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1. Probability and Odds 56 2 Get $150 Dollars Bankroll For Free ! EXCLUSIVE OFFER CLICK HERE! CLICK HERE TO DOWNLOAD POKEROFFICE FOR FREE Dr Mahmood N Mahmood The Science of Poker ♦♣♥♠ HIGH STAKES LONDON 2006 This revised edition published in 2006 by High Stakes Publishing 21 Great Ormond St London WC1N 3JB www.highstakespublishing.co.uk © Dr Mahmood N Mahmood 2003, 2006 The right of Dr Mahmood N Mahmood to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs & Patents Act 1988. All rights reserved. No part of this book may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the written permission of the publishers. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages. ISBN 10: 1 84344 031 8 ISBN 13: 978 1 84344 031 4 Printed by Cox and Wyman, Reading Text design and typesetting by Able Solutions (UK) Ltd Contents ♦♣♥♠ INTRODUCTION 9 PART ONE: BASIC CONCEPTS 13 CHAPTER ONE: POKER – PEOPLE – MONEY 15 1. People 16 2. Money 21 CHAPTER TWO: PROBABILITY – VALUE – IMPLIED ODDS – TELLS – BLUFFS 25 1. Probability 25 2. Mathematical expectations – value 26 3. Implied odds 28 4. Winning strategies 31 5. Tells 31 6. Bluffing 33 7. Golden rules 34 PART TWO: FOUR-CARD OMAHA 37 CHAPTER THREE: FOUR-CARD COMBINATIONS 39 1. Starting four cards 39 CHAPTER FOUR: PROBABILITIES AND ODDS 55 1. Probability and odds 56 2. Profitable draws 57 3. Probabilities of Omaha hands 58 4. Backdoor hands 61 5. Implied odds 62 CHAPTER FIVE: THE FLOP 63 1. Anatomy of the flop 63 2. Analysis of specific hands 65 CHAPTER SIX: POT-LIMIT OMAHA 79 1. Starting Hands 79 2. Beyond The Flop 88 CLICK HERE TO DOWNLOAD POKEROFFICE FOR FREE PART THREE: TEXAS HOLD’EM 105 CHAPTER SEVEN: PROBABILITY – ODDS 107 1. Introduction 107 2. Probabilities of Hold’em hands 108 3. Backdoor flush/straight 112 CHAPTER EIGHT: STARTING HANDS 113 1. Pairs 113 2. Other two-card combinations 115 CHAPTER NINE:THE FLOP AND BEYOND 137 1. Anatomy of the flop 137 2. Analysis of specific hands 139 CHAPTER TEN: POT-LIMIT HOLD’EM 153 1. Starting cards 153 2. Beyond the flop 156 PART FOUR: SEVEN-CARD STUD 165 CHAPTER ELEVEN: SEVEN-CARD STUD 167 1. Introduction 167 2. Starting cards 173 CHAPTER TWELVE: PAIRS 175 1. Third street 175 2. Fourth street and beyond 179 CHAPTER THIRTEEN: FLUSHES 201 1. Third street 201 2. Fourth street and beyond 202 3. Flush draws 204 CHAPTER FOURTEEN STRAIGHTS 219 1. Third street 219 2. Fourth street and beyond 221 3. Open-ended straight draws 222 CHAPTER FIFTEEN: TRIPS 235 1. Third street 235 2. Fourth street and beyond 237 CHAPTER SIXTEEN: OTHERS 243 1. Third street 243 2. Fourth street and beyond 244 PART FIVE: ONLINE POKER 245 CHAPTER SEVENTEEN ONLINE POKER 247 1. Online Tournaments 247 2. Cash Games 258 CHAPTER EIGHTEEN: POST-FLOP STRATEGY IN NO-LIMIT HOLD'EM TOURNAMENTS 261 1 Post-Flop Action 262 2. Is it a bluff? 270 APPENDIX: THE MATHEMATICS OF PROBABILITY 275 Introduction This new edition of The Science of Poker is divided into five parts. A brief discussion of some important Poker concepts is presented in the first part. The second part deals with four-card Omaha High, the third part is devoted to Texas Hold'em and the fourth part covers Seven-Card Stud. Finally the fifth part is dedicated to the most popular online Poker tournaments, No-Limit Hold'em. Parts Two, Three and Four contain comprehensive analyses of starting hands, odds and probabilities. They include the new concept of Probability Coefficient, as well as after flop play, for Omaha and Hold'em, and after third-street play for Seven-Card Stud. Although the last chapters of Omaha and Hold'em are dedicated to pot-limit games, I advise the owners of this book to read each part thoroughly because the information presented in each chapter is pertinent to both limit and pot-limit poker. Finally chapters Seventeen and Eighteen incorporate a detailed playing strategy for No-Limit Hold'em tournaments together with a full discussion of many actual hands. Appendix A, which deals with the mathematics of probability, is included for the benefit of readers who are interested in learning the basics of statistical calculations relevant to poker. As you read this book, you will realise that it is not a thriller. It will be obvious that you are reading a reference book. You cannot assimilate the wealth of poker information at your disposal by reading the book once, unless you are endowed with photographic memory. Do not, however, be intimidated by the large number of simulated/calculated statistical data that were utilised in the analyses of the many examples of contests between a wide range of poker hands. I advise you to read the book more than once and to refer to the relevant part/section every time you have had to make a tough decision during a playing session. This will enable you to remember most, if not all, of the data in the book and subsequently to apply your superior knowledge to your advantage, during your future 9 T H E S C I E N C E O F P O K E R playing sessions. I am a devout believer in learning by repetition. The number of starting hands that can be dealt in Omaha, Texas Hold'em and Seven-Card Stud is enormous. Therefore the task of selecting a winning starting hand can be difficult as well as confusing for the inexperienced player. In each part of the book I have classified starting hands into categories and then performed computer simulations on selected combinations from each one. Each selected starting hand was played at least 10000 times against 1, 2, 3, 4, 5, 6 and 7 opponents respectively. The opponents' starting cards were dealt randomly and every contestant played his hand till the end of the deal. At the conclusion of each simulation run, the win-rate (the number of times the hand wins, expressed as a percentage) of the selected hand was recorded. Its potential for making its holder richer, was then determined using the concept of the break-even point as described below. If you are playing against one opponent, then you should win 50% of the pots in order to break even. Similarly against two, three, four, up to seven opponents, your break-even win-rates should be 33.3%, 25%, 20%, progressively down to12.5% respectively. For example, with three opponents there are four players, including yourself, therefore your break- even win-rate is 100 divided by four, which is 25%. If, however, your starting cards' win-rate against three opponents is say 30%, then you are winning five pots over your break-even point. That means you are getting 20% Extra Pots ((5 ÷ 25) x100) over and above your break-even point when you invest your money in those particular starting cards in 4- handed pots. Clearly, starting hands that can offer such good results are superior to those whose performances hover around their break-even points. Those with win-rates below their break-even points are, in the long run, bad news. Thus, detailed analysis of the results of the computer simulations with the aid of the break-even point and the %Extra Pots will reveal the effect of the texture of starting cards on their performance against the specified number of opponents. This, to my mind, is valuable because one can extract the following information: (1) the number of opponents against which that category of cards will play best 10 I N T R O D U C T I O N (2) whether you are holding "high percentage" starting cards with which a raise is a must, or marginal/garbage cards, in which case they should either be played from late position, or mucked with the discards. I must, however, emphasise the following point: due to the compulsion of each player to go to the showdown, the computer simulations related to starting cards do not represent real playing conditions although, in some limit games, it is not uncommon for more than three contestants to see the river card (fifth board card). Consequently, the recommendations presented in the chapters related to starting hands should be taken as guidelines in the process of selecting the appropriate starting hand, rather than reasons to gamble all the way to the showdown. Throughout this book, X-X-X-X(s) or X-X(s) mean starting cards of which two are of the same suit and X-X-X-X(o), X-X(o), X-X-X-X or X- X stand for unsuited hand 11 Part One Basic Concepts 13 Chapter One Poker – People – Money Many old-fashioned players, whom I think of as the dinosaurs of the game, will argue that poker is a game of people. According to them, all you have to do is understand the psychology of your opponents. Once you have done that and identified your opponents’ playing and betting habits you can’t lose. They could not make a more misguided statement. Poker is a game of people, probabilities and money. These are the primary skills of the game. The successful player will find the right balance between these three skills depending on: (1) the structure of betting and the size of the buy-in of the game; (2) the type of the game, as well as the size of the ante/blinds and the number of betting rounds; (3) the level of the other players’ skill.
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