How do people make decisions?
A gut feeling is a big factor… sometimes the sole decider. Other times, guidance from someone we trust tips the scales. For bigger decisions, a list of pros and cons help us.
I advocate for incorporating the idea of expected value (EV) in decision making.
What Is Expected Value?
Uh what?!
I would describe EV as an average expected outcome given all the different possible outcomes and their likelihoods of happening.
In other words:
- First, expected value first takes each potential outcome associated with the scenario we’re considering
- Then it uses an assigned “value” to each outcome (this could be dollars or hours or something as fluffy as karma or utility)
- Next it considers a likelihood of each outcome
- Lastly, it combines all the above to give a single average value. This is what you can expect with the scenario, an expected value!
Example: Settlers of Catan
To make this idea more real, let’s turn to a popular board game: Settlers of Catan.
Would you rather have a settlement around a brick hex that produces on a 2 or a 6?
If you said 6, you have an understanding of expected value! It does not take much Catan experience to learn that hexes on 2 rarely produce whereas if you have a brick 6, you probably will not have too much of a brick shortage.
In this scenario, we are rolling two dice. The expected value of rolling two dice is 7. Since 7 is closer to 6 than 2, hexes that produce on 6 are (generally) more valuable than those on 2. Okay but where did that 7 number come from?
To get the expected value of rolling one die, we take each potential outcome, multiply it by its likelihood and sum each of those together. Let’s assume no loaded die, that each outcome is equally likely at 1/6. So the math works out to be:
(1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) = 3.5 = expected value of rolling one die.
Since we are rolling two dice in Catan, we multiply our 3.5 by 2 to get 7.
This illustrates mathematically why you want to put your settlements on hexes with numbers as close to 7 (could be higher or lower) as possible.
Example: Big Company vs Startup Job
In our Catan/dice example, we considered a scenario where each outcome was equally likely. In real life, most scenarios are not like this.
Let’s consider Jenny. She’s deciding between two different jobs and she will use expected value to understand how much money each will pay her.
Job 1 at Megacorp Inc: $50k per year salary
Job 2 at Sketchy Startup: 35k per year salary + equity
Over a two year timeframe:
Megacorp Inc will pay her $100k
Sketchy Startup will pay her $70k + equity
Without considering the equity, clearly Job 1 is better financially.
Jenny does some research and determines that in two years, the equity has a 40% chance of being worth $100k and a 60% chance of being worth $0. In order to correctly value the startup equity, it’s time for Jenny to use expected value.
EV = $100k * 40% + $0 * 60% = $40k
With this in mind, the pay comparison looks a bit different.
Megacorp Inc: $100k
Sketchy Startup: $70k + $40k = $110k
-> By the numbers, Sketchy Startup looks better!
Expected Value Is Only A Model
EV is a model, a simple representation of reality.
Jenny’s decision of which job to take is actually so much more than simply $110k > $100k therefore Sketchy Startup is better for her. This simplification does not consider many important factors such as: Jenny’s risk tolerance, career growth potential, networking opportunities, company culture, or even does a two year time horizon make sense for Jenny?
Similarly, in Catan, it does not always make sense to always try to build settlements on hexes on number as close to 7 as possible. There are important other considerations such as: varying supply and demand of different resource types, access to ports, likelihood of robber camping and more.
The point is that expected value is one tool Jenny can use to help her with a big life decision. Or if there’s a small life decision like where to place a little piece of wood on your table for the next hour, expected value can help there too 😅.
Beau and Expected Value
Expected value is why I do not buy lottery tickets. I think about it this way:
The vastly most likely outcome is I lose money equal to the cost of my ticket.
There is a tiny chance I make a ton of money. Yay.
I understand that there is a negative financial EV for me as I would be participating in a business transaction; I would not be benefiting from a charity. I also know even if I were extremely lucky and win big time, that there is a real chance that my life would become worse for it. Given all of this, I do not buy lottery tickets.
I’ve found it interesting to zoom in and zoom out with EV. One example is with soft drinks and short term vs long term perspectives. Generally, here is my take.
Short Term: Positive EV – “yummy sugary drink tastes good for only $1”
Long Term: Negative EV – “empty calories are unhealthy and I could’ve saved & invested that dollar”
However, with some effort and context, I was able to turn many soda purchases into long term positive EV experiences. A year ago, I decided to do a challenge where I bought a novel drink from a different vending machine each day for 30 days. Yes, I spent about $30 and yes, it was not the healthiest thing to do, but a year later, I feel very positive about the experience!
For much of the content I learned in school, I doubted its practical application in my life and/or forgotten it. Expected value stands out as an awesome exception. It is a model and as you may have heard “all models are wrong, some are useful”. I find EV useful and hope you do too.
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