Alright, today we’re discussing a mental model that can can be useful in helping you make decisions: Expected Value.
Expected Value, often abbreviated “EV,” is a term I first learned about from blackjack, and it encapsulates the amount you would “expect” to make from a certain number of hours of play.
But it is an extremely useful model for decision making elsewhere – in investments, and in life.
To explain the concept, I’ll start with a simple money example.
Say I’m flipping a coin.
If I flip heads, you win a dollar. If I flip tails, you lose a dollar.
Question: How do you feel about that game? And, importantly, do you overall expect to make money at that game?
No. If you were to play it over and over again, you’d probably break even. Sure, you might get lucky, or unlucky, given just one coin toss. But in the long run, flipping that coin a hundred times – you’d win the same amount that you’d lose.
Now consider this:
Say I offer you a game where tails, you lose a dollar, but heads, you win two dollars.
How do you feel about playing that game?
That’s a great game to play. Overall, you’d expect to make money from a game like that. Sure, you might flip tails the first time and lose, but if you kept flipping it, you’d win more money than you’d lose. (It’s a positive EV game.)
At it’s core, that’s the ENTIRE concept of “Expected Value” right there.
Now make sure you understand that, because things are gonna get real interesting real fast.
Say I offer you a dice. (Or “die” I guess, is singular).
If you roll a 1 through 5, you lose one dollar. But if you roll a 6, you gain six dollars.
You can play as much as you want.
How do you like that game?
Think it through for a second.
That’s actually a positive EV game. (Don’t worry if you didn’t catch it.) Your wins, though rare, will eventually more than make up for your losses.
What’s funny is – and this is key – if I just hand you that die for one roll, you’re more likely to lose than win.
After all, you have a 5/6 chance of losing, and a 1/6 chance of winning.
But, with repeated play, the wins from that 1/6 chance will slightly more than make up for all the losses.
To make this concept super obvious, let’s change the payouts:
Roll a 1 through 5, you lose a penny… but roll a 6, you win $1000.
Great game, right? With just one roll, odds are, you’ll lose. You’ll lose a whole a penny. But if you can play as much as you want, you’ll make great money, because the wins more than make up for it.
There it is, you’re an expert in Expected Value.
The mathematical formula for expected value is:
(%odds winning)x(amount you’d win) – (%odds of losing)x(amount you’d lose)
How do we apply this to life?
Well, in investing, if you have some possible investment that has a somewhat decent chance of working out – but the payout in the case of a win is significantly higher than the amount lost in the case of a loss– it may be a good idea to invest some money in it, since the Expected Value might be very high.
Repeated, positive EV investments will ultimately payout – as long as the odds of winning are decent enough, and the payout for winning is high enough.
(Of course, since you can’t guarantee any specific investment will work out, it is critical that when EV investing, you make small enough investments that you can in fact do them repeatedly, even if you incur losses. In blackjack, that’s called bankroll management.)
But perhaps my favorite application of this way of thinking is applying it to trying new things – exploring new hobbies and passions; going new places.
Considering trying a new hobby you’ve always thought about?
Or going somewhere new?
There’s always a possibility you’ll love it and it’ll be life-changing.
What are those odds of that? No idea, probably slim. Maybe 10, 20%?
But if you think about it, the expected value on that is actually really high.
10%x(LIFE CHANGING)–90%(tiny money/time investment) =
HUGE POSITIVE EV.
So if you’re considering going somewhere new, trying something new, or picking up a new hobby you’ve always thought might be fun: the sheer possibility of loving something in a way that is life-changing makes most new adventures very high in expected value.
^I feel like this is pretty insightful, so I’m just gonna take a second to pat myself on the back for that.
Of course, odds are, you won’t fall in love with the first new thing you try.
But that’s okay. If you explore, adventure, travel, and trial enough, the positive EV from trying new things will absolutely eventually pay off.
So get out, learn new skills, go new places, and try new things.
[Especially if you can do it inexpensively], the expected value is enormous.