Probability Guide to Gambling: The Mathematics of Dice, Slots, Roulette, Baccarat, Blackjack, Poker, Lottery and Sport Bets PDF

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PROBABILITY GUIDE TO GAMBLING The Mathematics of Dice, Slots, Roulette, Baccarat, Blackjack, Poker, Lottery and Sport Bets  ∏ This is a sample containing the title page, copyright page and content list. There is no electronic edition of this book. The printed edition can be ordered at minimal price...

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PROBABILITY GUIDE TO GAMBLING The Mathematics of Dice, Slots, Roulette, Baccarat, Blackjack, Poker, Lottery and Sport Bets

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

This is a sample containing the title page, copyright page and content list. There is no electronic edition of this book. The printed edition can be ordered at minimal price at http://probability.infarom.ro/books.html

Cătălin Bărboianu

Cătălin Bărboianu PO Box 1 – 230 Craiova, Romania http://probability.infarom.ro

INFAROM Publishing Pure and applied mathematics [email protected] http://books.infarom.ro http://www.infarom.ro

ISBN 973-87520-3-5 Publisher: INFAROM Author and translator: Cătălin Bărboianu Correction Editor: Sara M. Stohl

Copyright © INFAROM 2006 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of tables, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of Copyright Laws and permission for use must always be obtained from INFAROM.

Contents Introduction ....................................................................... Probability Theory Basics ................................................ Fundamental notions ........................................................ Sets ................................................................................ Functions ....................................................................... Boole algebras ............................................................... Sequences of real numbers. Limit ................................. Series of real numbers ................................................... Measure theory basics ...................................................... Sequences of sets .......................................................... Tribes. Borel sets. Measurable space ............................ Measure ......................................................................... Field of events. Probability .............................................. Probability on a finite field of events ............................ Properties of probability ................................................ Probability σ-field ......................................................... Independent events. Conditional probability ................ Total probability formula. Bayes’s theorem ................. Law of large numbers ................................................... Discrete random variables ............................................. Distribution function .................................................. Discrete classical probability distributions ................ Bernoulli scheme ..................................................... Poisson scheme ....................................................... Polynomial scheme ................................................. Scheme of nonreturned ball .................................... Combinatorics ................................................................... Permutations ..................................................................... Arrangements ................................................................... Combinations ................................................................... The Mathematics of Games of Chance ........................... Experiments, events, probability fields ............................ Probability calculus .......................................................... Odds and probability ........................................................ Combinations ................................................................... Expectation .......................................................................

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Relative frequency. Law of Large Numbers .................... Relativity of probability results ........................................ The Guide of Numerical Results ...................................... Dice .................................................................................. Two dice ........................................................................ Three dice ...................................................................... Slots ................................................................................. Three reels ..................................................................... Four reels ....................................................................... Roulette ........................................................................... Baccarat .......................................................................... Blackjack ......................................................................... Classical Poker ............................................................... Initial probabilities on the first card distribution for your own hand ..................................................................... Prediction probabilities after the first card distribution and before the second, for your own hand .......................... Prediction probabilities for opponents’ hands .............. Texas Hold’em Poker ..................................................... Immediate odds ............................................................. Preflop odds ............................................................... Flop odds .................................................................... Turn odds ................................................................... Other odds .................................................................. Opponents’ hands probabilities ..................................... Lottery ............................................................................. The 6/49 system ............................................................ The 5/40 system ............................................................ Enhancing the winning probability ............................... Compound variants ....................................................... Reduced schemes .......................................................... Sport Bets ........................................................................ The Probability-based Strategy ....................................... References ...........................................................................

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