We Live in a Sample Size of One

Six weeks ago, I published my book, The Stoic Systems Thinker.

During the year and a half I worked on the project, I said no to nearly every idea or opportunity that came my way. When I finally did publish, it felt as if a huge weight was lifted off my shoulders. I could finally pursue other interests again.

I recently wrote about how I’m spending some of that time — applying these systems concepts in the design of AI-powered business and personal workflows.

But I’m also still working on my book. That project isn’t going away anytime soon. The only thing that’s changed is the shape of the work.

I’ve spent much of this post-publishing period doing the unglamorous work of trying to get these ideas in front of as many people as possible. I like writing. I’m far less comfortable with self-promoting and selling.

But I believe in these ideas and want to share them. So I’ve sent emails and DMs to nearly everyone in my personal and professional network. I’ve pitched bookstores around Ann Arbor and Detroit on stocking my book. I’m posting on social media — a medium I think is a net-negative for the world — far more than I ever expected or wanted to. I’m scheduling podcasts and live readings for the coming weeks (more on both as they firm up). And I’m testing and learning with Amazon ads — the funny thing is that after a career in marketing measurement, this is the first time I’ve actually executed a campaign. I’m enjoying the learning process.

I’ve also begun recording the audiobook version. The mechanics are challenging on their own — reading over 70,000 words aloud, clearly and without stumbling.¹ The harder part is how I’m processing my own work. As I read it line by line, I’m finding sentences I would write differently today. My publisher warned me early on that a book is never truly done. An author will always tinker with it if given the chance. But at some point you need to declare it ready, publish it, and move on. I agree with that mentality, but it’s still difficult to hear the gap between the writer who wrote something six months ago and the one now reading it.

Still, that gap encourages me more than embarrassing me. It means the last eighteen months made me a better writer — and a more intellectually humble one.

This all matters today because reading my own book line by line keeps pulling me back to an idea that predates it — the book I didn’t write.

Before I ever committed to writing The Stoic Systems Thinker, I had an idea for a different book. I wanted to write about luck, variance, and distributions.

I’ve been obsessed with these topics for years. Play poker for 25 years, and you watch luck and variance decide significant sums of money, over and over. Once you’ve seen what randomness does to outcomes in an arena you can measure, it becomes impossible not to see them everywhere.

Variance and distributions are mathematical concepts. The textbooks written about them are usually dense and technical. But when I originally thought about this project, I didn’t want to rely on the numbers. The math is foundational, but it won’t draw in a broader audience.

I think these topics are fascinating nonetheless. And if they can be explained in a way that doesn’t require a statistics degree to understand, more people would think so too. So I wanted to write about them the way Adam Grant explains things — through history, research, and ordinary life examples. I wanted a reader to finish it and never look at a winning or losing streak the same way again.

I didn’t write that book. The project felt massive, and at that point I had never written anything longer than a several-thousand-word essay. I didn’t think I could do the topic justice. I was probably right.

But I’ve grown as a writer since then, and this website is where I get to find out how much.

It’s also an incubation chamber. The ideas I test here might grow into broader topics that I build upon later. Go back through my archive, and you can find the seeds of several of my book’s chapters sitting in essays from 2024 and 2025 (including one of my favorite early essays about finding meaning, which became the final chapter of my book).

I’ve started to think about variance again and decided it needed its own essay. And who knows? Maybe this one will grow into something bigger down the road.

Before I jump in, a brief disclaimer: the next two sections lean on poker examples. You don’t need to be an expert in the game to follow along. For the poker enthusiasts, I’ve shared my assumptions and the math in footnotes. I use poker because it’s the cleanest laboratory for luck I know. But as I hope to get across, what it reveals applies far beyond the casino.

Now, I’d like you to picture a poker player.

Not me, but a hypothetical one. The player is good, but not spectacular. He wins in most games he plays. He goes to his local casino every Saturday night and plays $5/$10 Texas Hold’em, winning at an average rate of $200 per session.² He plays fifty sessions per year (taking off two weeks for vacations), making about $10,000 from his hobby.³

Only this player won’t win $200 every session. In fact, he’ll rarely win exactly $200. Some sessions, he’ll be up much more than that. Some sessions he’ll break even. Some sessions, he’ll lose. That’s the luck element of poker. The cards don’t always go your way. So while we expect skill to dominate in the long run, results can be noisy along the way. That’s variance.

The good news: we can simulate this. Software lets us take our player’s win rate and replay his year again and again. For this exercise, I simulated one hundred versions of him. How different could their results be? As it turns out, very different.

The graph above represents the results of that simulation.⁴ One hundred cloned poker players, each with the same skill level, playing 10,000 hands of $5/$10 no-limit Hold’em.

Each line in the graph represents a single year-long run of 50 sessions. The luckiest version made almost $30K. The unluckiest one lost over $10K. That’s a $40K spread among players with identical win rates.

Yes, those are the extremes, cherry-picked from the tails. But when we look at the full distribution, we can see a wide spread of outcomes. And winning money is not guaranteed. This solid, winning player has about a one in ten chance of losing money over the year. After just seven years of play, our player’s odds of having at least one losing year are greater than 50/50.

Long losing streaks are a part of the game.

I just described cash games. In poker, they’re actually the calm version of this problem.

Tournaments — the kind of poker you’ve seen on TV — pay like lotteries. A thousand players can enter a weekend event, and only the top 125 or so get paid, with the real money pooling in the top ten. That prize structure massively increases the variance.

We measure tournaments differently than we do cash games. In cash games, we can get up at any time and cash in our chips, so we measure our success in dollars per hand. In tournaments, though, we pay an entry fee and play until we bust or outlast the field, earning a prize set by our finishing place. So we measure success as ROI — the percent we win relative to our entry fees.

Let’s again assume that our player is good but not great and has an ROI of 25%, meaning that for every dollar he puts in, he gets back $1.25 on average. Then we’ll give him a serious schedule — one thousand tournament entries, which at a committed pace takes about five years (200 entries per year). The math says that he should finish that stretch up $125K, or about $25K per year.⁵

Let’s clone that player again and look at one hundred of him. Surely, five years must be long enough to guarantee he makes money, right? Sadly, not even close.

The best of our hundred runs made over $700K, probably deciding to quit his day job along the way to play poker full-time. The worst lost over $200K. That’s almost a million-dollar spread between two players with identical win rates.

Two final points to close this argument. First, the chance that our genuinely good player is down money after five full years is one in four. And second, out of a hundred simulated careers, only one never dipped below breakeven. For the other 99, time spent underwater was just part of the process.

Think of what this means. Somewhere out there are players who could have become the next Doyle Brunson or Daniel Negreanu — poker’s all-time greats. But instead, they ran badly early, concluded they weren’t good enough, and quit the game.

Variance happens everywhere in life. We just don’t see it for what it is.

We look back at events and construct a narrative to make sense of the results. When someone wins, we organize everything they did into evidence of brilliance: a bold decision or the refusal to quit. When someone loses, we build out the same kind of list to scrutinize their mistakes.

Psychologists call this outcome bias — judging the quality of a decision by how it turned out rather than by what was knowable when it was made.

You can do everything right and lose. You can do things wrong and win. Both happen constantly, and neither survives the stories we tell afterward.

Nassim Taleb first put me onto these ideas. He’s often praised for The Black Swan and Antifragile, and rightly so, but his first book, Fooled by Randomness, is still the one I recommend most. Taleb argues that mild success can be explained by skill and hard work, but wild success — true outliers — is mostly variance. I’d soften that point a bit. Skill and hard work are real and will increase the odds of your overall success. But wild success usually requires a dose of variance and luck on top of the skill and the work.

Scott Galloway — NYU professor, serial founder, and modern podcast titan — makes the same point differently. He says that if you work relentlessly hard, you can reach the top 1%, because most people won’t sustain the effort required to get there. But with eight billion people on the planet, that top 1% is still eighty million people — roughly the population of Germany.

All eighty million of those people worked hard, and most of them have real talent. Hard work can get you into that group, but it alone won’t decide who becomes the billionaire. The inverse holds too — the fact that someone is a billionaire is not, by itself, evidence that they’re in the top 1% of anything except outcomes.

Taleb has another line, this time from The Black Swan, that explains why this is so hard to internalize: humans prefer the anecdotal to the empirical. One player’s story captures us. A hundred simulated lines on a chart do not.

Right now, somewhere, a mediocre poker player is on a hot streak and being praised for genius, and a great one is deep in a downswing, quietly believing he’s a fraud. Their results can’t tell them apart.

Neither can we.

The Stoic Systems Thinker is my first book, published in June 2026. It combines the emotional resilience of Stoicism with the analytical precision of Systems Thinking to close the gap between how the world works and how we think.

“‘Timely and timeless’ captures this book perfectly.”
Bethan Winn, Author of The Human Edge: Critical Thinking in the Age of AI

There’s a fair objection sitting under everything I’ve written so far: I haven’t looked at a long enough time horizon.

So let’s do just that. Let’s return to our one hundred cloned poker players and zoom out, extending our simulation to one million hands.

The Law of Large Numbers starts to dominate, and short-term variance washes out. Yes, there’s a sizable dollar gap between the luckiest and unluckiest version. But the spread relative to the expected value has tightened. And even the unluckiest player is a significant winner.

But look at what “enough” costs. Translate that back into Saturday sessions. The original fifty sessions take our hypothetical player a full year to play. Playing one million hands would require him to play for a hundred years. Even if he adopted a full-time five-day-a-week schedule, he’d need twenty years to reach one million hands.

The sample where variance truly washes out is a lifetime at the table. The long run is real, and it’s very, very long.

In life, it’s worse. We don’t get the same opportunities a million times, or a thousand, or even ten. Life rarely deals us the same hand twice. In my book, I put it this way:

Consider your health. You eat well, you train, you sleep, you follow all your doctor’s recommendations. Every one of those inputs improves your expected health. Yet you can still get a bad diagnosis.

It happens professionally. I once had a massive career opportunity that would have been a real step forward for me. The fit and timing were right. But it fell through because the deal it was budgeted against never closed. Nothing about my inputs failed. But the outcome turned out poorly because of something I had no control over.

I see this in business constantly. Donald Wheeler’s book, Understanding Variation, is about managers who read ordinary fluctuation as a signal — those who see a down month, declare a crisis, and act. Managers like that fill organizations around the world, reacting to the numbers first and building explanations after the fact. If that sounds like your company, your leaders are falling victim to outcome bias.

There’s an asymmetry that makes life harder than poker. The poker player can see the distribution. We can study the math, even if we choose to ignore it. We can run simulations and understand that our results are just one draw from a set of possible results.

In life, you draw that line exactly once. You never see or experience the others. Which is exactly why the story we tell about our own results feels so much like the truth.

If good decisions can produce bad results and bad decisions can produce good ones, what’s left to judge ourselves by?

The inputs. They’re the only measurement luck can’t corrupt.

I’ve carried one lesson out of poker into everything else. It’s a question I ask myself after every decision.

Was this bad luck, or was it bad process?

If it’s bad process, I own it. I try to find the flaw and fix the system. And once I do, I try again.

If it’s bad luck but my inputs were sound, I accept the results and leave my system alone. Because the fastest way to destroy a winning approach is to dismantle it in the middle of a losing stretch.

Telling those two apart in the moment is incredibly hard. Many poker players wreck their game by overcorrecting, myself included. If you’re forty sessions into a bad run and losing money, the doubt gets louder every week. The losing becomes its own feedback loop. So you start changing your strategy. But the strategy was never the problem. The variance did the damage.

I try to pass this lesson along to my daughters. I think I get through sometimes, although any parent knows the feeling of wishing your kids listened more. I once told my daughter after her team lost a basketball game: all you can do is the best you can do. She shot back at me with, “But Daddy, we still lost.” She was right, of course. The loss stings, and no philosophy can make that feeling go away. But progress is when we can feel the pain without letting it rewrite how we prepare for the next game.

We live in a sample size of one. We’ll never see the alternative simulations. We’ll never get confirmation that our process was sound.

We don’t get to write the results. We only get to write our decisions.

So keep a scorecard that counts the ones you make. It’s the only thing variance can’t touch.

Thank you to everyone who has bought a copy of The Stoic Systems Thinker, left a review, or written back to one of these emails. It means a lot.

I’m on vacation for much of August, so I’m taking a break next month. No full essay — just a shorter note mid-month with news on fall bookstore events and progress on the audiobook. I’ll be back with another in-depth one in September.

And if today’s essay was your thing, I explore some of these ideas more in the second interlude of my book, “The Illusion of Control.” The book is available on Amazon. If you’d rather shop from locally owned bookstores, it’s available in these wonderful Ann Arbor area stores: Booksweet, Serendipity Books, and Elephant Ear Books.

Enjoy the rest of your summer.

All the best,
-Michael