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As new depths of poker strategy continued to be discovered, Texas holdem
tables sound more like science labs than the scene of a simple card game.

Thinking players in today’s game casually toss out references to balancing or
merging their hand ranges, applying an “exploitative” approach to take advantage
of “suboptimal” strategies, and of course, integrating “game theory optimal”
plays into their arsenal.

Perhaps more than any other advanced strategy concept, the notion of game
theory optimal play – better known as GTO – has seeped into the mainstream poker
consciousness. Players of every skill level have at least familiarized
themselves with the idea of making their own game GTO, but as with any other
ubiquitous term, the exact definition of poker’s newest buzzword differs
depending on who you ask.

The steady advancement in the way players tackle Texas holdem problems is
only natural, as the Poker Boom of 2003 to 2006 prompted millions of thoughtful,
intelligent, and analytical individuals to take their talents from the classroom
to the card room. The merits of that choice are debatable on the individual
level, but what can’t be disputed is how the new generation of poker students
ultimately became masters of the field.

Eschewing traditional advice about “playing the man, not the cards,” young
poker players today focus their minds on the mathematical underpinnings of Texas
holdem gameplay. By using hand distribution to equity calculators like the Poker
Stove product, basing every possible decision on the all important variable
known as expected value EV, and scaling back the standard opening bet from three
times the big blind, modern Texas holdem experts have fundamentally altered the
game’s very foundation.

For beginners just now entering the world of Texas holdem, or even old hands
who simply struggled to keep up with the game’s accelerating advancement,
hearing smart and savvy opponents reference ideas that sound more like calculus
homework than a card game can be quite intimidating. It’s hard enough figuring
out what to do when you get four bet holding pocket jacks, so the thought of
learning about intricate game theory constructs and the higher level reasoning
behind GTO plays can be daunting to say the least.

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With this page, we don’t purport to be PhD holders or even Texas holdem
experts, but rather recreational players like yourself who simply wanted to
learn more about game theory as it applies to poker. In keeping with the
instructional theme, we’ll offer a syllabus of sorts, starting out with a basic
glossary of the key terms and concepts you’ll hear repeatedly during any
discussion on GTO play. Next up you’ll find a section detailing several common
examples, written from the perspective of a poker player, that help to
illustrate the technical terms described earlier. From there you’ll find a list
of applicable resources – written or developed by successful high stakes
professional players and game theory experts – through which you can pursue an
advanced education.

Glossary of Game Theory Terms

Before we move on to the descriptions, it’s important to discuss what the
concept of game theory really means.

According to Roger B. Myerson, whose introductory textbook titled “Game
Theory: Analysis of Conflict” was published by the Harvard University Press in
1991, game theory can be defined as “the study of mathematical models of
conflict and cooperation between intelligent rational decision makers.”

As you can see, this definition doesn’t mention anything at all about poker
or Texas holdem. That’s because game theory is applicable to any game or contest
which involves decision making on the part of players combined with access to
partial information. Additionally, the ideas put forth by game theory experts
have also been co opted for use by economists, political scientists, biologists,
and several other fields of study. Thus, while the study of game theory is
predicated on the various rules and procedures used to govern classic games like
Texas holdem, the ideas that emerge from game theory investigation are widely
applicable across a diverse range of subjects.

Although game theory wasn’t codified as a field of study until the 1920s,
evidence of GTO approaches to basic card games can be found dating back to the
early 1700s.

In 1711, Charles Waldegrave wrote a letter to his brother outlining a
“minimax mixed strategy” to the simply two player card game known as Le Her.

In 1913 a German mathematician named Ernst Zermelo developed “Zermelo’s
Theorem,” which states that

“In any finite two person game of perfect
information in which the players move alternatingly, and in which chance does
not affect the decision making process, if the game cannot end in a draw, then
one of the two players must have a winning strategy.”

As you might suspect, this
long passage was used by Zermelo to describe chess, which he successfully proved
to be a “strictly determined” game from a strategic sense.

Throughout the 20th century, mathematicians and logicians like John von
Neumann, Oskar Morgenstern, Merrill M. Flood, Melvin Dresher, and John Nash each
contributed fundamental theories and postulations to the field of game theory
study.

For poker players with an educational background in advanced mathematics – of
whom there seemed to be an endless supply during the Poker Boom – learning the
lingo of game theory and applying it to their favorite game proved to be a
highly beneficial proposition. These players were able to expand their lines of
thinking beyond the most basic constructs – what do I have or need, what does my
opponent have or need, etc. – to turn a seemingly simple poker hand into an
exercise in statistical modelling and probability based prediction.

But for the rest of us, the laymen at the table who haven’t memorized reams
of mathematical formulas, diving deeper into the subject of game theory study
can present a firm barrier. The average person can only take so many
abbreviations and hypotheticals before their head begins to ache, so breaking
things down to their basic meaning is a helpful way to begin.

Take a look below for a comprehensive glossary of essential terms and
concepts used within the world of game theory:

Exploitable Strategy

Any strategy that offers a reduced expected value EV,
compared to GTO strategy, when playing against an exploitive strategy. Any non
game theory optimal GTO strategy is, by definition, an exploitable strategy.

Exploitive Strategy

Any strategy that offers an increased expected value EV
than a game theory optimal GTO strategy, when playing against any particular
strategy. Any non GTO strategy that counters an exploitable strategy better than
a strictly GTO approach is, by definition, and exploitive strategy.

Game Theory Optimal GTO

The strategy that offers the highest possible
expected value EV when an opponent always applies an optimal counter strategy.
The classic GTO strategy example concerns the zero sum hand game known as “Rock,
Paper, Scissors.” In this game, the GTO approach involves selecting randomly
between rock, paper, and scissors while using an equal distribution. This
strategy provides the highest level of EV, at 0.50 percent equity, against any
opponent strategy that consists of all rock, all p

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