In the flop stage, what are your odds of achieving a straight by river and what are the odds of your opponents achieving something higher? If you will achieve the straight, what are the new odds of your opponents beating it in the river stage? How about the full house? How strong is your hand from mathematical point of view and how can you use this information in your play? This is the kind of questions that this book deals with. In improving poker skills, acquisition of information is vital, whether we talk about data a player collects during a specific game or pre-established mathematical facts behind the card distribution, including prediction. Texas Hold'em Poker is a game highly suitable for probability-based decisions. The power of a single card changing the hand hierarchies at every stage is a strong argument that every objective strategy should be probability based and so the card odds should be part of such a strategy. The book is a complete probability guide of Hold'em Poker, covering all possible gaming situations, an improved edition of the bestseller "Texas Hold'em Odds", published in 2004. In this edition, the author focused on the practical side of the presentation and use of the probabilities involved in Hold'em, while taking into account everywhere the subjective side of the probability-based criteria of each player's strategy. The first part of the book deals with the odds of specific card formations, from one pair to straight flush, at every stage of the game, grouped in three large categories: long-shot odds for own hand, long-shot odds for opponent's hands and immediate odds. These odds are collected in tables at the end of each section and, where generating two-dimensional tables was not possible, the compact formulas returning the odds are provided. All tables and formulas are followed by examples of how to use them for finding the desired odds in a specific gaming situation. All probability results were worked out through compact mathematical formulas and not by the use of any software based on partial simulations. The chapter "Operating with and Weighting the Odds" is the main new material added to the first edition and deals with the rules of estimating and evaluating the probabilities of complex gaming events in order to use them in a strategy, by using the odds provided in the first part of the book. When we are allowed to add together the partial probabilities of a union of events for an overall probability and when we are not, methods of approximation and tips of avoiding hard calculations, all have their dedicated subchapters, packed with suggestive examples of application on concrete hands. The author also introduces the concept of strength matrix of a hand, within the adequate mathematical model of the strength of a Hold'em hand, and argues why the strength of a hand should be defined through mathematical probabilities. At this point, he proves that what most of the so-called odds calculators return are not mathematical probabilities and cannot stand as objective strength indicators for Hold'em hands. The last chapter is a suggestive collection of probability-based hand analyses on concrete Hold'em hands that can be generalized to categories of hands having identical results associated. The author is a recognized authority on casino/gaming mathematics and his books are in the official bibliography of the students of several gambling institutes and organizations around the globe. This book is the most trusted and professional source for the mathematical facts of Hold'em Poker, a must-have completion for any strategy book.
In the flop stage, what are your odds of achieving a straight by river and what are the odds of your opponents achieving something higher? If you will achieve the straight, what are the new odds of your opponents beating it in the river stage? How about the full house? How strong is your hand from mathematical point of view and how can you use this information in your play? This is the kind of questions that this book deals with. In improving poker skills, acquisition of information is vital, whether we talk about data a player collects during a specific game or pre-established mathematical facts behind the card distribution, including prediction. Texas Hold'em Poker is a game highly suitable for probability-based decisions. The power of a single card changing the hand hierarchies at every stage is a strong argument that every objective strategy should be probability based and so the card odds should be part of such a strategy. The book is a complete probability guide of Hold'em Poker, covering all possible gaming situations, an improved edition of the bestseller "Texas Hold'em Odds", published in 2004. In this edition, the author focused on the practical side of the presentation and use of the probabilities involved in Hold'em, while taking into account everywhere the subjective side of the probability-based criteria of each player's strategy. The first part of the book deals with the odds of specific card formations, from one pair to straight flush, at every stage of the game, grouped in three large categories: long-shot odds for own hand, long-shot odds for opponent's hands and immediate odds. These odds are collected in tables at the end of each section and, where generating two-dimensional tables was not possible, the compact formulas returning the odds are provided. All tables and formulas are followed by examples of how to use them for finding the desired odds in a specific gaming situation. All probability results were worked out through compact mathematical formulas and not by the use of any software based on partial simulations. The chapter "Operating with and Weighting the Odds" is the main new material added to the first edition and deals with the rules of estimating and evaluating the probabilities of complex gaming events in order to use them in a strategy, by using the odds provided in the first part of the book. When we are allowed to add together the partial probabilities of a union of events for an overall probability and when we are not, methods of approximation and tips of avoiding hard calculations, all have their dedicated subchapters, packed with suggestive examples of application on concrete hands. The author also introduces the concept of strength matrix of a hand, within the adequate mathematical model of the strength of a Hold'em hand, and argues why the strength of a hand should be defined through mathematical probabilities. At this point, he proves that what most of the so-called odds calculators return are not mathematical probabilities and cannot stand as objective strength indicators for Hold'em hands. The last chapter is a suggestive collection of probability-based hand analyses on concrete Hold'em hands that can be generalized to categories of hands having identical results associated. The author is a recognized authority on casino/gaming mathematics and his books are in the official bibliography of the students of several gambling institutes and organizations around the globe. This book is the most trusted and professional source for the mathematical facts of Hold'em Poker, a must-have completion for any strategy book.
