Billy Murphy says poker made him a millionaire …
But not in the way you might guess.
Billy, now a serial entrepreneur, says poker taught him probabilistic thinking. He learned how to analyze the likelihood of various outcomes. He learned when to double down and when to fold.
He achieved financial independence at age 29, a feat that he credits to applying a concept known as “expected value” (EV) to his business decisions.
EV isn’t just a formula, Billy says. It’s a mental model for making smarter choices.
Expected value is the sum of all possible values for a variable, with each value multiplied by its probability of occurrence.
“Whaaaa? What does that mean?”
Here’s a simple example:
You flip a coin twice. The coin lands on heads both times.
Is the third flip more likely to be tails? Or heads?
Neither. The outcome of the last two coin-tosses doesn’t influence the third — even though our cognitive biases try to convince us otherwise. We like to believe that a “hot streak” will continue rising, or that a string of good luck will turn sour.
But the odds don’t change.
The expected value of the next coin-toss is 50 percent heads, 50 percent tails.
Rationally, you understand this. But when you notice variance — short-term swings — your logic gets tested.
You flip this coin 10 times.
Although it’s not a weighed coin — it’s a fair toss — the coin lands on heads every time.
There’s a crowd watching, and they start to whisper among themselves. Ten tosses? Heads on every toss? They think they’re watching a hot streak.
One guy offers a wager. He’ll bet $2 on heads; you’ll bet $1 on tails. Winner takes all.
Would you accept that offer? Of course. But why?
You’d accept that bet for two reasons:
#1: This wager holds positive expected value: the probability that you’ll gain is higher than the probability that you’ll lose.
#2: You won’t suffer from the risk of ruin. You can handle the downside.
Sure, you’re exposed to the risk of loss. But the odds are in your favor.
That’s the concept behind EV thinking.
Expected Value in Your Business and Life
How can we apply this to our decisions about money, business and life?
Here’s a simple example:
Imagine that you hold a full-time job. You’ve also built a side business that’s netting $20,000 per year.
Should you keep your full-time job?
Or should you quit your job and scale your side hustle into a full-time business?
You ask your two best friends for their opinion. One says, “business is risky! What if you fail?” The other says, “businesses make millionaires! Quit and grow rich!”
You realize that both of those remarks are fueled by emotion (fear, greed) and speculation. You want to make a cool, rational decision.
So you decide to compare the ‘expected value’ of your options.
You assess the market — studying demand, analyzing competitors, etc. If you focus full-time on your business, you determine, you could earn a $250,000 profit during your first year in best-case-scenario conditions. You calculate a one-in-four chance of this happening.
In middle-case-scenario conditions, you estimate that you’d bring home $100,000 per year. This is the most likely outcome; you’ll assign this 50 percent odds.
In worst-case-scenario conditions, your business stagnates at its current performance. You’d bring home only $20,000 in your first year. You assess that there’s also a one-in-four chance of this situation unfolding.
What’s the expected value of staying at your current job?
EV of job =
Your salary + $20,000 in side hustle income.
What’s the expected value of scaling your side hustle into a full-time business?
EV of biz =
- 25% chance of earning $250k = $62,500
- 50% chance of earning $100k = $50,000
- 25% chance of earning $20k = $5,000
EV = $117,500
Which option holds the higher expected value?
Obviously, the decision is more complex.
You’d also consider:
- The growth potential of your business — e.g., the 5-year outlook, the 10-year outlook.
- The growth potential in your 9-to-5 job — e.g., could you get a major promotion?
- Psychological factors — e.g., finding happiness and purpose within your work.
- Lifestyle factors — e.g., flexibility, location independence.
But this illustrates a framework for making smarter decisions. Rather than saying, “oh, that’s risky!,” you can contextualize risk and reward through expected value.
Most people don’t make rational choices.
Emotions, cognitive biases and social pressure often override our thinking processes. We rationalize, rather than reason. That’s why decision-making frameworks like EV can help us make better choices.
In this episode, Billy describes how he applies EV thinking to his daily decisions.
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