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Can you be good at Russian roulette?

Why probability is unintuitive to us and why it matters

Humans have always been obsessed with seeing the future. Centuries ago, the Mayans filled out there future calendars so far out that every high-powered startup CEO can only look in envy. More recently, hobbyists turned into serious traders during the covid pandemic, drawing every line imaginable to see if a stock is going to go up or down. The common thread across generations is humans trying to predict the future and failing miserably at it.

Mercury looks like its in retrograde which probably means stonks go up

While we try and fail, I think most people would have no qualms about admitting that they are bad at predicting the future. This admission itself makes shaky predictions about the future harmless to us — if we know not to trust our predictions, we tend not to overcommit to them. On the other hand, there seems to be no reason to doubt our understanding of past events. Past events seem quite simple and straightforward with very little room for debate. While we may reliably understand the outcome of past events, I think the causation is often murkier than we believe. And our irrational confidence in our understanding of the past leads us down some dangerous paths. To see why we don’t fully understand our past and why it matters, let’s take this winding road and chat about human evolution, statistics, psychological biases, an Israeli-American economist and… Russian Roulette?

History has Happened Already

Our view of the past is entirely outcome focused — what happened rather than what could have happened. It seems like a perfectly reasonable thing to focus on. Rather than busying ourselves with the seemingly academic pursuit of what could have happened, why not focus on what did happen and call it a day?

A useful way to think about it is to try and link our uncertainty about the future with the past. If we agree that the future is nearly impossible to reliably predict, why do we treat things after the fact as foregone conclusions? If it becomes clear after something happens why it would turn out that way, why couldn’t we isolate those important factors beforehand? The truth is that we know that the coin toss wasn’t always destined to be heads, the back-bencher you knew in school wasn’t always going to turn their lives around, and a complex geopolitical situation wasn’t certainly going to play out the way it did. Yet it always seems obvious in hindsight, and there is a name for this phenomenon coined by French philosopher Henri Bergson — retrospective determinism.

In retrospect, it is all too easy to count the factors that contributed to the way things played out and lull us into a false sense of inevitability. Of course the markets went up yesterday, the earnings reports were great! Right? Well what if the markets had gone down instead? The truth is we would’ve found a way to retrofit a narrative to that as well — the jobs report was down or the industrial index is slowing or inflation is rising. With the number of factors at play with most things, it is very easy to find some reason why things transpired in the way they did after the fact. But that doesn’t mean that things were predestined to happen a certain way — and this uncertainty is something we find difficult to digest.

The truth is that our minds are incredibly good at creating convincing stories around events after they happen. Stories are just much simpler to remember and make sense of compared to facts and numbers. No one recounts the statistical likelihood of them ending up together with their spouse during their wedding speech, they recount the great stories.

We made each other laugh more than 95% of people on their first date! That’s how I knew she was the one

Ape Brained Evolution

We have seen that a part of the reason why past events, however unlikely they were at the time, usually seem quite obvious to us is our love for narratives. That is not the entire story though.

Daniel Kahneman is a Nobel prize winner for revolutionizing the world of economics by introducing behavioral economics as a concept to the world and asking the groundbreaking question of what if economies are actually made up of real people?

In his seminal work, “Thinking Fast and Slow,” Kahneman explores our understanding of the world and our decision-making under various circumstances. While one would assume that people usually make logical decisions when dealing with issues requiring logic, Kahneman found that our brains don’t really work that way.

Our thinking processes can broadly be classified as system 1 or system 2 thinking. System 1 refers to our ape brains — centuries of survival instincts packed into one small fight or flight box in our heads. System 1 thinking is our default setting — instinctive, intuitive and effortless. As we go about our day we don’t have to consciously think of how to make coffee every morning, or how to button our shirts, or how to open up Instagram as soon as we enter the bathroom. These things come naturally. System 1 thinking is our “gut feeling,” the instinctive decisions that our brains make.

System 2 thinking, which is only engaged when we are thinking consciously about a certain problem, is a more recent feature of human brains. System 1 evolved over centuries of human existence where outcome-based feedback loops were key to the only measure of success - survival. If the guy next to you touched a red colored flower and died soon after, no one was going to go near any red colored flowers. Doesn’t matter if the flower was poisonous or if the poor man actually died of a heart attack, it simply was not worth the risk.

For most of human history, our chief concerns were finding food and staying warm. There was no time for our post-modernistic search for the "meaning of life."

With the increasing role of technology and with the world being connected in unprecedented ways, human life has changed exponentially more in the last 500 years than in the 5000 before it. So system 2 thinking developed quite recently as a result of a new, significantly more complicated world designed by humans. This complicated world has been incredibly good for people across the globe, but it has presented a new set of challenges as well.

Simply surviving is not equivalent to being successful any more. We need to be able to navigate ever changing professional landscapes, earn money, invest, afford pet-grooming salons and understand probability.

On the 8th day, god gave humans the need to learn statistics

So while the world around us has compounded in complexity, our brains have remained fundamentally similar to those of our ancestors. We still feel more than think, let emotions get in the way of decisions more than we’d like to admit and usually find statistics unintuitive and unpalatable.

We inhabit two different worlds in our minds and in reality. The world within our minds looks like a straight line from cause to effect — an investment you make turns out to be a winner because you saw the potential early, or you get fired from your job because you didn’t work hard enough. The real world is quite different from that — that winning stock pick may have been a result of unexpected policy changes favoring the sector, and you may have been fired from your multinational company because of some rumblings about a rumor of an expectation of interest rate changes in a country you don’t even live in. This is not to say that the ground reality is always detached from actions you control, but instead that in our highly networked world, there are always countless factors playing their part in invisible ways.

Russian Roulette World Championship

If you’re with me so far, it turns out that our decision-making is almost entirely outcome focused while the outcome itself is affected by many invisible factors. This means that the feedback loop that worked so well for human survival is not quite as effective as it used to be. Since this feedback loop’s effectiveness in our complex world is reducing, we sometimes end up with good decisions that look like bad decisions and vice versa.

To illustrate, imagine your friend walks up to you, unable to bottle their visible excitement, to inform you they are $1 million richer than when you last saw them. Turns out an unhinged stranger offered your friend a chance to play a round of Russian Roulette with a million dollar payday if they survive. So your friend has clearly survived and has won themselves a rather life-changing amount of money, but was it smart to play this game at all?

With an example as blatant as this, most people instantly understand that playing a game with a 1 in 6 chance of getting shot in the face is not a decision to write home about. So despite the fact that your friend ended up surviving and winning, it is easy for you to isolate the moment when the decision was made from the end result.

A mistake is not something to be determined after the fact, but in light of the information available until that point.

Nicholas Nassim Taleb, Fooled by Randomness

But real life is not as black and white as this example, and the trouble really starts if your friend starts thinking of themselves as being “good” at Russian roulette. The cold objectivity disappears, for instance, when you replace this game with stock trading. While most people will abstractly agree that beating complex adaptive systems such as the stock market consistently is nearly impossible, many will still hold an incompatible belief that they can do it based on certain past successes.

Russian Roulette World Championship

But what is the problem with a little bit of unearned confidence, you may ask. It seems innocuous, harming no one in particular. Well, if we continue on with the example of someone who wrongly thinks they are great at trading, the odds are that they will start risking an increasing percentage of their money under the mistaken belief that they understand the markets better than everyone else. That is the biggest problem and gets us back to our understanding of feedback loops. If we think we are good at something, we are likely to risk more and more behind it. If it then turns out that our initial assumption was false, then the blowup from our mistaken belief is likely to be huge when it happens.

Historical Probability

Probability is not a mere computation of odds on the dice or more complicated variants; it is the acceptance of the lack of certainty in our knowledge and the development of methods for dealing with our ignorance.

Nicholas Nassim Taleb, Fooled by Randomness

Thinking of events with a “Historical Probability” lens is important to counteract this fallacy. The outcome for an individual instance may be influenced by innumerable invisible factors, but we still tend to debrief a decision based on its outcome rather than the strength of the decision based on the information available at the time. Think about the moment where the decision was made, independent of what followed after, along with the probability and the expected value at that point to really understand the quality of a decision.

If you make high probability decisions consistently and over the long run, you will win. Even if you get unlucky a few times, over a long enough period, the scales should balance in your favor. Let’s say you play a game where you win if a fair dice shows any number from 1 through 5 and only lose if it shows 6. Even if your first roll shows a 6, the logical decision is to keep playing the game over and over because 5 time out of 6, you will be a winner.

Understanding expected value is even more important than probability in real life. Imagine we are playing the dice game again, but this time with dollar values attached to the outcomes. So you win $1 each time numbers 1 through 5 show up on the dice, but lose $10 every time you roll a 6. In this case the simple probability of getting a winning number is still 5/6, but the expected value of a dice roll is actually -$5/6. So if you win a dollar on the first roll, take it and run.

Expected value is more crucial to real life than probability because rewards and losses are not equal across actions. If we go back to the stock market example, making 10 winning trades that win you $10 each will likely leave you $100 richer but with priceless confidence about your ability to game the stock market. But this confidence will be the cause of your downfall if you bet and lose $1000 on your next trade. Making the right trade 10/11 times is pointless if you lose $900 in the process.

By the way, the problem of not understanding historical probability is bidirectional. As much as it is responsible for giving people a sense of unearned hubris in certain cases, it is also responsible for making people doubt their own abilities when they shouldn’t. While the cases of mistaken confidence tend to be more harmful, the other type of mistakes have the potential to hurt you as well. Think about decisions that are fundamentally sound that turn out poorly due to external factors, for example a person choosing to leave their job and learn a higher paying skill but failing to find a job due to a recession. It would be just harmful as the previous examples for this person to abandon their path and chalk it up as a mistake due to extraneous factors.

Paying the Rent with Lottery Tickets

I know I have spent many minutes rambling about the theoretical universe of probability expected outcomes, but the real world is results focused. You cannot pay your rent with a high probability bet slip and you cannot find solace simply in making probabilistically sound decisions. Additionally, thinking in system 2 all the time will be debilitating in its own way, and you cannot take an hour each morning to decide based on probability whether your mood will be improved more by getting a coffee or a tea.

I’ll get a coffee… Wait I’ll get some tea… Wait actually…

The point is to add this way of thinking as an additional lens to view the world, and use it when you face moments of high uncertainty. Adding this nuance to decision-making should help make more sound decisions over the long run… probably.

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