I got a car from a nearby dealership the other day. As part of the sales routine, the sales manager offered me a 5 years warranty against any unexpected repair for $2,000. Should I take it? If the car doesn’t require any substantial repair within that time frame, that’s money down the drain. But what if there are major breakdowns? Taking up the warranty would seem like a smart move. Although I’ve no idea how much the car would cost me in repairs, one thing for sure is, collectively, the warranty company is making a profit selling these covers at $2,000. In other words, most of the cars cost less than that amount to repair. Far from saying it won’t happen at all, I gave it a 45% chance (50% if I’ve no information) that it would cost me $2,000 in repair and a 55% chance the car doesn’t suffer any breakdown. Based on the expected value of -$200, I decided not to take up the warranty.

Expected value is the probable payoff of all possible outcomes. Warren Buffett explained using expected value to make decisions, “Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect but that’s what it’s all about.” Let’s say you’re planning to pick up a $100 ticket for an outdoor concert tonight. But there’s a risk. If it rains tonight, you’ll forfeit that $100 investment. In most circumstances, we rely on our intuition to make the call, which is often accurate but has its limitations. A better way is to think in term of a decision tree and expected value. If meteorology forecast tells you there’s a 30% chance of rain tonight, you should still get the ticket because the expected value remains positive. [(70% of No Rain*$100) + (30% of Rain * -$100)] = $40. In contrast, any rain forecast above the 50% mark would be considered risky.

We are not used to thinking probabilistically, much less to think in expected value. The reason is that figuring out the chance of an event happening is hard. While meteorology can forecast weather for the next 5 days with a 90% accuracy, it is a different ball game in investing. What’s the chance the revenue will double in 5 years as a result of the acquisition? How will the market react to the new product launch? What’s the probability that the layoff can turn around the business or it’s just a canary in a coal mine? We have to rely on our subjective experience to make judgment in most scenarios since no two situations are the same.

But here’s the thing: You’re already guessing. When you make a decision whether to buy a stock, the decision is based on what you think is going to happen. When you say “I think this stock is likely to perform well…” or something along the line, you’re saying there’s a high probability the future will unfold the way you imagined. You’ve already made the decision. But the danger with this intuition is we always fail to ask: What if it doesn’t? As Philip Tetlock wrote in Superforecasting, the key is to explicitly translate “vague-verbiage hunches into numeric probabilities.” When you translate hunches into numeric probabilities – “This stock has a 70% chance of performing well…”, you establish an objective view that there’s a 30% chance something else could happen. Instead of sticking to your own beliefs and reject contradictory information, you’re more receptive to opposite opinions when making a decision. You’re more interested in seeking the truth than defending your own ego. Thinking in probability create open-mindedness. And your ability to synthesize information by looking at things from multiple lenses will bring you closer to the reality. You’ll be more prepared and less likely to get surprised since you’ve considered all possible scenarios before going into an investment. Instead of only having Plan A where an event occurs as you predicted, you have Plan B, C, D and so on in place should the future take an unexpected turn.

Not thinking in probability or expected value has another bigger problem: fuzzy thinking. As Nassim Taleb reflects in Fooled by Randomness, people get confused when he says there’s a 70% chance the S&P 500 will go up next week yet he is shorting the index in large quantity. How can someone be bullish yet bearish at the same time? Because of asymmetrical payoff.

If the market carries a 70% chance of going up by 1% and a 30% chance of going down by 10%, the expected value is negative. Making this kind of investment is like going to the casino, do it long enough and you’ll end up broke. This applies to individual stock as well. Think of probability as to how often will you see an event occurs – the frequency; and outcome as the magnitude – how big is the changes if an event occurs. Most investors prefer to put their bets on stocks that have a higher frequency of going up because seeing gains is better than seeing losses. But probability has little meaning if you ignore magnitude, how big is the change if the opposite happens.

Just as investors tend to become more confident as their investment goes up, the opposite is just as true, they become over-pessimistic when a stock performs poorly. We don’t predict; we extrapolate. That’s how Walter Schloss makes a killing in his 28 years career by taking advantage of this bias to buy things below scrap value. Jeff Bezos echo the same view on taking positive value bet when he illustrates the success of Amazon “Given a ten percent chance of a 100 times payoff, you should take that bet every time.’ They are thinking in asymmetrical payoff. They don’t mind having frequent losses as long as the bet carry positive value. This further shows words of advice like ‘don’t try to catch a falling knife’ or ‘don’t chase the market’ have little meaning. What matter is – Does it has a positive or negative expected value?

To be clear, making a positive value bet doesn’t mean you’ll always get a positive outcome. My decision not to take up the car warranty because it has a negative value doesn’t mean it won’t cost me more than $2,000 in repair. There’s a 45% chance that it will. We can’t control luck. Whether that’s in business, investing, or life. But we can control the process. The thinking quality of our decision. That’s what Warren Buffett, Philip Tetlock, Walter Schloss and Jeff Bezos all have in common. Every time you make a decision that has a positive expected value, you are putting odds in your favor. You allow luck to find you in the long run. You’ll be more vigilant before making an investment and stay prudent in a market euphoria. You’re also better prepared than others when the unexpected happens and as a consequence, make fewer mistakes. All these small, little good decisions add up to create compound effect when you do it consistently for 10-20 years. But first, you’ve to be comfortable with uncertainty, start thinking in probability and make decisions based on expected value.

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