In Bill Chen and Jerrod Ankenman’s book *The Mathematics of Poker*, there’s a thought experiment. Imagine you’re playing against a superhuman—the authors call him the ideal opponent. “He knows absolutely everything about your game and always acts according to a strategy that maximally exploits you.” He can’t see your cards in any particular hand. He doesn’t need to: he knows how often you bluff, how often you fold, and how much you bet with a strong hand. The moment you change a habit, he adjusts.
Chen and Ankenman came up with this opponent to derive the mathematics of optimal play. Every day I play half an hour of fast online poker, around three hundred hands, and then review the session using the numbers. In September, I saw that its logic works at a real table, too. Nobody plays perfectly there, but opponents look at the same things it does. Over half an hour, three hundred people sit across from me; almost none see me twice, and yet each bets money against me based on how often people like me do one thing or another. Some use software that calculates those frequencies for them.
In investing and business, there’s an opponent like this, too: the market and
counterparties. We’re used to examining decisions one at a time: a committee approves a single deal, one project gets reviewed after a failure, a board asks about one quarter. And almost every decision, viewed on its own, can be defended. But an ideal opponent doesn’t look at one case; it looks at the pattern.
How often do you give in
In one session, opponents pressured me with a heads-up bet 27 times, and 19 times I gave in without ever raising. Most of those folds turned out to be correct when I reviewed them. But a player who pressured me without any cards would have taken almost ten times more than they lost. Throughout September, in those situations I folded 54 times out of a hundred; the other players at the same tables folded 46 times. An ideal opponent doesn’t need to know whether my latest fold is right: it sees that I fold more often than other people, and puts pressure on me in particular.
In 2021, Cybereason surveyed 1,263 cybersecurity professionals about ransomware, which encrypts data and demands payment for its release. 80% of those who paid suffered a second attack, and nearly half of them believed the same people were behind it. The survey was repeated a year later: again, nearly 80%, and in more than two-thirds of repeat attacks, the attackers demanded more than they had the first time. The survey was commissioned by a security vendor, but the logic is clear even without it: by paying, a company told the market that it pays.
The same thing happens with a supplier who raises the price, a founder who asks for another bridge round, or a co-investor who changes the terms at the last minute. Each concession makes sense on its own. Together, they become your reputation.
How often do you make deals
A poker room is a marketplace. Players sell each other time and skill, while the platform takes a cut from every pot without judging which of us is right. In the first weeks of September, for every dollar I earned, it took more than five from the tables I played at. It earns its cut from every deal, while I earn mine only when I’m right.
In 2000, economists Brad Barber and Terrance Odean obtained six years of trading records for 66,465 individual accounts from a large American brokerage. The market rose 17.9% a year, while the most active fifth of investors—those who turned over their portfolios more than 2.5 times a year—earned 11.4%. On average, they chose stocks no worse than other investors did, but every trade came with a commission, and the more often they traded, the more of their returns they handed over to the broker. The paper’s title says it all: “Trading Is Hazardous to Your Wealth.”
None of their trades was stupid on its own. The stupid part was making so many of them.
How often do you pay to be right
Chen and Ankenman also show the flip side of the same idea. Against an ideal opponent, only a strategy that can’t be predicted can win, and it has to include actions that look like losing moves on their own. You can only evaluate them together with the rest.
In one session, I folded 227 out of 300 hands without putting in a cent: almost for free, and almost always correctly. But there was one hand where folding at that price wasn’t an option, and I called and lost. It cost as much as all 227 folds combined. A reputation for discipline is built from cheap, visible folds. The outcome is determined by the rare times when calling is right, even if you lose that time.
Mexico’s Ministry of Finance buys insurance against falling oil prices every year. It costs about a billion dollars a year, and in sixteen of the last twenty years, the premium was completely lost. The program has never been discontinued. It paid out four times, including in 2009 and 2020, and brought in 6.4 billion dollars in the record-breaking year of 2015. Paying for sixteen years without getting anything back is the price of not having to slash the budget in the other four.
The same goes for any protection in a portfolio. In a good year, a hedge just eats into returns, and by year’s end you always want to get rid of it. But you buy it for the entire cycle, and you can only evaluate it over the entire cycle.
What follows from this
Chen and Ankenman’s ideal opponent doesn’t read your mind. It simply counts your habits. So every decision is one instance of the rule you follow, and it’s the rule that gets evaluated. It’s useful to ask yourself about your own pattern from time to time. How often do I give in when I’m under pressure? How often do I make deals, and what does each one cost? How many years in a row am I willing to pay for protection that hasn’t yet paid off?
What’s dangerous here is predictability. It doesn’t matter whether I give in more or less often than other people: once my behavior settles into a consistent pattern, it can be figured out and used against me. I only saw my own pattern because I started recording every hand. Maybe your counterparties are already recording your “hands” for you?ㅤ