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The Drunkard’s Walk by Leonard Mlodinow

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Leonard Mlodinow. A name that most people would find it hard to pronounce and unfamiliar. What if he co-wrote books with Stephen Hawking? Hopefully, this would encourage you to give him some credentials and read on about his book, The Drunkard’s Walk.

In short, his main message in the book is that humans have a false impression that we have control over things when they are actually random events. We take too much credits for success and blame too much for failures. He viewed himself as a product of randomness, where his father escaped the Holocaust and met his mother, who was also a refugee, in New York.

Humans are biased

We all suffer from availability bias:

“we give unwarranted importance to memories that are most vivid and hence most available for retrieval.”

For example,

“Which is greater: the number of six-letter English words having n as their fifth letter or the number of six-letter English words ending in ing? Most people choose the group of words ending in ing. Why? Because words ending in ing are easier to think of than generic six-letter words having n as their fifth letter… the group of six-letter words having n as their fifth letter words includes all six-letter words ending in ing.”

Also, we use heuristics in our daily lives. Although heuristics are helpful in shortening our decision making, it creates biases. I have written another post about heuristics and you can refer to that if you are not sure what it means.

In short, we observe what we want to observe.

Humans are bad with probabilities

The Monty Hall is a famous probability problem. It was based on a television game show Let’s Make a Deal, hosted by Monty Hall. Marilyn vos Savant, the person with the highest IQ of 228, wrote in a column:

“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 the contestant’s advantage to make the switch?”

Marilyn proposed to switch due to the higher probability of getting the car. But 92% of Americans agreed she was wrong, and many were math professors. By switching, your probability of win is 2/3. See here for explanation.

Another test would be the “two-daughter problem”.

“Suppose a mother is carrying fraternal twins and wants to know the odds of having two girls, a boy and a girl, and so on… What are the chances, given that one of the children is a girl, that both children will be girls?”

If you answered 50%, you are wrong.

“…we eliminate the possible outcome (boy, boy) from the sample space. That leaves only 3 outcomes in the sample space: (girl, boy), (boy, girl), and (girl, girl)… so the chances that both children are girls is 1 in 3, or 33 percent.”

Hence, the key principle is “The chances of an event depend on the number of ways in which it can occur.”

Somehow, many things are not random because of imperfections

A statistician from Hebrew University, Moshe, believed truly random numbers do not exist. Even a die is biased because of the different faces. Likewise, a century ago, Joseph Jagger wondered if the roulette wheel perfectly balanced. He hired assistants to record the frequency of the numbers and found one of the wheels favoured nine numbers. He betted heavily and won big money. Jagger noticed a tiny scratch on the wheel but the casino swapped it during closing. In subsequent nights, the casino also adjusted the frets to fail him. Jagger lost money and quit eventually.

Things that are rigged are not random and unless you can find out your edge, you should not get involved in it. This applies to stocks that are manipulated or betting games that are fixed. In a way, you can tell if something is rigged by doing randomness checks…

Testing for fraud

Benford’s law:

“According to Benford’s law, rather than all nine digits’ appearing with equal frequency, the number 1 should appear as the first digit in data about 30 percent of the time; the digit 2, about 18 percent of the time; and so on, down to the digit 9, which should appear as the first digit about 5 percent of the time… Many types of data obey Benford’s law, in particular, financial data. In fact, the law seems tailor-made for mining large amounts of financial data in search of fraud.”

Regression to the mean

In a series of random events, the phenomenon of regression to the mean dominates. In the context of fund managers’ performance, some will perform better than the market index and some will perform worse. Over a period of years, those who performed worse will have a better chance to outperform the index in the future. Of course, the assumption is that the market is random and this is still a hotly debatable topic.

I like the quote from Immanuel Kant,

“Each, according to his own inclination follows his own purpose, often in opposition to others; yet each individual and people, as if following some guiding thread, go toward a natural but to each of them unknown goal; all work toward furthering it, even if they would set little store by it if they did know it.”

I found the description is very apt for the stock market. We buy and sell shares with different purposes and for different prices. Somehow, the collective effort pushes the market towards efficiency, or determine the so-called market price.

Humans yearn control

Humans do not like uncertainty and we love to be in control. When events are random, we are not in control and this often make us uncomfortable and even reject the events are random in the first place.

“That clash is one of the principal reasons we misinterpret random events. In fact, inducing people to mistake luck for skill, or pointless actions for control, is one of the easiest enterprises a research psychologist can engage in.”

If you want success, do not give up

He went on to explain success is uncertain and no one can predict accurately if a piece of work will get recognised by the masses. For example, J. K. Rowling’s Harry Potter manuscript was rejected by 9 publishers. But she went on to approach more publishers and eventually became one of the bestselling authors. However, John Kennedy Toole committed suicide after being rejected numerous times. His mother persevered and got A Confederacy of Dunces published 11 years later. The work went on to win the Pulitzer Prize for Fiction and has sold almost 2 million copies.

“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.”

“But I find it encouraging because, 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.”

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