Poker legend Doyle Brunson is rumored to have been asked whether he would take the following bet. A coin is flipped. If it comes up heads, Doyle loses his entire net worth. Tails, he wins 10 times his net worth. Doyle responded, “I’d have to take that bet.”
He’d “have to” take that bet because of a concept called expected value. Even if some of us wouldn’t take that particular bet, the concept of expected value can help us make better decisions in many areas of life, especially those involving time and money.
In this post, I’ll define expected value and show how you can use it to save time and money.
Definition of Expected Value
“Expected value” is what a situation would be worth, on average, if the situation were to recur many times. A concrete example can make that abstract definition much more intelligible.
Take the role of a six-sided die. Each roll, the die will come up 1, 2, 3, 4, 5, or 6. The expected value (EV) for each roll of the die is 3.5, the average of (1+2+3+4+5+6)/6.
Real Life and the Brunson Bet
For the Doyle Brunson bet, let’s say his net worth was $1 million at the time the question was put to him. There is a 50% chance the coin flip results in him losing $1 million. And there is a 50% chance the coin flip earns him $10 million. The expected value of the bet is, thus, $4.5 million, i.e. 50% x -$1 million + 50% x $10 million.
This example is extreme because it is an all-or-nothing proposition. If you’re like me, what you’re left wishing for is the opportunity to take that bet repeatedly, but in smaller increments.
For instance, can I wager 5% of my net worth with the risk of losing it all but the reward of gaining 10 times as much? And then, after I make that bet, can I wager the next 5% of my net worth, and so forth, until I’ve wagered 100%?
The EV of breaking that bet down into 20 chunks, each worth 5% of my net worth, is still $4.5 million. It’s just much less risky because there is more time for the odds to play out.
The good news is that that is exactly how life really is. We are presented with thousands of opportunities to make, or refrain from making, small “bets” of time and money. The bets we want to make are those where the expected value is in our favor.
Why it’s Unnatural to Think in Terms of Expected Value
Thinking in terms of expected value does not come naturally to most people. A key reason why is because the expected value of a situation often does not equal any of the possible, particular outcomes.
The expected value of the role of a die is 3.5 despite it being impossible to role a 3.5. Or in the Doyle Brunson example, the EV is $4.5 million despite the fact that Doyle will either lose $1 million or win $10 million.
That said, striving to think in terms of expected value can save you time and money, as the following examples illustrate.
How to Save Time with Expected Value
Take, for instance, the following question. Should I drive the backroads to work or take the highway, given that the backroads always take 18 minutes whereas the highway takes 10 or 40 minutes depending on whether there is an accident?
What most people do in that situation is try to guess whether there is an accident. But (for the sake of this example), they have no way of knowing. If they suppose there is an accident, they’ll take the backroads. If they suppose there isn’t an accident, they’ll take the highway.
A better way to decide would be to start by estimating the probability that there is an accident. That’s something they are equipped to do based on past experience.
Let’s say they estimate there has been an accident about once every other week. One accident out of 10 business days of driving means there is an accident 10% of the time.
So 10% of the time driving on the highway will take 40 minutes. 90% of the time it will take 10 minutes. The expected value of their commute time, by taking the highway, is thus 13 minutes. 10% x 40 minutes + 90% x 10 minutes = 4+9 minutes = 13 minutes.
As a result, they will save time over the long-haul—5 minutes per day—by taking the highway every day rather than by driving 18 minutes on the backroads.
How to Save Money with Expected Value
Or take this example involving money rather than time.
Your mechanic asks if you want to spend $250 to replace a car part. If you don’t, he says, it could lead to a problem that would require a $1,000 repair down the road. What do you do?
The mistake would be to try to make the decision based on a shot-in-the-dark guess as to whether the problem will, in fact, arise. You just can’t know.
Rather, ask your mechanic what percent of the time he thinks your car will experience the more significant problem if you don’t replace the part today.
Let’s say he thinks there is a 10% chance.
In that case, the expected value of not replacing the part today is -$100, i.e. 10% x -$1,000. The expected value of replacing the part today, on the other hand, is -$250, i.e. 100% x -$250. So you are better off not replacing the part because that decision has a more favorable expected value.
Using expected value in decision-making doesn’t come naturally, but it is a skill well worth developing. Along with concepts like the minimum effective dose, putting more load on the arch, and the 80/20 rule, thinking in terms of expected value is a key principle for saving time and money.
Question: For what decisions could you use expected value to help save time or money? You can leave a comment by clicking here.
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