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A Basic Guide to Game Theory

Jun 25, 2013  |  Posted by PokerSnowie  |  4

Background

Game Theory was developed during the Second World War by John von Neumann, a mathematician, and Oskar Morgenstern, an economist, and developed by US mathematician John Forbes Nash Jr. In a 1951 article on Non-Cooperative games, Nash stated that at least one ‘Nash Equilibrium’ is present in any mixed strategy game with a finite set of actions. In relation to poker, it means that there exists an equilibrium called game theory optimal (GTO).

Nash Equilibrium

A Nash Equilibrium is defined as a situation in which players’ strategies result in the best possible decisions, taking into account the decisions of others. Taking the game of poker to the stage where players are in Nash Equilibrium results in maximum expected value (EV) play for every decision the player makes assuming he faces perfect opponents. The principles of Game Theory detail the process via which you reach Nash Equilibrium and hence a more profitable level of play.

Strategy

Game theory is an optimised strategy which is intuitive and simple to understand. It is a purely mathematical model that is independent of opponents’ skill and playing style. In the simplest terms, GTO strategy provides the best decision at a given moment for a poker player by taking into consideration what your opponent's best strategy is.

Example

Taking the example of bluffing: should you bluff for £50 when attempting to win a £200 pot? If you always bluff, your opponent should always call with his semi-weak hands. And if you never bluff, your opponent should never call with his semi-weak hand. Of course the player shouldn't bluff all of the time, but must bluff some of the time to improve his EV. But more importantly, he must consider his opponent's options. If he has a weak hand does this mean a bluff will succeed? What if he raises? Should he just give him the pot, or should he re-raise? Through Game Theory, players can determine how often they should bluff, and how often they should take any other poker actions. Following GTO strategy allows players plenty of opportunities to collect positive EV from opponents that make GTO mistakes.

Advantages & Disadvantages

Critics have argued that Game Theory is very defensive, and prioritises not losing over attempts to win. It’s true that Game Theory does not necessarily mean the most profitable play in a certain situation: it simply means making a decision that will show a profit – no matter what your opponent does (profit can also mean losing as little as possible, e.g when playing in the Blinds). Opponents are still liable to make mistakes, meaning a loss in EV, while those employing a GTO approach will never hand out EV to their opponents.

Game Theory centres on maximizing profit, and making the decision that will profit the most. To that end it is unexploitable, and can be viewed as being without risk. The one acknowledged deficiency of the strategy is that it doesn’t maximise profit against weak opponents. When facing such opponents, alternative strategies (such as Heads-Up Displays, or HUDs) can yield greater returns.

 

Comments

Mike (not verified)

Sat, 03/01/2014 - 16:15

I have just started using PokerSnowie but it says I am making pre-flop errors whenever I set mine - vene whne I have the correct implied odds - why is this ? Is it GTO related ?

Christopher J. ... (not verified)

Sun, 03/16/2014 - 13:46

It's just what Snowie has found to be the EV of the situation over however many times it has been in this situation, beyond that, Snowie doesn't 'know' why (or maybe it does, but that's best left for philosophic ponderings or maybe, even better, an episode of the Twilight Zone), nor do any of those who developed Snowie. Instead, do your best to figure out why it could be negative EV by playing around with different variables in the scenario, as well as using various other poker software tools (Equilab, Flobzilla, Cardrunners EV, etc), and from there you can figure out if it's an adjustment you want to make to your game or not (most of the time the negative EV is pretty small from set mining, but when it's not--there are some very logical reasons for why that spot may be a bad idea, speaking in terms of GTO). First, keep in mind--at all times--that Snowie is playing (or approaching) GTO, and not an exploitative style, and so it is thus playing in a way that assumes its opponent is playing GTO as well. Some players will happily call all-in, while deep, with A2o on an A38 flop, but not Snowie, nor would it go all-in with 33 on that flop hoping it's up against such a calling station. Some things to consider adjusting in the scenario: set mining when it's only you and the raiser (e.g., they are UTG, and all fold to you in the BB, or any time when you close the action as opposed to having people left to act after you); set mining when deep stacked (go nuts; believe it or not--or better, test it--things change when you are 5000BB deep vs. >1,000,000BB!!) vs. short stacked; set mining vs a wide range, and then vs. a bottom capped range; set mining when you have position vs. OOP; facing a 3bet or 4bet (again with varying stack sizes); after having called a raise, you see a 3bet, and everyone else folds to you, and you close the action. Some things to think about: What range is Snowie expecting villain to have in the situations when you plan to set mine? What is villain's range, and how often is she likely to hit the flop hard enough to make or call a decent bet? How often will their range make a hand by the river that is behind our set, but that they are still willing to stack off with us with? What effect would raising have on all the above? This is my first day playing with Snowie (after having read a lot about it), and I noticed the same thing about set mining, which caused me to stop and really work on just why it would suggest what it is suggesting ... very eye opening! And, I believe working on it yourself (the above are merely starting points, points of research I've come upon, but I'm certain there are MANY more questions and situations to be analyzed!), will give you tremendously more insight than if I were to give you a snapshot of some of the things I've found in analyzing the same situation. That said, once you have delved in and come to some conclusions, insights, and confusions, then it makes sense to exchange notes and help each other go even further down the rabbit hole!

Christopher J Valade (not verified)

Fri, 03/21/2014 - 09:52

It's just what Snowie has found to be the EV of the situation over however many times it has been in this situation, beyond that, Snowie doesn't 'know' why (or maybe it does, but that's best left for philosophic ponderings or maybe, even better, an episode of the Twilight Zone), nor do any of those who developed Snowie. Instead, do your best to figure out why it could be negative EV by playing around with different variables in the scenario, as well as using various other poker software tools (Equilab, Flopzilla, Cardrunners EV, Odds Oracle, MATLAB, etc), and from there you can figure out if it's an adjustment you want to make to your game or not (most of the time the negative EV is pretty small from set mining, but when it's not--there are some, at least IMNSHO, very logical reasons for why that spot may be a bad idea, speaking in terms of GTO). First, keep in mind--at all times--that Snowie is playing (or approaching) GTO, and not an exploitative style, and so it is never looking to exploit poor play, or anything like that. Some players will happily call all-in, while deep, with A2o on an A38 flop, but not Snowie, nor would it go all-in with 33 on that flop hoping it's up against such a calling station. Some things to consider adjusting in the scenario: set mining when it's only you and the raiser (e.g., they are UTG, and all fold to you in the BB, or any time when you close the action as opposed to having people left to act after you); set mining when deep stacked (go nuts; believe it or not--or better, test it--things change when you are 5000BB deep vs. >1,000,000BB!!) vs. short stacked; set mining vs a wide range, and then vs. a stronger range; set mining when you have position vs. OOP; facing a 3bet or 4bet (again with varying stack sizes); after having called a raise, you see a 3bet, and everyone else folds to you, and you close the action. Some things to think about: What range is Snowie expecting villain to have in the situations when you plan to set mine? What is villain's range, and how often is she likely to hit the flop hard enough to make or call a decent bet? How often will their range make a hand by the river that is behind our set, but that they are still willing to stack off with us with? What effect would raising have on all the above? This is my first day playing with Snowie (after having read a lot about it), and I noticed the same thing about set mining, which caused me to stop and really work on just why it would suggest what it is suggesting ... very eye opening! And, I believe working on it yourself (the above are merely starting points, points of research I've come upon, but I'm certain there are MANY more questions and situations to be analyzed!), will give you tremendously more insight than if I were to give you a snapshot of some of the things I've found in analyzing the same situation. That said, once you have delved in and come to some conclusions, insights, and confusions, then it makes sense to exchange notes and help each other go even further down the rabbit hole! So I will be looking forward to discussing this with you, or anyone else who does some analysis.

Mike (not verified)

Sat, 04/05/2014 - 18:27

Thanks Christopher - you make some very good points which I think begins to explain why Snowie was finding my set mining -EV...I will go away and do some analysis and share my findings...