Probabilistic Thinking: Better Decisions and Lower Risk

Probabilistic Thinking is trying to estimate the likelihood of any specific outcome, using logic and a bit of math. This helps us improve the accuracy of our decisions and focus on the most likely outcomes. You’ll be less influenced by the words of others, recent developments skewing your opinion (recency bias) and less likely to make poor emotional decisions.

Probabilistic thinking is especially useful for any money-related decisions, but can also be applied to other areas of life.

Two factors are important:

• The probability of a certain outcome
• The magnitude of a certain outcome

This allows us to calculate the expected value (EV): multiply the magnitude of each outcome by its probability and add the products.

A simple example: in a game of heads-or-tails, we pay $5 if we lose and gain $5 if we win.

Since the only possibilities are heads-or-tails and we ‘know’ that they are equally likely (each is 50% likely to happen), the expected value becomes:

($5 x 50%) + (-$5 x 50%) = $0

So, essentially, there is no benefit to us playing this game.

But if we gain $10 if we win and only have to pay $5 if we lose, the expected value becomes positive and we’ll likely benefit from playing this game:

($10 x 50%) + (-$5 x 50%) = $2.50

In the above example, the odds for winning or losing are the same, but the positive outcomes gives us double the reward compared to our loss (a 2-to-1 benefit-to-loss ratio). This way you can make rational decisions based on whether the expected value is positive or negative. 

But what if we increase the rewards and the loss in our heads-or-tails game? If we win, we get $1000 but if we lose, we pay $500.

The expected value is still positive – ($1000 x 50%) + (-$500 x 50%) = $250 – and greater than before, but are you willing to risk $500 on a 50/50 bet? That’s why the magnitude of the outcome makes a difference.

More importantly, however, is the likelihood of the outcome and why it’s so powerful to add this mental model to your everyday life.

What if our heads-or-tails game is rigged and there is a 90% probability of winning $1000 and only a 10% probability of losing $500? All of a sudden our expected value has increased to ($1000 x 90%) + (-$500 x 10%) = $850. But, more importantly, we are 9 times more likely to win than to lose. Not only is the expected value positive, but also we have a high likelihood to be successful.

This brings up an important point: extreme outcomes, commonly known as Black Swan events.

What if we further increase our odds to 99% probability of winning and a 1% probability of losing? What we gain stays the same, but what we can possibly lose increases drastically to $90,000. In that case the expected value becomes:

($1000 x 99%) + (-$90,000 x 1%) = $90

The expected value is still the same, but in the small (1%) chance that we do lose, we have to pay $90,000…which to most of us is our entire fortune…or an amount of money we don’t have (yet).

Therefore, while the odds of success are stacked in our favour, unless we have absolutely no other choice in life, nobody would take this bet. The downside risk is simply too great. Most people call accepting this kind of a bet a gamble. And yet we do it all the time in our lives.

Think about it: how often do you consider the potential damage of driving, getting on an airplane, running a red light, jaywalking or driving under influence (DUI)? In some cases, our vehicle gets damaged or we receive an injury, in worse cases we become paralyzed, and in the worst case we die (or someone else does).

The idea here is that by using some logic and a little bit of math, we can make more conscious and well thought out decisions – in life, in business, with our careers and with our investments.

The more decisions you can make where 

1. The odds are in your favour – i.e. the expected value is positive. 
2. You avoid (or limit) decisions with great potential loss – i.e. “betting the house”.
3. You are aware of and do everything you can to reduce or exclude the possibility of extreme (negative) outcomes – i.e. black swan events.

…the easier, and likely happier and more successful, your life becomes.

That leaves us with one last thing: how do we know the probability of a certain outcome?

The unfortunate answer is: for most decisions we cannot know the probability, we can only estimate it.

Michael Mauboussin in his book More Than You Know gave us three ways to estimate the probability of an outcome:

• Frequencies – the probability is based on a large number of observations in an appropriate reference class. Example: we can quite accurately estimate how many, how often and where earthquakes occur in Japan because we have 100+ years of earthquake-related data. The more observations we have, the more we can trust that a certain probability is accurate.
• Propensities – This reflects the properties of the object or system. Example: a die has 6 sides so the probability of a rolling a particular side is 1-in-6 (unless the die is rigged). This does not always consider all factors that shape an outcome: sometimes human error can greatly influence the probability.
• Degrees of belief – These are subjective probabilities: how likely do you think it is? Use this in the case the other two are unavailable. While it’s not bulletproof, it does help reduce uncertainty by forcing you to think. Often you’ll realize you don’t know enough about a subject to come up with a probability you’re confident in. In that case, either avoid making a decision or learn more about the subject. Inaction is always a choice. 

Often you can reduce your risk and increase the odds in your favour by becoming more knowledgeable in a subject. Preferably, you only make decisions that are within your circle of competence.

When using subjective probabilities, keep in mind that we humans are programmed to be overly optimistic (overconfidence bias) about the probabilities we come up with. It’s always better to be more conservative with our subjective probabilities. Also pay attention to the notion of randomness: we tend to see patterns where there might not be any. 

Successfully applying probabilistic thinking means roughly identifying which outcomes matter, estimating the odds, checking our assumptions, and then making a decision. This way we can act with more certainty in complex, unpredictable situations by evaluating what the world will most likely look like. But remember: we can never know the future with exact precision. 

With probabilistic thinking you can stop gambling and instead make rational decisions with favourable outcomes. You’ll no longer depend on luck, but have luck work in your favour.

How to use Probabilistic Thinking

In investing, most successful investors use probabilistic thinking as follows:

• Estimate the intrinsic value of an investment for 3 scenarios: optimistic, neutral and pessimistic.
  • Most investors determine intrinsic value by using a discounted cash flow (DCF) analysis.
• Assign a probability to each scenario. A good starting point is 20% each for the optimistic and pessimistic scenarios and 60% for the neutral scenario.
• Calculate the expected value for the investment in each scenario.
• Add the 3 expected values together to have the overall expected (intrinsic) value of the investment.
• If the overall value is below the price you can buy the investment for, it’s a bargain and a likely positive investment. If the overall value is above the price, it’s a premium and a likely negative investment.

In marketing or business, you can estimate the return-on-investment (ROI) for advertising campaigns on different platforms and compare to decide which one provides the best return.

For example, if you have a $100 budget and you can spend it on (a) Facebook advertising, (b) TikTok advertising or (c) Google advertising, you can compare them as follows:

1. $100 spent on Facebook will give us between 25 and 100 new leads.
   Worst-case (20%) we get 25.
   Neutral case (60%) we get 45.
   Best-case (20%) we get 100.
   We expect (25 x 20%) + (45 x 60%) + (100 x 20%) = 52 new leads.
2. $100 spent on TikTok will give us between 1 and 200 new leads.

Worst-case (10%) we get 1.
Neutral case (80%) we get 30.
Best-case (10%) we get 200.
We expect (1 x 10%) + (30 x 80%) + (200 x 10%) = 44 new leads.

3. $100 spent on Google will give us between 40 and 60 new leads.

Worst-case (20%) we get 40.
Neutral case (60%) we get 50.
Best-case (20%) we get 60.
We expect (40 x 20%) + (50 x 60%) + (60 x 20%) = 50 new leads.

We can now compare the 3 platforms based on expected value and see that $100 spent on Facebook advertising gives us most likely the most leads. But, we can also see that Google’s range of expected results (between 40 and 60) is smaller than Facebook’s, and that TikTok provides the biggest upside potential (best-case = 200 new leads). Which factor is more important ultimately depends on your situation and needs of the business. 

The important note here is that probabilistic thinking allows you to make this consideration in the first place and applying this mental model consistently over time will greatly increase the number of “good” decisions you make, leading to a more successful business over time.

In life, you can use probabilistic thinking to help you make relocation or career change decisions, or simple everyday decisions like “Where should I take my family on a date?” or “Which mode of transport should I use?”
Ask yourself: 

• Which options do I have? 
• What is the expected outcome for each option? (if needed: what is the worst-case and what is the best-case outcome for each option?)
• How likely is each outcome to occur?

It’s probably more difficult to assign a number to each outcome, but simply thinking in this probabilistic way helps you figure out which option gives you the biggest upside potential for the lowest downside risk. In other words: which option gives the best asymmetric return?