Challenging Empiricism with Poker

Poker is the most challenging game I’ve ever played. Not because of the strategy, but because of the philosophy behind it. Poker has an infuriating relationship between theory and data – between knowledge and execution; between understanding and demonstration.

Here’s what I mean: you can play perfect poker and lose all your money. You can clearly understand the game of poker and be beaten by an unknowledgeable fool. The fool, by contrast, can play objectively horrible moves, and yet walk away a winner.

This isn’t the case with games like chess. In chess, if you play correctly and understand what you’re doing, you will win every game against foolish players. It’s very easy to demonstrate chess-competence. If you know what you’re doing, you will win; if you win, it’s a demonstration that you know what you’re doing.

We could explain this away by simply saying, “Poker has an element of luck; chess has no luck. That’s the difference.” But this misses a much larger philosophic issue: the relationship between theory and data. Or, more broadly, the relationship between rationalism and empiricism.

Rationalism and Empiricism

The question is this: how do you know when you understand the game of poker? Is it when you start winning – when you get an empirical validation that you’re doing something right? Or, is understanding poker entirely cerebral – meaning, you can understand the game without empirical data?

These questions parallel debates in epistemology. How can you understand knowledge about the world? Can you merely sit in an armchair and think about it, or do you need to “go out in the world” and gather data? Furthermore, what happens when data isn’t in accordance with our theory – do we revise our theory, or do we dismiss the data?

The rationalists (roughly speaking) say this:

“Knowledge is ultimately based on rational analysis. You can know certain things by sitting in an armchair and thinking about them. Theory is primary; data is secondary. No data speaks for itself, and in some circumstances, theories can be known to be true despite empirical data to the contrary.”

The empiricists (roughly speaking) say the opposite:

“Knowledge is ultimately based on sensory information we gain about the world. We have to experience the world before we can understand it. All hypotheses have to be tested to see whether they are true. We cannot simply think in an armchair and learn something about the world. Theory must conform to the data, not the other way around.”

I am a rationalist, and poker is a great example why.

Math and Psyche

Let’s start with the basics: there are objectively correct and incorrect ways to play poker. If your goal is winning hands (and money), then certain techniques are superior to others. You can loosely categorize the techniques into two fields: mathematics and psychology.

Mathematics is the straightforward one. Card games are fundamentally probabilistic. There are only 52 cards in a deck. If you’re looking for the Ace of Spades, then you have a 1-in-52 chance of getting it right on your first draw. The more cards you draw, the higher your chances. From a mathematical perspective, poker is simply a complex analysis of probabilities – what are the chances that your opponent has a better hand than you, given the cards that you can see?

The difficult part of poker, for me, is the psychological part. Master poker players aren’t just calculating probabilities. They are aware of your previous betting patterns, any “tells” that you have, your general disposition, your likelihood of bluffing, the way that you put your chips into the pot, etc. Plus, they are aware of their own psychological projections – how they think they are perceived by others. The master poker player might establish a reputation of being “loose” at the table – meaning, he plays weaker hands than he should. Then, just when you think you’ve got him beat, he’ll lay down a killer hand. Or vice-versa – he’ll establish a reputation of playing only strong hands, and then he’ll get away with bluffing at the right time.

The goal is to outplay your opponent both mathematically and psychologically. You want your opponents to confidently bet into your strong hands, and you want to know when you should fold because you’re beaten.

Ultimately, what determines a strong hand from a weak one is mathematics. A strong hand versus a weak hand means that the vast majority of the time, the strong hand will win. For example, say the cards were just dealt. You’ve got pocket aces, and your opponent has a 2-7 offsuit. If it’s just the two of you, the pocket aces will win around 85% of the time. It’s possible that your opponent could get lucky and make two pairs, but it’s not likely. Therefore, if your opponent bluffs and bets all of his chips, the objectively correct thing to do is call him.


But here’s where things get tricky. Imagine that your opponent gets lucky. Two 7’s come down and he beats your aces with three of a kind. Bummer. Maybe next time.

Imagine it happens again. He keeps getting lucky, over and over. Instead of 85% odds, you get him to bet everything with 98% odds in your favor – total domination. But he gets lucky again and takes all of your money.

This isn’t unheard of. Poker players have incredible stories of so-called “bad beats”, where they get strings of terrible luck – sometimes costing them gigantic sums of money. This happens because of “variance” – the inherent randomness in card games. It’s like flipping a coin. If you flip long enough, eventually you’re going to have an unusual streak of 20-heads-in-a-row.

Data versus Theory

Let’s examine this a little deeper. After taking all of your money, imagine your opponent is interested in understanding the game of poker, and he’s a strict empiricist.

You explain, “The reason you won isn’t because you were playing better poker. In fact, I was outplaying you every hand. You simply got lucky. I can fully explain why your moves were incorrect.”

He responds, “The data isn’t on your side. Clearly, I kept winning, which means my moves were more correct than yours. If your theory were right, then you would have beaten me.”

You respond, “No, my theory fully explains why you beat me. And it isn’t because you were playing better moves. I understand this despite losing all of my money to you.”

He responds, “Why do you believe your theory? I am treating your claims as empirical hypotheses, and as such, all of the data contradicts you. Your theory should adjust accordingly.”

You respond, “I am appealing to the logic of the game! Just by analyzing the concepts involved in poker, and understanding the related mathematics, I clearly understand why I played better than you. It was just variance; eventually, my theory will be demonstrated as superior.”

He responds, “Alright, prove it. Let’s test your theory some more.”

You play more games, and the same story unfolds. He keeps getting lucky and taking your money. You understand it’s just variance, but he challenges you and says,

“At what point will you abandon your theory? If I keep winning, won’t that prove your theory wrong? Are you going to dogmatically cling to your theory regardless of the data?”

You respond, “You just keep getting lucky! If you understood the game of poker, then you’d understand why I don’t have to appeal to empirical tests. I am appealing to the logic of the game. Ultimately it doesn’t matter how much I lose, I know that I understand what’s happening.”

This is precisely the argument between rationalists and empiricists. The rationalists say, “You can know some things just by logical analysis, even if the data suggests otherwise”, and the empiricists say, “At some point, if your theory does not accord with the data, then you must abandon it.”

Notice how the rationalist and empiricist cannot make headway. The rationalist keeps appealing to his theory; the empiricist keeps appealing to his data. The rationalist won’t be persuaded by more data, and the empiricist won’t be persuaded by more theory. Neither side can “prove” his claims to the satisfaction of the other.

The rationalist claims to fully understand what’s going on, while the empiricist does not. The empiricist keeps his options open, just in case the data changes in the future.

A rationalist would say, “You can understand correct principles of poker simply by sitting in an armchair and thinking about them.” While the empiricist says, “You have to actually play poker to get the real-world feedback. Thinking you can deduce the principles of poker in an armchair is dogmatic and naïve.”

Logical Framework

As a rationalist, I can’t help but conclude the empiricist is dead wrong, and he’s sticking his head in the sand. You can indeed understand certain truths in poker regardless of the data, and no data will convince me otherwise. That isn’t because I’m being dogmatic. It’s because I see the logical framework behind the game of poker. And logical truths, as I keep writing about, are not open for revision; they are necessarily true. You can rationally deduce certain principles of poker for the exact same reason that you can know square circles do not exist: logic. You don’t need to “go out and test” whether square circles exist; they certainly don’t, nor will they ever.

This phenomenon – of understanding the logical framework of a topic – is not unique to poker. Every area of thought comes with an inescapable framework that you can analyze. You can call it “conceptual-analysis”, and it’s the realm of logical reasoning, not empirical hypothesizing.

Economics is my favorite example. A limited set of truths can be known with certainty; they are logically necessary given the concepts involved. There are plenty of empirical hypotheses in economics, but none of them contradict economic theory. You might even say that “theories are the presupposed conceptual frameworks into which empirical data gets added.” Specific economic data will never contradict sound economic theory – just like the specific results of poker hands will never contradict the theory of poker. The data only makes sense in context of the theory. It doesn’t matter how many times in a row pocket aces loses to 2-7 offsuit; the truth is a matter of logic.

The same principles apply to theories of physics, which is why I wrote my article on quantum physics. Simply by analyzing the concepts involved, you can know that the abused Copenhagen interpretation of quantum physics is wrong. It’s a matter of logic. (Note: in this circumstance, pure logic doesn’t tell you what the correct theory is; it just tells you what the correct theory isn’t.)

Now, there is certainly a role for “testing theories” and coming up with concepts that are empirically derived, rather than logically derived. But this is a topic for another article. The case for rationalism is most clearly made with strictly logical examples.

In certain circumstances, you can indeed understand something regardless of the data – and that doesn’t mean you’re an enemy of the scientific method. The resolution is simple: not every proposition is an empirical hypothesis, and some theories can be accurately deduced from an armchair.