Poker Is All About Heuristics, Not Math
By: Stian Pedersen
Tags: Mathematics, Games, Data Science, Gambling, Poker

Poker Is All About Heuristics, Not Math

Beginning players are misled about how to become great poker players. There’s very little complex mathematical analysis. The pros rely on heuristics.

Many beginning poker players who become obsessed with learning the game often fall into the trap of delving too far into the theoretical side, ignoring the practical value of playing.

Beginners who get past the psychological aspect of the game eventually fall for the mathematics of the game, never to come out on the other side, as real players. It’s a classic case of paralysis by analysis.

We can use math to improve our general understanding of the game and, subsequently, our play, but the time put into the math is often not very rewarding compared to the time put into playing.

I’ll freely admit that I don’t understand all the math that goes into all the various software that calculates ranges, expected value, and game theory optimal strategy.

It’s some form of probability calculus, but I have no idea how to do any of it. Neither do any of my friends who are professional poker players… But they know how to play the game.

I have, however, discovered that an intricate understanding of math is not necessary to become a great poker player. It’s so obvious, you’ll think I’m stupid for even saying it…

The best poker players are not math PhD's.

Dan Bilzerian, probably the most notorious poker player in the world right now. Not a mathematician.

You’re more likely to find two polarities:

1) Gamers-turned-gamblers and other nerds who are fascinated by the game, and want the freedom that poker gives them.

2) Gamblers who enjoy snorting lines of coke off of hookers’ tits and asses, and shooting guns in the middle of the desert.

Howard Lederer, nicknamed The Professor, also not a mathematician. Actually not a professor at all. He was sued by the DOJ in 2011 for being part of a Ponzi scheme that almost crippled the poker world.

A PhD in math is more of an obstacle to becoming a great poker player than a help.

The amount of play required to become a winner is so big that there is no chance that anyone who wanted to become professional poker players through a mathematical understanding of the game would actually have time to do it.

How To Use Math To Exploit The Meta

Math does a great job at explaining poker in retrospect, but it removes all the external factors that influence the decision. Math kills the human aspect of the game, which makes it extremely valuable for analysis. It also makes it very dangerous for setting strategy. Let me explain.

When you can use math to identify holes in your opponent’s game, you can gain an edge in the long run. If you know you’re playing your opponent multiple times, this type of analysis can be extremely valuable. You can use this type of analysis on a large scale as well.

You can analyze a pool of players, and see what their ranges look like in certain situations. If, for example, you realize that people overreact to cards that complete draws, then you can use that knowledge to your advantage.

If enough people have a weakness, you now have a read on the current meta (a so-called population read) that allows you to exploit a vast pool of players.

The only way you can really figure this out at scale is through data analysis. The other way is manual labor: analyzing hand histories, one-by-one, for hours on end. At that point, you’re better off playing than analyzing.

How Great Players Exploited The Meta During The Poker Boom

A lot of money has been made by exploiting the meta. Back in the early 2000s, players were very timid. Everyone and their mother folded to three-bets, and everyone played face-up against continuation bets. The people who made money were the ones who found this hole in the meta, and exploited the hell out of it.

Three-betting became all the rage, continuation betting flops became all the rage. Whenever these good players got called, they stopped firing. If someone called, it meant they were on a draw or had a pair.

Another hole in the meta was that no one ever folded top pair. If one of these good players could beat top pair, they would pound it as hard as they could.

Today, it’s a lot harder to find these glaring weaknesses. The meta of 2008, the so-called “solid, tight aggressive” strategy had a lot of holes that have been exploited by great players.

In order to survive, winning players have had to adjust so that they don’t get exploited as easily. It’s a lot harder to find holes in the meta today, and they’re not as profitable as they once were.

What Gives You An Edge In The Toughest Games?

The world of science is very quiet compared to the highly volatile world of poker. Although scientists compete for citations and jobs, it’s nowhere near as emotionally taxing a downswing. Professors never come home from work with less money than they left with.

Patrik Antonius doesn’t tilt. He’s too good-looking.

Of course, the rigorous logic that comes with mathematical thinking is extremely important in poker, but logic is not reserved for mathematicians.

When skill is not the determining factor between winning and losing, emotional control, risk tolerance and whatever combination of other skills play a much more important role for the winrate of top poker players.

Several high stakes pros have told me that their edge in the very toughest games actually comes from tilt control. These players stay in games that, on the surface, look incredibly bad, because one great player is prone to losing control and wasting a lot of money.

If a loose cannon starts tilting, a bad game quickly becomes a good game.

You Can’t Do Probability Calculus On Ten Fingers

Mathematical analysis is very useful for figuring out how to play, but it does not equip you with the all-encompassing skills you need to become a full-time professional.

The theoretical knowledge makes for great journalism, entertainment, and post-game analysis. However, when you’re at the table, you don’t have time for math. You’re playing by feel.

You are left to your own devices, and under the pressure of time and potential loss of money, theoretical knowledge takes a hike. You don’t have access to an excel spreadsheet, you don’t have access to a graph calculator, nor do you have access to paper that lets you solve equations. You’re playing by feel.

Mike Matusow is famous for his blowups and ‘fuck you plays’. Granted, he lost a lot of confidence after being cheated out of millions of dollars playing against a superuser (an opponent who could see his cards), but his reputation remains.

If you’re on a losing streak, you’ve angered the poker gods, and you don’t have any emotional control, you start making ‘fuck you plays’.

Logic goes out the window when emotions take over. We’re already mathematically handicapped, and when emotion clouds our reason, we can’t do math. We become especially bad at probability calculus on ten fingers.

We’re not designed for probabilistic thinking (with some exception potentially made for frequencies). Those us that think we can even come close to playing game theory optimal no limit hold ’em suffer from an idealistic delusion. The game is simply too complex for any human being.

Game Theory Optimal Play: The Sales Promise Of The Century

Most players have gotten very good using a simple mix of mathematical concepts and an understanding of how the game is played. In no limit hold ’em, all you need is basic probability and gambling math, such as pot odds, implied odds, expected value, and combinatorics. Anything beyond that is mostly for poker researchers who develop tools that players use to improve.

Here’s the thing though. If you’re developing software for poker, you’re not a poker player. You’re a poker entrepreneur. Nothing wrong with that. Just don’t confuse the two.

The holy grail of poker is game theory optimal play. The promise of game theory optimal poker is one of the greatest sales pitches ever to have been written. There is a notorious company that sells poker training software that’s trying to take advantage of this lurid idea right now.

Game theory optimal strategy makes sure you never lose, and any adjustment that your opponent makes (that is not game theory optimal play) makes sure that he loses. You’re not always making the most you could ever make, but you’re never losing. And people hate losing.

Unfortunately, the game is too complex for us to memorize the exact strategy for all of it. There are 1,326 combinations of starting hands. There are 117,600 possible flops. 5,527,000 possible boards come the turn. When you’re on the river, you’re looking at 254,251,200 possible combinations of boards. Good luck remembering even one percent of what to do on those boards with one of your 1,326 combinations.

How Do We Deal With Being Mathematically Challenged?

We use rules of thumb, also known as heuristics. Heuristics are a set of rules that help us increase the probability of solving a problem. Great poker players are really good at using heuristics.

This is especially true if you play online, because the time pressure is so intense that you often don’t have time to give every single aspect of a hand the time it requires.

This is where off-table analysis becomes extremely useful. Analysis allows you to understand the game at a much deeper level, and lets you develop some very advanced heuristics.

For example, when the pre-flop raiser is out of position, and bets a wet flop, then check-calls the turn, he’s probably check-calling the river if the board remains unchanged.

Here, post-game analysis has been condensed into a heuristic that allows you to make quick decisions. If a lot of players end up doing this, and it becomes part of the meta, you have a meta-read that you can exploit.

The incredibly likable Sammy Farha doesn’t like math. In an interview with Bluff Magazine, he said: “Some pros, they play certain hands against me, and they talk about the math, and I think, ‘You shouldn’t even be in this hand. You contradict yourself.’”

Notice, though, that the simplified analysis I just gave is not rooted in equations and complex mathematics.

Instead, it comes from the fundamentals of the game, which only requires basic high school math.

However advanced your analysis, your focus should always be on developing heuristics for playing the game.

Heuristics That Matter: No One Ever Has Anything

In flop games like no limit hold ’em and pot limit omaha, an incredibly well-known heuristic is the “rule of four and two”.

You multiply your total number of outs by four on the flop or two on the turn to get an approximate percentage of your chances of hitting a draw. Add five percent to your chances if you have a backdoor flush draw.

Subtract that number from 100 if you have the best hand right now. Very useful when you’re facing a “Do I have the odds?” decision.

These heuristics are much more crucial to the development of good, pragmatic play than the incredibly complex calculations required to find your optimal range, the equilibrium point of a calling range, or the optimal bet size given your range on a certain board at a certain point in the hand.

In 2016, Aaron Jones won $5,000,000 in the DraftKings Fantasy Football World Championship. Before that, he was a professional poker player and built his reputation as an outspoken poker coach.

Complex math in poker is only useful to players when they are boiled down to simple heuristics.

The bright side is that the more people we have digging into these problems, the more solutions we will find.

If you’re one of these poker scholars, just remember that any discovery you make is only useful as a heuristic.

And it should be as simple as Aaron Jones’ famous theorem: