Icosian Reflections

…a tendency to systematize and a keen sense

that we live in a broken world.

IN  WHICH Ross Rheingans-Yoo—a sometime quantitative trader, economist, expat, EA, artist, educator, and game developer—writes on topics of int­erest.

When each proud fighter brags

content warning: As heavy as this blog gets.


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I met Max Chiswick in June of 2024 because I wrote something wrong on the internet. He tracked me down at Manifest to tell me so—I had written about the shortcomings of poker as a teaching tool, but I had made several wrong assumptions about how one would play poker differently with the goal of learning instead of recreation.

First, you'd play with two players instead of eight. We nearly always play with eight-ish players because we want a relaxing game, where large gaps in the action are considered a feature. With two players, though, not only is it your turn four times as often, but more of your decisions are "live" because it's correct to play more (initial) hands and there are fewer that you should fold on sight.

Second, you'd play a game with fewer chips—meaning that you'd make bets in coarser increments and with a smaller ratio of largest-possible bet to smallest-possible bet. This makes the decision tree shallower and more amenable to explicit case-by-case reasoning, and it also has the nice effect of making the highest-stakes decisions less terrifying (while keeping the stakes of bread-and-butter decisions suitably meaningful).

But most importantly, if you're playing poker as an exercise for training your mind, you should focus less on becoming a theoretically-optimal robot. You can read books and blogs about "game theory optimal" play (e.g., Nash equilibrium) and drill yourself to get arbitrarily accurate at executing it, but that's simply not the useful part.

The part of poker that makes you smarter—Max explained to me—is observing the non-optimal patterns in your opponents' play, and

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John Nash, 1928-2015

CNN | Mathematician John Nash, wife killed in car crash

John Forbes Nash Jr., the Princeton University mathematician whose life inspired the film A Beautiful Mind, and his wife died in a car crash Saturday, according to New Jersey State Police.

Well, okay, somehow the fact that his life inspired a Hollywood film made it into the obit before the fact that he won the 1994 Nobel Prize in Economics. (Note: "Nash called the film an 'artistic' interpretation based on his life of how mental illness could evolve -- one that did not 'describe accurately' the nature of his delusions or treatment.") But in actuality, it's enormously difficult to describe the impact that this man had on the field of Game Theory, which now underlies much of economics, politics, and has even been applied to describe the strategy of penalty shootouts in soccer (where it closely predicts the strategies that top players actually use).

And if you're anything like me, you'll find his 1950 dissertation a refreshing respite from page after page of obituary:

Non-Cooperative Games (typewriter facsimile)

Introduction

Von Neumann and Morgenstern have developed a very fruitful theory of two-person zero-sum games in their book Theory of Games and Economic Behavior. This book also contains a theory of n-person games of a type which we would call cooperative. This theory is based on an analysis of the interrelationships of the various coalitions which can be formed by the players of the game.

Our theory, in contradistinction, is based on the absence of coalitions in that it is assumed that each participant acts independently, without collaboration or communication with any of the others.

The notion of an equilibrium

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