Game Theory – What it is and how to apply in Poker

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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:

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.

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.

The Mathematics of Poker by Bill Chen and Jerod Ankenman

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