The ideal opponent knows your habits, not your cards
The first of a series of columns for OnInvest, first published in Russian. The full English version is below.
There is a thought experiment in Bill Chen and Jerrod Ankenman's The Mathematics of Poker. Imagine you are playing against a superhuman – the authors call him the ideal opponent. «He knows absolutely everything about your game and always plays the maximally exploitative strategy against you.» He cannot see your cards in any given hand. He does not need to: he knows how often you bluff, how often you give up and how much you bet with a strong hand. The moment you change a habit, he adjusts.
Chen and Ankenman invented this opponent to derive the mathematics of optimal play. Every day I play half an hour of fast online poker, about three hundred hands, and then go through the session with the numbers. In September I saw that his logic works at a real table too. Nobody there plays perfectly, but my opponents look where he looks. In half an hour three hundred people sit down across from me, almost none of them sees me twice, and yet every one of them bets money against me based on how often people like me do one thing or another. Some of them with software that counts those frequencies for them.
Investing and business have this opponent too: the market, together with your counterparties. We are used to taking decisions apart one at a time. A committee approves one deal, a post-mortem looks at one project, the board asks about one quarter. And almost every decision, looked at on its own, can be defended. But the ideal opponent does not look at one case. He looks at the pattern.
How often you give way
In one session my opponents bet into me heads-up 27 times, and 19 times I gave way, never once raising back. On review, most of those folds were right. But a player who pressed me with no cards at all would have taken in almost ten times what he lost. Over the whole of September, in that spot, I gave way 54 times in a hundred; the other players at the same tables, 46. The ideal opponent does not need to know whether my latest fold was right. He sees that I fold more often than the others, and he presses me in particular.
In 2021 Cybereason surveyed 1,263 cybersecurity professionals about ransomware – the software that encrypts data and demands a ransom. Of the companies that paid, 80% were hit a second time, and almost half of them believed the same people had come back. A year later the survey was repeated: again almost 80%, and in more than two thirds of the repeat attacks the demand was higher than the first time. The survey was commissioned by a vendor of protection, but the mechanism needs no vendor to explain it: by paying, the company told the market that it pays.
The same happens with the supplier who raises his price, the founder who asks for one more bridge round, the co-investor who changes the terms at the last moment. Each concession is reasonable. Together they become your reputation.
How often you make deals
A poker room is a marketplace. Players sell each other time and skill, and the platform takes a percentage of every pot without judging which of us is right. Over the first weeks of September, for every dollar I earned, it took more than five from the tables I was sitting at. It gets its cut on every transaction; I get mine only when I turn out to be right.
In 2000 the economists Brad Barber and Terrance Odean obtained from a large American broker the six-year history of 66,465 retail accounts. The market returned 17.9% a year; the most active fifth of investors, who turned their portfolios over more than 2.5 times a year, earned 11.4%. Their stock picks were on average no worse than anyone else's, but every trade cost a commission, and the more often they traded, the larger the share of their result went to the middleman. The paper is called exactly that: «Trading Is Hazardous to Your Wealth».
Not one of their trades was stupid on its own. What was stupid was making that many of them.
How often you pay to be right
Chen and Ankenman have the other side of the same idea. Against the ideal opponent the only strategy that wins is one that cannot be predicted, and such a strategy necessarily includes moves that look losing on their own. They can only be judged together with the rest.
In one session I left the hand without putting in a cent 227 times out of 300: almost free, and almost always right. And a single hand where, at that price, folding was not an option, where I paid and lost, cost as much as all 227 folds put together. A reputation for discipline is built from cheap, visible folds. The result is made by the rare cases where paying is right, even when this time you lost.
Every year Mexico's finance ministry buys insurance against a fall in the price of oil. It costs about a billion dollars a year, and in sixteen of twenty years the premium burned away in full. The programme has never been cancelled. It paid out four times, including 2009 and 2020, and in the record year of 2015 it brought in 6.4 billion dollars. Sixteen years of paying and getting nothing is the price of not having to cut the budget in the other four.
Every form of protection in a portfolio behaves the same way. In a good year a hedge only eats into returns, and at year-end you always want to take it off. But you buy it for the whole cycle, and it can only be judged over the whole cycle.
What follows
Chen and Ankenman's ideal opponent does not read your mind. He simply counts your habits. So any decision is one instance of the rule you act by, and it is the rule that gets judged. It is worth asking yourself about your own pattern from time to time. How often do I give way when pressed? How often do I make deals, and what does each one cost? How many years in a row am I prepared to pay for protection that has not yet paid off?
The danger here is predictability. It does not matter whether I give way more often than others or less: as soon as behaviour settles into a stable pattern, it can be worked out and used against me. I only saw my own pattern because I started recording every hand. Perhaps your counterparties are already recording your «hands» for you?