🧠 Expected Value Thinking
FIRE BTC Issue #29 - Making decisions like a poker player
One of the biggest traps on the road to financial independence is craving certainty in an uncertain world. We want clear answers, safe plans, guaranteed wins. But life and money don’t work like that.
One powerful concept from investing that has transformed how I approach important decisions is Expected Value Analysis (EVA). It offers a practical way to cut through uncertainty and focus on choices that can compound positively over time.
I like to focus on process over results, and EVA helps me do exactly that in a quantifiable, measurable way.
I was inspired this week listening to my friend Clay Finck on the We Study Billionaires podcast discussing a book I read years ago: Thinking in Bets by legendary poker player Annie Duke. I hope this post will show you how to use EVA to strengthen your FIRE + bitcoin plan and arm you with a new tool for making better decisions in life, whatever they may be.
🎲 Understanding expected value
Every decision you make — save or spend, hold or sell, stay or leave — is a bet on an uncertain future. That’s the key insight Annie Duke drives home in her book: life is one long series of bets.
What separates great decision-makers from the rest isn’t certainty. It’s weighing probabilities accurately, acting when it the odds are in your favor, and understanding that even small, positive bets can add up over time. Expected Value Analysis gives us a framework for making decisions that provide a mathematical advantage for achieving success over the long run.
So, how does it work?
Expected Value = (Probability of Outcome A × Value of Outcome A) + (Probability of Outcome B × Value of Outcome B) + …
Imagine a hand of Texas Hold’em: you’re on the river with a flush draw, and the pot holds $500. You’re deciding whether to call a $100 bet. If you estimate a 20% chance you win $600 and an 80% chance you lose $100, your expected value is (0.2 × $600) + (0.8 × -$100) = $120 - $80 = $40. That’s a positive EV, so over time, making this call pays off.
From a skilled poker player's perspective, the outcome of the hand doesn't matter. I repeat, the outcome does not matter. The goal is not to win every hand, but to make decisions that put you in a position to win over the long run. That doesn't hinge on whether you "get lucky" on one hand, but whether you are good at estimating:
the probabilities of the various outcomes of your decisions
the actual risk you are taking, and
the payoff you expect when you're right, relative to the loss if you're wrong
You may call that $100 bet and lose — in fact, you most likely will, with 80% probability. But the asymmetry of the payoff when you win means it makes mathematical sense to call every time you see that situation. Whether you win that particular hand or not, you've "made" $40 in EV terms.
🤑 From thinking in bets to thinking in bitcoin
EVA can help you figure out how cheap or expensive an asset is at a particular moment relative to your expectation of future returns.
Bitcoin is currently trading around $103k. For easier math, we'll round down to $100k. Let's say you're a bear, who estimates a 10% chance it hits $1M in 10 years and a 90% chance it goes to zero. In other words, for every $1k investment, you have a 10% probability of ending up with $10k, and a 90% probability of a goose egg. The EV on that bet is (0.1 × $10,000) + (0.9 × $0) = $1,000. That’s break-even on paper, but if you believe the upside odds are even slightly better, the EV tilts positive.
If you're slightly more bullish and give it a 25% chance of reaching $1 million, then all of a sudden your expected value on a $1,000 investment jumps to $2,500. In essence, you’re buying $2.50 for $1.
Personally, I think the odds of $1 million BTC in 10 years are WAY higher. If you agree with me, then buying bitcoin today at $100k is hugely positive EV, and you should be doing it hand over fist.
Bitcoin is the most asymmetric trade on the planet, and EVA puts that asymmetry in quantitative, decision-focused terms. You could run the analysis for other assets that may compete for your funds for comparative purposes, like the stock market.
This can give you a helpful approach for weighing investment options to identify the biggest bang for your buck at any given moment.
🎯 EVA applied to FIRE
There are very few decisions in life that are made with certainty, and pursuing FIRE is no different. EVA can strengthen your approach to FIRE, which is all about making tradeoffs today to maximize freedom tomorrow. Understanding the expected value of each decision helps quantify those tradeoffs.
Take the classic FIRE question: should you buy a home or rent? Buying might seem like the obvious “smart” choice because you’re building equity. But ownership also comes with maintenance costs, property taxes, transaction fees, and the risk of needing to move. Renting offers flexibility but leaves you exposed to rising rents and no home price gains.
Suppose you estimate a 50% chance you’ll stay in a city for 10+ years (where buying pays off) and a 50% chance you’ll need to move in 3 years (where selling early costs you). Staying might earn $100,000 in equity; moving early might cost $30,000 in transaction fees. Your expected value of buying:
→ EV = (50% × $100,000) + (50% × -$30,000) = $35,000.
This shows buying still has a positive expected value, but not as much as it might appear without factoring in uncertainty. It helps clarify whether the flexibility of renting or the potential payoff of buying aligns better with your goals.
Not only that, this particular analysis doesn’t factor in the opportunity cost of buying bitcoin or stocks with the money that would otherwise be used for a downpayment on a home. You could layer that into your EVA calculation as well.
Expected Value Analysis isn’t just for investments. It’s a mindset for evaluating life decisions.
By weighing probabilities and outcomes, you make choices that tilt the odds in your favor. Over time, these higher EV decisions compound, bringing you closer to financial independence with greater confidence.
The only thing really certain in life is bitcoin’s 21 million hard cap. For everything else, there’s EVA.
That’s it for this week. Thanks for reading!
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Until next time,
Trey ✌️