There’s a probability tool that Warren Buffett uses every time he evaluates an investment. The same tool is used by professional poker players in most of the hands they play.
This exact same tool is also useful in everyday life. It’s often valuable when making big decisions — for life in general, not just in terms of investments.
Warren Buffett swears by this tool. He would probably feel lost without it. The same is true of top poker pros. They wouldn’t know how to approach the game without it.
Every single investor should have this probability concept in their toolkit.
And not just every investor, but every student. The concept is based on simple math, and a way of thinking available to everyone. It should be taught in schools from an early age.
And yet, despite the vital importance of this probability tool … and the simplicity of the math behind it … the majority of individual investors don’t know about it. Most of them haven’t even heard of it.
And even among those investors who are familiar with the terminology, they don’t have a basic grasp of how it works … or don’t have a habit of applying it on a regular basis.
This is crazy. Everyone should understand this tool. If there were such a thing as an “investing driver’s license,” familiarity with this tool would be on par with knowing how to make turn signals.
And yet, once again … most investors don’t understand this concept (or don’t know about it at all) … and that’s something that needs to change.
This simple tool is called “expected value,” or EV for short.
It involves a little bit of math, but the math can be done on a napkin. Or you could use the calculator in your smartphone. For the most part, what’s hard about using EV isn’t the math — it’s adjusting your way of thinking to use it regularly.
At one of his Berkshire Hathaway annual shareholder meetings — fondly described as “Woodstock for capitalists” — Warren Buffett once explained how expected value works. It only took three sentences. Here’s the direct quote:
“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.”
Expected value is the probability-adjusted value of an investment. Let’s break down what that means.
Let’s say you have a raffle ticket with a 50% chance of winning. For the sake of argument, we’ll say there are only two tickets in the whole raffle — and one of them is yours. The prize is worth $100. How much is your raffle ticket worth?
If the prize is worth $100 … and the raffle ticket has a 50% chance of winning … the EV of the ticket is $50.
To say the expected value of the raffle ticket is $50 does not mean you will literally receive $50 for it.
The actual result is binary: If there is only one drawing, you will either get a prize worth $100 … or you will get zero.
But let’s say the raffle drawing was held 100 separate times. In that case, with a probability of 50 percent, you would win the $100 prize about half the time and win zero the other half the time … for an average gain of about $50.
Expected value tells you the probability-adjusted value of a result. It is most useful when you imagine the same type of event happening over and over again.
Let’s try another example. Say you make a stock investment with a 25% chance of a $1,000 gain. What is the expected value of that investment?
Putting aside transaction costs, the EV would be $250. That is because $1,000 x 25% is $250.
But the upside is only half the equation. You also have to consider the possibility of losing money … and then subtract the probability-adjusted loss from the probability-adjusted gain.
That’s why Buffett said “Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain.” In formula form it looks like this:
EV = (Amount of Gain * Probability of Gain) — (Amount of Loss * Probability of Loss)
Imagine a speculative investment of $100 where one of two things will happen.
- There is a 60% chance you will double your money for a gain of $100.
- There is a 40% chance the investment goes to zero (for a loss of the original $100).
What is the EV on that investment?
Based on the EV formula we can think it through like this:
($100 gain * 60% probability) — ($100 loss * 40% probability) = $60 — $40 = $20 EV
If the assumed probabilities are correct, the EV of the speculative investment is $20. You can also see this by imagining what would happen if you made the same investment 100 times over:
- 60 times you would make $100 for a gain of $6,000
- 40 times you would lose $100 for a loss of $4,000
- The net gain would be $2,000 over 100 trials or $20 per trial
Another way to think about expected value is to ask the following series of questions:
- How much can I gain?
- What is the likelihood of making that gain?
- How much can I lose?
- What is the likelihood of experiencing that loss?
Expected value is the result of adding those probabilities together.
Investors like Warren Buffett use EV because they always consider upside and downside simultaneously.
It’s never just “How much can I make?” It is always “How much can I make?” versus “How much can I lose?” … with the attractiveness of the investment determined by the combined result of those two things.
Professional poker players use EV on a regular basis when deciding how much to bet. They also use it when deciding whether to call, check or fold.
Here’s a simple example …
Let’s say we’re playing no-limit Texas hold ‘em and there is $100 in the pot.
My cards are worthless, but I have an opportunity to bluff. My calculations tell me that, if I bet $50, there’s a 50% chance you will fold and let me win the pot. What is the EV of my bluff bet?
The potential gain is $100 (because there is $100 in the pot). The potential loss is $50 (because I will lose $50 if you call or raise, but I can’t lose any more than that). So the EV formula looks like this:
($100 gain * 50% probability) — ($50 loss * 50% probability) = $50 — $25 = $25 EV
The EV of my $50 bluff in this situation is $25.
Again, this does not mean I will literally win or lose $25. In fact, I will either win a $100 pot or lose my $50 bluff bet entirely. It means that … if the situation were repeated a thousand times … I would gain $25 on average from all the repeated trials.
This bluff has a positive expectation, which means all things being equal, it is a money-making move on average. That’s why a skilled poker player would make this bluff every time it was available — and not be disturbed by all the times it didn’t work out!
Investing is a game of averages. Poker is also a game of averages. That’s why expected value is so useful as a tool.
As an investor, you won’t make just one investment in your life. You will make dozens, or possibly even hundreds or thousands. What matters is the average outcome — the expected value — per investment over time.
With poker, it’s even more extreme. The professional poker player sees hundreds of hands per week and thousands of hands per year. What matters is the average result of what happens over and over again.
Expected value has surprising implications. For example, the size of the gain or loss is often more important than the frequency of wins or losses. To illustrate:
A 30% chance of winning $1,000 and a 70% chance of losing $100 is excellent, even though it produces a loss seven times out of 10. The EV on this bet is a gain (positive expectation) of $230. The size of the wins more than compensates for the low frequency of winning.
On the flipside, a 70% chance of winning $100 and a 30% chance of losing $1,000 is terrible … even though a gain is produced seven times out of 10. The EV on this bet is a loss (negative expectation) of $230. The frequent small wins are dwarfed by the outsized losses.
Once you get used to thinking in probabilities, the expected value concept is also useful in life.
Thinking in probabilities as a habit encourages two very useful behaviors: leaning toward decisions that have the potential for big gains, and leaning away from decisions that have the potential for big losses.
Expected value can also help put things in perspective.
If you are really excited about a possible outcome … but you stop and realize it realistically has only a 30% to 50% chance of happening … then you will adjust your expectations to think more about the risks and the costs of the decision.
And on the positive side, EV can sometimes help you see the upside of a life decision so large that … even if the best scenario only has a 25% chance of happening … it’s still an obviously smart move relative to the risks and costs, which can increase your confidence and peace of mind in making the call.
Thinking in probabilities is an alien concept to most people. Our brains weren’t wired for it.
But in the world of investing — and also, the world of poker — the ability to think in probabilities is literally one of the key separating factors between winners and losers.
That’s why Warren Buffett defines his whole investing approach in terms of expected value … and why professional poker players use EV every time they play.
Richard Smith, PhD
CEO & Founder, TradeSmith