In game theory, a cooperative game (or coalitional game) is a game with competition between groups of players ('coalitions') due to the possibility of external enforcement of cooperative behavior (e.g. Through contract law). Little did I know it’d be the start of a journey that would impact many different aspects of my life way beyond the game itself, as most of the fundamental principles learned through poker can be applied to your decision-making outside of the game, especially when it.

by RaBaTaJ_

Why you should learn poker and game theory:

My story is similar to that of many: I learned about the game 10 years ago (during the golden age of online poker) when some friends of mine invited me to play a home game. Although I initially thought of poker as just another game of chance akin to playing slots or roulette in a casino, I quickly came to realize that there is a lot more to it as my more experienced friends would repeatedly get the best of me during these home games, which led me to start watching videos and reading strategy books to improve my skill… Little did I know it’d be the start of a journey that would impact many different aspects of my life way beyond the game itself, as most of the fundamental principles learned through poker can be applied to your decision-making outside of the game, especially when it comes to money management and investing. Now, let’s dive into a few of these principles:

The same goes for poker hands. The variance for 100 poker hands in NLH 6max is, say, 10000 (100 squared). To calculate the variance of the sum for 10 thousand hands you have to think how many groups of 100 hands does 10000 have? Well, 10000/100 = 100. In the nal chapter, we will attempt to apply game theory to a poker game. Chen and Ankenman provide exhaustive work in their book, about how poker can be solved step by step via mathematics. From their work we will take the game theoretical approach to solving poker. We will start by extending the poker models of Chapter 5 to an actual game of poker. The game of poker is a card game played among two or more players for several rounds. There are several varieties of the game, but they all tend to have these aspects in common: The game begins with each player putting down money allocated for betting. During each round of play, players are dealt cards from a standard 52-card deck, and the goal of each player is to have the best 5-card hand at.

– Risk management (i.e. Bankroll management)

When learning about how to be successful playing poker, the first big piece of advice most people come across is bankroll management or BRM. To understand BRM, you must first realize that poker has a lot of variance: you might be vastly ahead in a given hand but there is almost always a slim chance that you will lose in the end if one specific card hits. This implies that you will sometimes lose even though you were a 99% favorite, and that you will sometimes get unlucky and lose 2, 5 or maybe even 20 such encounters in a row. THIS is variance. It doesn’t mean that you played bad or that you made bad decisions, but rather that you got unlucky. Over time you will have lucky streaks and unlucky streaks, and these will average out in the long term… It’s just the way the game goes.

Now that we understand variance, let’s get back to BRM. What is it exactly? Let’s say you are the best poker player in the world but you only have 1000$ that you can EVER use to play with. Taking your whole 1000$ on one table and multiplying your stack at an exponential rate might seem like a good idea. Surely nothing can go wrong since you’re the best player in the world right? But variance can be a bitch ;) Even if you’re the best you will lose regularly and you will sometimes get unlucky, it’s just part of the game. The correct move here is to apply BRM, which means only using a small % of your available capital for each game you play in order to reduce the risk of going broke. Using only 100$ per game would already be a lot safer, but you still run the risk of going under on a streak of bad luck. If you only allocate 10$ per game you play, then it becomes virtually impossible for you to ever go broke, even on a huge streak of bad luck. Sure it’s not as exciting and you won’t be making money quite as fast as you could, but this is the way to go to make sure you don’t go broke…

This approach to risk management translates very well to investing:

– Only invest what you can afford to lose. Once the money is on the table it’s as good as gone, which is why you should only use your “spare” cash and never invest with your living expenses or worse, borrow money to invest.

– Diversify your investments. There is always a chance, however slim it might be, that you will lose most of your investment. This is why going all-in on a specific investment is generally a bad idea (this applies particularly well in the crypto space).

Proper BRM allows you to make sure that you will come out ahead in the long run if you play well, which basically comes down to making more good decisions than bad ones. But that’s assuming you don’t let emotions come in the way of your decision-making, which brings us to our next point…

– Emotional management (i.e. Handling tilt/Positive mindset)

Nobody likes losing… In the same way we enjoy winning because of the dopamine rush, we feel bad when we lose which is totally natural. Overcoming this and avoiding tilt (irrational decisions made out of anger/frustration) is an essential skill for any successful poker player. You might play a sound game of poker and apply good BRM, but you will still lose if you let your emotions get the best of you.

After a loss, rather than being angry and frustrated, you should evaluate your decision-making. If your decision-making was good, you just got unlucky and you shouldn’t worry about it since you are playing for the long run (remember that variance teaches us that anything can happen in the short-term). If your decision-making was bad, you need to learn from your mistakes and move on. The key here is to always have a positive mindset: making mistakes is part of the learning process and should be seen as an occasion to improve. Being angry and ranting, on the other hand, rarely result in anything positive.

Again, this translates very well to investing:

– Don’t be impulsive, don’t let your emotions cloud your judgment. You should not FOMO because the price is pumping, nor should you sell because of FUD or price corrections. If you believe in a project, short-term price changes (did I hear someone say “variance”?) shouldn’t bother you.

– Don’t get stuck up on losses. You bought the top and it crashed immediately after? You sold the bottom right before a huge rally? Don’t let this bother you: what’s done is done and you just need to move on and make the best of your current situation.

– Have a positive mindset. Anger and frustration lead to nothing. Yes you could have bought in 2009 when you first heard about it, hindsight is always 20/20. Stay positive and keep learning/improving yourself.

The good thing about all this is that it goes way beyond poker or investing. Being aware of your emotions and how they affect you, learning how to handle losing even when you were “supposed” to win, etc… All this can tremendously help you in all aspects of life by making you less impulsive and more rational in your decision-making. Now, this leaves us with our last fundamental principle of a sound poker strategy:

– Basic stats and probabilities (i.e. Expected value/Odds)

To become an accomplished player, you will inevitably have to learn about these simple mathematical tools that poker players use all the time in their decision-making process, such as odds and expected value. To make it very simple, the expected value (EV) of any bet is (REWARD * WinRate – RISK), meaning that if you can bet 1000$ with a chance to win 10k$ half of the time, your EV is (10000*0.5)-1000 = +4000$. Obviously these are great odds to take as long as you have enough capital to overcome variance. But things would be very different if the odds of winning were only 5% as your EV would then be negative (10000*0.05)-1000 = -500$. Now this is clearly a bet you should not take…

Now that you know probabilities, statistics and game theory are useful decision-making tools in poker, guess what? They are also extremely useful in investing! Even better, the study of game theory with problems such as the “Byzantine generals” or the “Three prisoners” has been, along with cryptography, the foundation on which blockchain technology was built, enabling the trustless and decentralized services that are about to revolutionize our world…

Assuming this was enough to pique your interest and make you want to dig deeper, I’ll just add that just like the other topics we discussed and as you might have guessed, this translates very well to investing and also to pretty much anything in your life:

– Learn how to break down complex situations. Logical thinking paired with a statistical approach will help you break down any complex problem into several easier problems, making the whole thing a lot easier to approach/comprehend.

– Base your decisions on a methodical and rational approach. List every possible outcome along with its associated upside/downside, estimate the probability of each outcome to occur and make the best decision based on the information available.

My point here is that risk management, emotional management and statistics/game theory are all awesome tools that you should definitely add to your arsenal. Not only will it improve your money-management and investing, it will also be beneficial to your decision-making and to your life in general. Of course poker is not the only way to learn about these, but I personally found it to be the best practice ground to refine and improve them, which is why I strongly encourage you all to try it out and study the game.

I hope you enjoyed the article, and I wish you all a happy 2021 bull run! May we all come closer to retirement and financial independence!

TL;DR:more than a game, poker is a school of thought. It teaches you to be reasonable, to assess the risk of every single choice you make, to overcome you emotions, to play the long game rather than the short game, to make informed decisions, etc… This has made me a lot wiser in every aspect of my life, which is why I strongly encourage to try it out and read about poker strategy.

The movie A Beautiful Mind (Full Screen Awards Edition) beautifully describes the life of John Nash, who is very famous for his works in the area of game theory. I suggest you read more about him (Biography of John Nash) and especially understand what a “Nash Equilibrium” is (Wikipedia Article about Nash Equilibrium). Not only is the topic and the person John Nash extremely interesting, but it also widens ones horizon and – after all – will dramatically increase your understanding of poker. I believe this is crucial to improving. I don´t have a very high opinion on learning tricky lines, how to play 2nd pair in reraised pots. You´ll learn some easy guidelines that will do the job for a certain time, but following rules without a deep understanding of them (besides some poker idol saying “that’s fine”) will not get you anywhere long term.

I cannot stress often enough the importance of understanding game theory. I´m no math expert, nor any sort of “feel bs player”, I think my biggest strength is “thinking like game theory”. It’s not about exact numbers (unless you play vs Bryce Paradis), it’s about knowing what you´re doing. What if, then, but if this, then what, but if he does this against, how do i, considering that…
Almost every reader has probably heard about game theory, and more specifically in poker about “game theoretic optimal” (=GTO) play. It has been discussed and talked about a lot. Whenever the term is used, we like to think we´re talking about an extremely advanced concept.
I don´t agree with this. Game theory is not only extremely simple to understand, but also very intuitive. With “simple” I do not mean that everybody can understand it within seconds, but more that every step to understanding it is comprehensible – at least in regards to poker. Before we get deeper into the topic, let us define some terms that will be frequently used. The definition is rather simple and if you´re looking for something to use in your doctoral thesis, I´m not going to be a great help – your search slave Google can do this for you.

Game theoretic optimal play (= GTO):

Does NOT mean most profitable play in a certain situation. It simply means to make a decision that will show a profit – no matter what your opponent does (profit here can also mean to lose as little as possible, i.e. when playing in the Blinds). The beauty of GTO play is that – if exercised perfectly – your opponents can´t do anything about it. If you bluff with a GTO frequently, they will usually either fold too much or call too much, both way netting you with a profit.

Exploitative play:

You´re taking advantage of a weaknesses of your opponents, despite doing a GTO mistake yourself. One common leak used to be that players would cbet 100%. This was exploiting the fact that people folded too much to cbets. The trend changed to people checkraising 80% of the time, because players would fold everything that couldn’t beat 2 pair. This is exploiting another tendency. Exploitive play is NOT optimal.

Maximizing profit:

This is what we want to do while playing poker. Maximizing profit means, making the best decision that will profit the most. In this decision every current and factor is already included. If we can exploit a player, we will play exploitative. If we play against a very good player, we play GTO (practically speaking, as close to GTO as possible).

Practical Examples:

You have a soccer/basketball game and the opposite team always attacks you by using a key player. Now you can exploit this by covering him up with 4 people at once. Since the team will still try to involve him in their attacks every time, you will have no problem beating this team. The “flaws” of this strategy is pretty obvious, since you open up yourself for a deadly attack, because 4 players can´t defend where they usually defend.
This is EXACTLY what exploitative play is. You´re opening up yourself, because your opponent has a big leak and will not take advantage of you. This strategy works, until your opponent finds out.
The two described “methods” only worked because the opponents were rather unaware. What if your opponents start to counter-attack you? Are you prepared to fight back with counter-exploitation and with the ultimate weapon – GTO ?! Or does your understanding stop after “being checkraised”. This situation occurs every time you “don´t know what to do”. This happens exactly when you learn to “not call checkraises with one pair”. It’s the reason why it is so dangerous to implement “rules” without understanding WHY.

When to err on the side of exploitative play:

Your opponent is clearly very bad. Bad means, he knows exactly what he is doing. Lets say we are only raising on the flop with 2pair or better, but at the same time a huge calling station.

No-Limit Hold’em, $20.00 BB (2 handed) – Hold’em Manager Hand Converter from HandHistoryConverter.com

BB ($2887)

Hero (= Weaktight Station) (SB) ($3184)

Preflop: WEAKTIGHT STATION is SB with 3, 3

Hero bets $30, BB raises $120, Hero calls $100

Flop: ($280) 3, 10, 9 (2 players)

BB bets $180, Hero raises $680

Let say BB has AA:

Game Theory Applied To One Card Poker

If BB plays GTO his play is either to reraise all in or to call (more likely reraise all in). Folding AA in a reraised pot is criminal. If BB is folding AA to our raise, he is folding approximately 80% of his range. This again means that we *could* be raising with any hand and exploit him. For that reason, he is simply never folding those AA, no matter what.

Game Theory Applied To Poker Chips

If BB plays exploitative, he will have made his decision very quickly. As we described, we are only raising 2pair or better on the flop, but call a lot. His bet with AA is very good, but after we raise, it’s time to release. He is exploiting us extremely by folding. If we knew that he is folding AA, we would be bluffing any two cards (=ATC).

If we try to maximize our value, we will have to call in this spot. We know that our opponent will fold way too much and he will continue to put in more money with a lot of worse hands

When to err on the side of GTO (Game Theoretic Optimal) play:

In the same example, if our opponent knew that we can be raising any Top pair, flush draw, straight draw and gutshots or total air, he of course should not even think about folding AA. Also, he should be going all in with a wide variety of hands.

More examples and articles about this topic will follow. For today Ii´ll keep it to that.

Bill Chen has wrote an amazing poker book. It probably is the most “scientific” book to this day. I have to warn you though, it is not easy material. Nevertheless invest the couple bucks, and be patient with yourself. I am the owner of this book for over 1,5 years now, and I will openly admit that I haven´t finished it. I treat this book like an exercise book. Every time I want to know more, I´ll devote some hours and dig deeper. It will increase your understanding. Again, it’s pretty dry and if you´re not completely, seriously interested in this topic, save yourself guilty feelings and the money. You shouldn’t feel guilty at all. The book is there to help you, and you choose when. If you don´t at least play NL200, I also advise you to save the money for later.

Game Theory Applied To Poker Strategy

The Mathematics of Poker by Bill Chen and Jerod Ankenman