Saturday, March 1, 2014

Poker is evolving

Over the past few years, the level of play in No Limit Hold’em, particularly online, has increased dramatically.  As Phil Galfond put it, “Five years ago, I was one of the top HUNL players in the world.  You can take any excellent $5/$10nl regular from today, put him in a time machine, and he’d have beaten 2009 Phil”.  

Many of the weaknesses of the players of the 2000s were a result of only taking certain actions with a very specific set of hands, thus making it very easy for a competent opponent to dissect and destroy their strategy.  As a result players begin to work game theory concepts into their play and now it is common to find even micro stakes players discussing concepts like balancing ranges, playing with and against capped ranges or polarized ranges, when even just a few years ago these ideas were rarely discussed, and poorly understood.

However, from a game theory perspective the discussion around trying to “balance your range” and play “GTO poker” is still in its infancy and game theory concepts are often being applied to poker non-rigorously or incorrectly.  

Even the phrase GTO is never actually used in formal game theory and is something that was pulled out of the ether of poker forums and people (and companies) get away with using it inaccurately in all sorts of situations.  In most cases, no one actually knows what the “GTO” (game theory optimal) play in a given situation is so people throw the word GTO around without bothering to actually prove that the strategy they are advocating is GTO which leads to a lot of false claims and misinformation.

What does GTO mean?

In a mathematical sense, a set of GTO strategies is a Nash Equilibrium, or as wikipedia defines it, a set of strategies “in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.”  In general, finding Nash Equilibrium strategies in complex games is extremely difficult, but verifying them can actually be quite easy (I’ll get into the details of that in another post).  Currently, the only poker situation where Nash Equilibrium strategies are easily found and widely used is in constructing linear shove fold situations late in SnGs and tournaments when the players stacks are very short.

In a practical every-day sense, in poker, creating GTO strategies involves considering how you play a group of hands rather than an individual hand, and looking for synergies between specific hands that make it as difficult as possible for your opponent to react properly to your decisions, even if they know exactly what strategy you are employing.

The simplest example of this type of hand synergy comes up in “nuts or air” situations with a polarized range (when the only hands you might have are extremely strong hands or extremely weak hands).  If you were to only ever bet with the strongest hands hoping to be called, a clever opponent would always fold, while if you only ever bet with your weakest hands as a bluff, a clever opponent would always call.  

However if you instead bet with a properly weighted group of strong hands and weak hands you put your opponent in a difficult position.  By folding they risk losing a big pot when you are bluffing with a weak hand and by calling they risk paying you off when you have a strong hand.  By betting your weak hands you can increase the expected value of betting your strong hands, and vice versa.  This is what building GTO ranges is all about.  This simple example is discussed in depth via the “toy” AKQ game The Mathematics of Poker which is a must read.

Why GTORangeBuilder?

There are millions of other ways to build ranges that synergize different levels of hand strength to increase your EV that are less intuitive than the simple polarized range case of the AKQ game and the linear shove fold ranges that SnG players use, but until now, no one has really had to tools to effectively build and analyze them.

GTORangeBuilder is designed to solve this problem by making it possible for anyone to compute Nash Equilibrium strategies for almost any river situation so that we can transform the discussion around GTO poker from hand waving and “toy” examples to something concrete, exact, and verifiable that can be applied at the tables to increase your win-rate on a daily basis.

GTORangeBuilder lets you define a river scenario by entering hero and opponent hand ranges, stack sizes, and some bet sizing assumptions.  GTORangeBuilder will then compute equilibrium strategies for both players for every possible decision in the hand.  These strategies are game theory optimal and are presented in a way that makes them mathematically verifiable. 

Right now, its up to you to do your own hand reading and range balancing up to the river, but from there GTORangeBuilder can determine optimal play that requires no hand reading, or psychological guessing games and if you play GTORangeBuilder strategies it guarantees you a given expected value against any opponent on earth.

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