Theory and practice of playing no-limit Texas hold'em. Poker theory Poker theory

For an avid participant in card competitions, poker odds are one of the most exciting aspects of the entire tournament.

For those who play poker regularly, it will not be difficult, as they say in school, to memorize such possible options developments of events.

Those gambling participants who are familiar with the concept of probability theory from university will be able to perfectly apply the acquired knowledge in practice in poker.

Calculations can be performed either manually or armed with special poker programs, of which there are a great many offered today. But, one way or another, you need to think and reason independently, analyze and make decisions, because not a single program will help the brain develop and improve.

Below you will find information that will help you calculate the probability in poker in order to win. After time has passed, it is important to keep all the presented data in your head so as not to depend on tables on electronic or, for example, paper media.

This is the only way to establish the fact that success is guaranteed!

Poker odds are a measurement from zero to one hundred percent. It shows the frequency with which one or another development of events can occur during a poker tournament.

Understanding this term and its meaning provides the poker player with the opportunity to realistically assess the situation, analyze the perspective of each action, which can be performed in a specific scenario.

A poker odds chart is a useful guide to help you figure out what your pot odds are in poker. It is this data that will help you make the right decision during a card competition.

Variations of tables

There is no single standard described in one table, armed with which you could consider yourself the “master” of poker and win uncontrollably. Everything would be too simple and boring.

Poker is a canvas of mathematical calculations. Which, as a result, can answer the question whether it makes sense to take risks or whether it’s worth folding. The calculation of probability in poker depends on how the hand went, and the table is formed based on this.

The following probability variations are known:

Preflop;
with traditional preflop exposures;
forming a combination with a pocket pair;
with two card elements in the same suit;
with 2 cards of different suits;
with two unpaired cards on the flop in poker.

And this is not the whole list. There is also a table of poker probabilities called “flop textures”. This information will be useful to the participant preflop. Here you can get acquainted with the possibility of flops of a specific structure.

So, collect preflop:

Three cards of the same rank have a probability of 0.24%;
Combination with a pair in a set (for example, 7-7-2) - 17%;
Three cards of the same suit - a little more than 5%;
2 suited cards - 55%;
“Rainbow” combination (complete diversity) - 40%;
3 by increase (one after another) - 3.5%;
2 ascending - 40%;
The absence of cards by seniority in order is more than 55%.

Based on the above data, which is presented to the participant in the form of a table, you can independently, having really assessed what you saw, understand that there is a high probability of hitting a paired flop, but at the same time, a flop with 3 cards of the same rank is often an exception rather than a regularly repeated rule.

Armed with the table, you can study the probability of combinations in poker for a specific hand and evaluate your own chances of success!

The prospect of improving your own situation?

There is an answer to the question posed, but it is difficult to call it unambiguous. It all depends on the distribution. The theory of probability in poker in the matter of improving the dropped combination also appears in the form of tabular data.

Below we present prospects in percentage terms that will answer the question, what is the probability of combinations in poker to improve a combination in poker from flop to turn:

set in poker up to Full Haus - 15%;
Two pair to Full House Combination on the turn - 8.5%;
a combination of a flush in poker before a Flash on the turn - 19%;
open-ended straight draw to straight on the turn - 17%;
gutshot to straight on the turn - 8.5%;
a pair to trips on the turn - about 4.5%;
a pair to one of the 2 over cards on the turn - about 13%.

Calculating the probability in poker of strengthening and improving your own positions during the competition makes it possible to make a decision about whether to leave the game or continue to fight for the pot, because the tabular information indicates the real prospects of winning.

More about probabilities

The table of probabilities in poker, based on which the prospect of improving the set from flop to river is viewed, appears in the form of the following prospects, expressed as percentages:

Set - full house/river - 33%;
2 pairs - Full House/river - 17%;
Flush draw - flush/river - 35%;
Runner-runner draw - flush to river - a little more than 4%;
Double-sided straight draw - straight to the river - 17%;
Pair to one of the 2 overcards - river - 24%.

The above situations will come to the aid of a poker player when it is necessary to analyze post-flop variations.

The probability of combinations in poker, or rather their improvement from turn to river, is possible in the following percentage terms of data:

Set up to Full House or even higher - 22.7%;
2 pairs to a full house - 8.7%;
Flesh-dro to flush - 19.6%;
Two-way straight to straight - 17.4%;
“holey” straight to straight - 8.7%;
Pocket pair to trips - 4.3%;
A pair to one of the over cards - 13%.

So, armed with the data above, you can evaluate the prospect of improving the set with the last card of the river. Analyzing information on different situations, it is worth focusing on the fact that the probability increases significantly when compared with a similar opportunity from the flop to the turn due to the card that has already come out.

One way or another, in order to conduct a successful and exciting fight, it is imperative to calculate the probability in poker. Being well-versed in this matter, you can safely enter tournaments and play big.

The main thing is that passion does not play a cruel joke and fails to push a sound mathematical miscalculation into the background.

True experts are well aware of the rule: the more time spent thinking and reasoning about card combinations, the better this will affect the professionalism and dexterity of the poker player.

Poker is a long game. Even a simple calculation will sometimes help you figure out your opponent and understand what cards he has in his hands. Such knowledge allows you to control the situation and faithfully follow the right path to victory.

The theory of probability in poker plays an important role. It allows you to adequately assess your own capabilities and the realities of the competition and its outcome. Possession of information about probability is an excellent hint, which, if necessary, can come to the rescue and save money, or it will become a reliable support in obtaining victory and winning a large cash prize.

What about finances!? The enormous pleasure from the process of a reasonable, logical, deliberate competition is incomparable to anything.

Today, No-Limit Hold'em is perhaps the most popular poker discipline, played daily by tens of thousands of poker players all over the planet. The fact is that the reason for such demand lies in the simple and understandable game rules for every player, as well as the “easy composition” of winning combinations and a wide range of bets.

Therefore, about 85% of the largest championships are held exactly according to the rules of Texas Holdem. There can be from 2 to 10 players at the table at the same time . Once upon a time, the legendary live poker player Doyle Brunson gave No-Limit Texas Hold'em the name "Cadillac of Poker." As a rule, all professionals play this type of card game, because here you can win really decent money.

Texas Hold'em“requires” non-standard skills, vast experience, and the ability to correctly read opponents and exert psychological pressure on them.

At the moment, No-Limit Hold'em is an extremely famous type of poker, which has a fabulous number of its own adherents in every online poker establishment. The rules for lining up hands and gameplay are identical to other disciplines.

Rules and theory of playing No Limit Hold'em

In fact, Texas Hold'em can be played in both limit and pot-limit versions, but it is No-Limit Hold'em that is in great demand today, both among beginners and experienced poker players. However, the main advantage and distinguishing feature from existing species card entertainment is the size of the bet, which may be limited by the size of the participant’s stack or the limit of a specific table.

Thus, everyone has the opportunity at any stage of the game (for example, preflop or flop) to go all-in, that is, play with all the available chips. The gameplay itself in Hold'em is very simple. Mastering the rules of Texas Hold'em is a simple task.

So, first of all, players make “blind” bets, which are called blinds. They are made only by two participants in the card party, who sit to the left of the dealer button. Thanks to the blinds, the initial bank is formed, for which the distribution participants subsequently fight.

During a card game, the game bank constantly grows due to additional player bets. As a result, by the end of the game it can amount to an impressive amount. When blind bets are made, all participants in the hand receive two hole cards. Based on them, as well as 5 more cards that are dealt at the next stages of the game, each poker player will have to collect a combination.

After receiving two cards, players begin the betting round. As part of it, you can leave the game by discarding your hand, put a regular one or increased rate to continue the game. Then three community cards are dealt to the table and the second round of betting begins, then another card is laid out and the betting round begins again. When the fifth card is placed on the table, the final bidding begins.

If after this there are at least two players left in the hand, then they reveal their pocket cards and show what combinations they managed to collect. The one who has it is stronger and takes all the money at stake. Texas Hold'em is played with two hole (face down) and five community (up) cards. One distribution is divided into four stages:

Preflop – each player receives two cards;
Flop – three cards are laid out on the table;
Turn – one card is laid out on the table;
River is the last one General Map on the table.

Each of these stages is accompanied circles of trade - an essential component of fair play. During the bidding process, players can raise or call bets, fold their cards, or pass a turn.

To make a winning combination in Texas Hold'em, you must use 2 pocket cards and 3 community cards.

Although in the poker discipline of Hold'em no-limit format it is not prohibited to collect a combination of 5 cards on general principle or one pocket and four community cards.

Practice No Limit Texas Hold'em

As can be seen from the above, the rules of the game in Texas Hold'em are very easy to understand and remember, even for a person who has just begun to learn poker. In theory, it may seem that players only need to play this poker discipline for two or three hours, and they will be able to more or less master the important points.

But in practice the situation is completely different. This can be explained by the fact that behind this seemingly naive simplicity lies serious mathematical calculations. That's why it took some professionals years to fully learn Texas Holdem.

The good news is that today on the Internet you can easily find a huge number of manuals and video lessons, where the authors examine in detail various aspects of the game. For example, in the book “No-Limit Hold'em: Theory and Practice,” authored by Ed Miller and David Sklansky, they share their experience on how to play No-Limit Texas Hold'em for successful results, as well as what actions it is better to refrain from.

Although this publication was published 11 years ago, visual tips and game tactics described in the book do not lose their relevance . The bestseller deals with both the nuances of behavior at cash tables for No-Limit Texas Hold'em and tournament competitions. Also here the features of Hold'em and comparison with limit poker varieties are described in as much detail as possible.

The book “No-Limit Hold'em: Theory and Practice” allows you to plunge headlong into the very essence of poker, to understand every little detail that many novice poker players simply lost sight of when studying this format of poker, separately from other variants of card games.

The manual consists of two sections: theory and practice. The first one is devoted to the basics of no-limit Hold'em, and from the very first lines the author prepares the reader for a professional approach to the gameplay. The second section, called “Ideas of Defense and Attack,” allows you to consolidate your acquired knowledge by testing the responsibilities of an expert, analyzing various game moments.

Like the rest of David Sklansky's works, this printed publication is a valuable storehouse of knowledge that allows you to thoroughly study the basics of poker, and in the future bring positive gaming results. Despite the fact that the book on No-Limit Hold'em is set out on 260 pages, we recommend it to every amateur and established poker player who wants to play profitably over long distances.

Because it teaches competent management of your personal bankroll, reveals the secrets of basic and professional strategies, and also helps to significantly reduce the number of mistakes made during the game. And, most likely, the most important thing is that you will learn to manage your own emotions and psychological state.

Not all great decisions are made from pulpits, but it would be a mistake to assume that our decisions would be the same if there were no lecturers and book authors accumulating and then transmitting information to their audiences. Another thing is that it is university classrooms that become the vanguard of interaction between science and the public, thereby acquiring the image of “open doors” to the world of science, however, what about those who do not have access to classrooms?

Now we are not talking so much about the benefits higher education, so much about the number of intermediaries between us and the information itself. The concepts of “probability theory” and “game theory” are considered important in poker. I am more than sure that you have heard about them, but not everyone discovered them while sitting in classrooms. On the Internet, reading books, maybe even just discussing them with friends, you gained access to information that once came exclusively from the lips of representatives of the scientific community.

We will try to consider the essence of these concepts, we will try to find points for their application, and in addition, we will accompany them with examples from the game. For people who speak English, at the end of each paragraph, we will attach links to the corresponding online versions of courses offered by Harvard and Yale universities as part of open educational programs.

Probability theory

The main content of probability theory is to develop methods for calculating the probabilities of some random events (relatively complex) using the probabilities of other random events (simpler), which are somehow related to the first. The probabilities of second, simpler, random events in the vast majority of real applications of probability theory are estimated based on experimental data, conducting massive homogeneous experiments. After this, using probability theory formulas, the probabilities of more complex events (the word “random” in probability theory is usually omitted) associated with simpler events are calculated, without conducting any experiments.

However, when we talk about probability, we always mean the probability of the occurrence of a particular event. The concept of an event is one of the basic concepts of both the general axiomatic probability theory and the naive elementary one. The term random event is used in probability theory only in relation to stochastic experiments, and the term “event” is used as a shortened form of the term “random event”.

We cannot separately define the terms “random event” (in the sense of probability theory) and “probability”. A probabilistic-random event is a random event that has a probability (which implies the possibility of unlimited repetition of the experiment under unchanged conditions), and only a probabilistic-random event has a probability (random events associated with unique experiments do not have a probability).

It is important to understand that if we are talking about an event associated with a unique experiment, then only one thing can be said: it will either happen or it will not happen. Unique experiments with random results are not the subject of probability theory.

In probability theory, the following are important: the concept of “event”, the classical “definition” of probability; total probability formula; Bayes formula; the concept of independent events; concept of conditional probability.

In applications of probability theory, it is important to understand the following. For real problems, the stability of the frequencies of occurrence of certain events, i.e. the existence of probabilities for these events, and the values of the probabilities are usually established through experiments. This gives grounds to use theorems of mathematical probability theory to calculate the probabilities of more complex events associated with the experiment being studied. However, since in reality the stability of frequencies and the very values of the probabilities of initial events can only be established approximately, it cannot be guaranteed that the conclusions obtained using these theorems in relation to the experiment under study are at least approximately correct (it would be better to say, with the degree of accuracy with which it is established frequency stability) - with the lengthening of the chain of logical conclusions and the increase in the number of operations performed with the initial probabilities (which in real problems are always known only approximately), the accuracy of the obtained values and the reliability of the final conclusions decreases.

However, for poker this concept has become an entire worldview. Every decision you make must have a mathematical basis, based on knowledge of chances and probabilities. Popular in the community are ready-made probability tables containing solutions for all typical situations. How useful can this be? If we try to summarize this in a few words, the concept of “probability” in gambling has always existed, but the concept of “mathematical probability” is inextricably linked with poker as a “game of skill”. In fact, examples of the use of probability theory are very widely represented in the life of any player. Some of them, more than others, have “lecturer” abilities, and are able to convey this knowledge, and most importantly, understanding, to other players. Vivid examples include the works of Rounder, Moshman, Janda, etc. In addition to these books, as mentioned earlier, English-speaking users can familiarize themselves with the open course of lectures by Joe Blitzstein (personal website and twitter) link .

Game theory

The branch of mathematics that studies the choice of optimal strategies in conflict situations, in which there is a struggle between participants, is called “Game Theory”. We should not forget that each party pursues its own interests and seeks, first of all, the most advantageous solution, possibly (but not necessarily), to the detriment of its rivals. Game theory allows you to choose taking into account information about the participants in the interaction, resources, and also takes into account possible consequences the decisions they make.

Game theory has a tendency to popularize. This is largely due to the names of John Harsanyi, John Nash and Reinhard Selen, as well as Robert Aumann and Thomas Schelling.

To determine the essence of game theory, one should turn to its basic definitions. A game is a mathematical model of a situation characterized by the following characteristics: the presence of several participants; uncertainty of participants' behavior; discrepancy between their interests; interconnectedness of the behavior of the participants (since the result obtained by each of them depends on the behavior of all participants); Finally, it is important to have some rules of behavior known to each of the participants. Strategy is a set of rules that determine the sequence of player actions in each specific situation that arises during the game. Party – each of the game implementation options. A move is a player’s choice of one of the valid solutions. The outcome of the game is a payoff function, the value of which depends on the strategy used by the player.

The basis for the calculation procedure in game theory is the expression various characteristics in a quantitative way. In this sense, we turn to the “utility theory” of J. Von Neumann and O. Morgenstern, which posits that decisions have a utility function.

Depending on the conditions existing at the time of decision-making, game theory qualifies the decision-making process into the following qualifications: First, decision-making under conditions of certainty; Secondly, decision making under risk conditions; thirdly, it separately examines elections under conditions of uncertainty (which specifically applies to poker); and, finally, fourthly, game theory especially considers decision-making in situations of conflict or enemy opposition.

Why should game theory be remembered by poker players? The minimax theorem guarantees that every zero-sum game has optimal strategies. It gives existence, but does not determine how to look for these optimal strategies. In addition, it has a number of specific methods for each type of game and their features, but all of them, one way or another, depend on the methodology for determining usefulness. Now remember again the books of Rounder, Moshman, Janda - after all, this is exactly what they are all talking about. Determining the usefulness of decisions under conditions of uncertainty.

Fold: The EV of folding is 0. Always, this is the first rule of the club (if you know what I mean).

Call: The EV of the call in this situation is -$500. I call this situation a bluff call - a product of our genius. In our case, the only case when we do not lose money is when we share it with 23 others.

Rise: <1501$ поскольку после нашего рейза у соперника 2 варианта: он принимает нас, и мы теряем 1500$; фолдит, и мы забираем банк 1000$ + 500$ ставки соперника.

We designate the raise as X, and the fold as Y, and let the math (or rather, its deep micro-limits) begin.

How to beat micro with one click?

The opponent must choose, so X+Y=1
Then, X=1-Y
EV of the raise 1500$ will be (1500)*(Y)+(-1500)*(1-Y) = 3000*(Y) – 1500
We if
3000Y-1500>0
3000Y>1500
Y = 1/2 (for us consider Y>51%) - fold probability, with which the opponent must meet your raise so that it is

If you want to go deeper into this topic, but understand the very concept of game theory, without being forced into games in a state of uncertainty, we invite English-speaking users to listen to a course of open lectures by a professor at Yale University

David Sklansky is the son of a mathematics professor and himself a mathematician by training. Even in his youth he demonstrated a penchant for theoretical research. In particular, he developed a mathematical model of the activities of an insurance agent.

In 1978, before he became known as a successful gambler, David published a small edition of the book Sklansky on Poker Theory. It was intended purely for professionals and did not bring wide fame to the author. But following the principles he developed, David soon achieved stunning success in practical play. He won the WSOP bracelet three times and more than once found himself at the final tables of tournaments in the company of such greats as Phil Hellmuth, Doyle Brunson, etc.

Successes in practical play prompted David to rework his first book into a more popular version, understandable to the widest range of readers. It became “The Theory of Poker” - a textbook that has gained worldwide fame and fame as a fundamental tool for everyone who wants to master the game of poker and improve their level in it.

Poker theory and theorem

“Poker Theories” amazes, first of all, with its thoroughness. The author examines the game not only in Texas Hold'em, but also in all the main varieties of poker literally from “A” to “Z”. From how the pot is formed by antes or blinds, to higher mathematics poker: ways to calculate equity, etc.

It was in “The Theory of Poker” that Sklansky formulated his famous “Fundamental Theorem of Poker”. In the original, the theorem is formulated very scholastically and difficult to understand, but its meaning in a nutshell is as follows: “To win, you must play as if you knew your opponent’s hand.”

It is from this theorem that two main directions in the development of poker theory come from:

The art of identifying an opponent's cards by the nature of his calls, raises and folds, combined with those signals about the strength of his cards that he gives involuntarily - random movements, gestures, etc. — psychology of poker.
The doctrine of ranges, spectra - i.e. about ways of mathematical formalization of ideas about the opponent’s cards.

In fact, these two areas are covered by David Sklansky in his book, focusing not so much on the poker player’s decisions during the game, but on the logic of his decision-making. This is the value of the textbook: it does not tell you how to do it; he explains why it is necessary to do this.

Reviews of “The Theory of Poker” by Sklansky

Although “Poker Theory” is positioned as a book for the general reader, many users note that understanding it requires preparation. Not only experience in playing poker, but also knowledge in the field of mathematics and mathematical logic.

Typical reviews on forums:

“Textbook for Universities. Poker graduate students. After the very first pages, there was a desire to apply the acquired knowledge.”

David Sklansky puts his fundamental theorem of poker to the test

“The book is well written, everything is accessible, but it’s hard to get your head around it right away.”

As one of the advantages of Sklansky's book, users note the presence of a poker dictionary; However, one of the readers immediately makes a reservation: “Without it (the dictionary), half the text would not be understandable at all.”

Where to download, are there any problems with purchasing?

“Poker Theory” is a classic of the genre. You can download it not only from specialized poker resources, but also from many literary sites. For example, on E-Reading.Club (http://www.e-reading.club/book.php?book=1028104).

Downloading is free everywhere: taking money for something sacred is a sin!