See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/257820901 The Mathematics of Lottery: Odds, Combinations, Systems Book * March 2009 CITATION 1 READS 2,238 1 author: Some of the authors of this publication are also working on these related projects: Metatheoretical analysis and structural alternatives of the resolving of the philosophical problem of the applicability of mathematics in natural sciences and Wigner's puzzle View project Editing/Proofreading/Commenting/Research Designing in philosophy of science/philosophy of mathematics Collaboration and co-authorship View project Catalin Barboianu University of Bucharest 27 PUBLICATIONS 5 CITATIONS SEE PROFILE All content following this page was uploaded by Catalin Barboianu on 03 March 2016. The user has requested enhancement of the downloaded file. THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems  ∏ 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 INFAROM Publishing Applied Mathematics office@infarom.com http://www.infarom.com http://probability.infarom.ro ISBN 978-973-1991-11-5 Publisher: INFAROM Author: Cătălin Bărboianu Correction Editor: CarolAnn Johnson Copyright © INFAROM 2009 This work is subject to copyright. All rights are reserved, whether the whole work or part of the material is concerned, specifically the rights of translation, reprinting, reuse of formulas and 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 ...................................................................................... 5 The Rules of Lottery ....................................................................... 11 Supporting Mathematics ................................................................ 15 Probability space .......................................................................... 16 Probability properties and formulas used ..................................... 19 Combinatorics ............................................................ 22 Parameters of the lottery matrices ....................................... 25 Number Combinations ........................................................ 27 Probabilities of Winning with Simple Lines .................................. 37 General formula of the winning probability ............................ 37 Cumulated winning probabilities ....................................... 53 Intermediary probabilities .............................................. 67 Enhancing the Winning Probability ........................................ 75 Probabilities of winning with systems .................................. 76 Probability thresholds ................................................... 91 Compound Lines ................................................................. 107 Unfolding compound lines ................................................. 108 Winning probabilities ..................................................... 111 The number of prizes ................................................... 127 Systems of compound lines ........................................................... 136 Bridgehead Systems ....................................................... 141 Winning probabilities ..................................................... 142 The number of prizes ................................................... 155 Reduced Systems ............................................................. 159 Obtaining the reduced systems ......................................... 161 Winning probabilities ..................................................... 173 Probabilities of Repeated Events ......................................... 177 The Strategy of Choosing ................................................ 191 References ......................................................................................... 203 View publication stats