Expected Value
I absolutely loved my probability course in college. Who doesn’t want to learn about the chances of winning in gambling? One very useful concept is expected value which is the average outcome of a random variable. You can calculate by taking the probability of each result times the payoff.
Would you play a game where you pay $3 to roll a die and if you get money equal to what you rolled back? Well the expected value of the roll is 1/6 * -$2 + 1/6 * -$1 + 1/6 * $0 + 1/6 * $1 + 1/6 * $2 + 1/6 * $3 = $0.50. A positive value means you’ll make money on average, and indeed if you could play this game as much as you wanted you’d be rich. I’m sure you can guess by now that in a casino the expected value is negative for the customer and that’s why we have the gambler’s ruin.
You don’t need a huge margin to win. If a high frequency trading firm wins 51% of the time, they’ll make loads of money. Even Roger Federer, one of the best tennis players ever, only won 54% of his points.
Our Lives
Now, what’s the application to our lives? You can apply expected value to EVERYTHING. The amount of variables may not be as simple as a die, but you can try. Say you have two job offers, one is a fixed salary of $80k and the other is $60k plus tiered commission. You have to come up with how many units you think you can sell in order to weigh the two options. Should I take the freeway or the local route? Based on your previous experiences you have a sense of the expected time each should take. Maybe one route sometimes gets stopped by a train and that makes the upper bound unacceptable because you’re running late and don’t want to potentially be even latter.
For many decades there was a pretty well-worn path. Go to college, get a good job, collect paychecks and buy a home that would appreciate. Maybe that was the life your parents or grandparents had. With stability it is pretty easy to plan out your life. If you know you are going to get 5% raises every year, inflation will be low, and your cost of housing won’t change much, then it’s pretty easy to plan what you want to do. You know if you can afford a vacation, a nicer car, a third child.
But things aren’t that way anymore, are they?
The New Normal?
Now we have frequent layoffs, you may go to college and have just a large monthly debt payment to show for it, or maybe you were a government worker, once considered the most stable of jobs, who is getting fired by the new administration. How can you sign up to take care of a kid if you aren’t reasonably certain you can stay employed? The number of variables going into the expected value calculation gets so big that there are high levels of uncertainty. You only have one life, so one die to roll, and when there’s a chance of a big loss you may choose to limit yourself to another path. And there are people choosing to do that. Instead of college, they are going to trade school because it’s pretty predictable what your job will be if you go to a plumbing school. A plumber! And the wages are pretty well known.
Home ownership rates have been decreasing each generation. Why buy a house if you might not be able to pay it or have to move for a new job? Instead we focus on experiences and why not YOLO every so often. Marketing tries to tell us we “deserve” everything. It’s the reality, and it’s tough.
So, if you find yourself in a place where it seems like there’s no clear path forward, remember it’s ok to walk away. Calculate the expected value of various options. Find what is acceptable to you. Sometimes doors open and sometimes they close. It sure would be nice to know the chances of each though.
If you’d like to read more about these changes I highly recommend Kyla’s article.
