenure at Paramount Motion Picture Group and how companies may just have bad luck for a short time, and how much ‘control’ CEOs really have on their company.

If you’re interested in baseball, you might be interested in just how likely it was for ‘average’ Roger Maris to beat Babe Ruth’s 1927 record of 60 home runs in one year. The author calculates that in a 70-year period, a random spike of 60 home runs is to be expected for players who typically achieve only 40 home runs in a year. The question of “good” vs. “lucky” is asked several times throughout the book.

Historical breakthroughs

The book progresses through history. Several key breakthroughs discussed in the book were

1576 – Gerolamo Cardano who developed the idea of a sample space and being able to answer the ‘monty haul’ game show question above.

1583 – Galileo Galilei who worked out why when you throw three dice that the number 10 appears more frequently than the number 9, among many other major scientific discoveries.

1654 – Blaise Pascal. Famous for his triangle which he used to solve the ‘problem of points’. For example, what are the odds of the Atlanta Braves beating the New York Yankees after they’ve won first 2 games of the baseball World Series.

1713 – Jacob Bernoulli who discovered his “Golden theorem” which started the science of statistical sampling and was the basis of the “law of large numbers“, that you can’t accurately predict results if you don’t have sufficient data.

1761 – Thomas Bayes. He created “Baye’s theorem” which addressed conditional probability. The different probability of two things happening is the basis of many wrong judgments in everyday life – for example it’s very likely that if your customer is not interested in your products that they won’t respond to your queries. But the probability that your customer is not responding to your queries because they’re not interested is much lower – they might be busy, on vacation or for many other reasons. These two outcomes are often mixed up.

1733 – Abraham De Moivre who discovered the bell curve made famous by Carl Freidrich Gauss and which forms the basis of modern statistics.

The birthday problem

Consider the recent news about the family in the UK who won the lottery twice. Apparently the odds of that happening are “293 billion to 1”. But yet in Germany in 1995, the same six winning numbers 15-25-27-30-42-48 came up in both June 21, 1995 and in December 20, 1986 in the 6 from 49 numbers German Lotto after 3,016 drawings. Coincidentally this is mentioned in the book and the odds are not as remote as you might think, with the chance of a repeat over that time being about 28 percent. This is a form of the “birthday problem” where it takes only 23 people in a room for there to be a 50% chance of two people to share a birthday, and a 99.9% chance if 70 people are in the room.

We like to overthink things

In simple experiments where a person is shown a series of cards which can have two colors e.g. red and green and after watching a sequence such as red-red-green-red-green-green-red-red, the person is asked to predict each next color. People typically try to determine the pattern behind the sequence as in “oh a green shows after two reds so the next color would be green”, whereas animals base their decision on simple frequency – “there were 5 reds and 3 greens, so the next color will be red”.

This example can be easily related to investing – do you seek our “average” returns with an index-based approach or do you aim to “beat the market”? There’s more reward in aiming to beat the market if you succeed, but also more chances of not beating the market.

Looking smart by chance

Let’s say you met someone who had correctly predicted if the stock market would increase or decrease each year over the last 7 years. That certainly lends weight to whatever he might say about the stock market’s price next year – I mean an accurate prediction 7 years in a row, that must take a lot of skill right?

Of course it’d take exactly 7 years to find such a person, but it’s easily done. Simply start with 64 people and divide them into two groups – the “yes” group who think the stock market will go up next year and the “no” group who think the market will go down. The following year, half of the people were wrong and are removed from the search. The remaining 32 people are split into the two equal “yes” and “no” groups of 16 each and the process repeats. In the second year, half the people are wrong leaving 16 who were correct two years in a row and so on. Now if the search continues, in 7 years there will be one person left who correctly called out the rise / fall of the stock market for each of the last 7 years. Have we just discovered a new financial genius or was someone just lucky?

You can apply this example to many cases and it’s important to keep in mind when reading about the “mutual fund that has consistently beaten the market”, “the investing strategy that will guarantee you higher returns” and so on.

Even Warren Buffet, arguably one of the world’s most famous investors, can not accurately predict the value of the S&P Index in (say) June next year. No-one can, although many people will confidently say exactly that. And given enough people, someone actually will predict the correct value. You’re more likely to be successful in investing however, if your strategy doesn’t rely on you needing to know the future market prices, for example with buy and hold investing as opposed to day-trading.

Illusions and patterns

The last two chapters in the book are of most practical use and touch on how we interpret events with some behavioral psychology thrown in. People need to be in control when presented with randomness, and will convince themselves that they are in control even if they need to change their perception of what they’re seeing. Not only that, once we’ve formed an opinion then confirmation bias will push us to prove that opinion to be correct rather than prove it to be wrong.

This was understood long ago – Francis Bacon wrote in 1620 that “the human understanding, once it has adopted an opinion, collects any instances that confirm it, and through the contrary instances may be more numerous and more weighty, it either does not notice them or else rejects them, in order that this opinion will remain unshaken.” Or in a more succinct form, “people are just plain stubborn.”


I enjoyed reading The Drunkard’s Walk. My main take-away from reading it is that perseverance is critical for success, as many random factors affect a successful outcome, and sometimes just hanging in there is all that’s needed. Consider the man who tried to make it as an actor for 7 years unsuccessfully in NY until he flew out to LA (to watch the Olympics or visit his girlfriend depending who you believe) and landed the role of David Addison after auditioning for a new television series named Moonlighting. Was it skill alone that shot Bruce Willis to fame or was it more about being in the right place at the right time?

If you’re interested in this subject, here’s a video of Leonard discussing his book at Google where he covers the best money market manager, expected CEO performance and the Baseball World Series. Check out the part around 29:30 where he manipulates the audience into underestimating the number of countries in Africa using Anchoring bias.


Q1: A, Q2: C, Q3: B, Q4: B, Q5: A

Question 1 – If you answered B, congratulations – you’re in the majority. But you’re also wrong, since the first answer – six letter words with ‘n’ as their fifth letter includes all of the six-letter words ending in ‘ing’. But it’s easier to guess at how many words we know that end in ‘ing’ than estimate the number of words we know with ‘n’ as the 5th letter, so the answer B is more common.

Question 2 – the answer is C: the results of the previous coin flips have no impact on the next one, so the next flip is just as likely heads than tails. We don’t like winning streaks like that since they don’t seem ‘random’, but it is a perfectly random result.

Question 3 – the answer is B: you’ve more chance of winning if you switch doors than if you stick with your current door. When you first picked the door, your odds of winning were 1 in 3 – so there is a 2 in 3 chance that the car is behind one of the other two doors. When the host opened the door to reveal an empty space, your original odds didn’t change; so you still have a 1 in 3 chance if you stick with your original door and a 2 in 3 chance of winning if you switch doors.

Question 4 – With two children, one of which is a girl there are three possible combinations: (girl, boy), (boy, girl) and (girl, girl). So for both to be girls it’s 1 in 3.

Question 5 – the answer is A: 1 in 2. This is a little trickier. There are technically 5 outcomes: (boy, girl-F), (girl-F, boy), (girl-NF, girl-F), (girl-F, girl-NF) and (girl-F, girl-F). But since Florida is an extremely uncommon name, it’s very unlikely that both girls would be named Florida, this leaves 4 equally likely cases and only two of them satisfy the answer, so it’s 2 out of 4 which is 1 in 2.

What are you reading?”

Quote of the day

Just remember, you can do anything you set your mind to, but it takes action, perseverance, and facing your fears.