Table Of ContentHow
to Win More
Strategies for Increasing a
Lottery Win
How
W M
to in ore
Strategies for Increasing a
Lottery Win
Norbert Henze
Hans Riedwyl
(d* CRC Press
Taylor & Francis Croup
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
AN A K PETERS BOOK
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
First issued in hardback 2017
© 1998 by A K Peters, Ltd.
CRC Press is an imprint of Taylor & Francis Group, an Informa business
ISBN-13: 978-1-5688-1078-2 (pbk)
ISBN-13: 978-1-1384-6968-6 (hbk)
This book contains information obtained from authentic and highly regarded sources. While all reasonable
efforts have been made to publish reliable data and information, neither the author[s] nor the publisher
can accept any legal responsibility or liability for any errors or omissions that may be made. The publishers
wish to make clear that any views or opinions expressed in this book by individual editors, authors or
contributors are personal to them and do not necessarily reflect the views/opinions of the publishers. The
information or guidance contained in this book is intended for use by medical, scientific or health-care
professionals and is provided strictly as a supplement to the medical or other professional’s own judgement,
their knowledge of the patient’s medical history, relevant manufacturer’s instructions and the appropriate
best practice guidelines. Because of the rapid advances in medical science, any information or advice on
dosages, procedures or diagnoses should be independently verified. The reader is strongly urged to consult
the relevant national drug formulary and the drug companies’ and device or material manufacturers’ printed
instructions, and their websites, before administering or utilizing any of the drugs, devices or materials
mentioned in this book. This book does not indicate whether a particular treatment is appropriate or suitable
for a particular individual. Ultimately it is the sole responsibility of the medical professional to make his or
her own professional judgements, so as to advise and treat patients appropriately. The authors and publishers
have also attempted to trace the copyright holders of all material reproduced in this publication and apologize
to copyright holders if permission to publish in this form has not been obtained. If any copyright material has
not been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or
hereafter invented, including photocopying, microfilming, and recording, or in any information storage
or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses
and registration for a variety of users. For organizations that have been granted a photocopy license by
the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are
used only for identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Library of Congress Cataloging-in-Publication Data
Henze, Norbert, 1951-
How to win more: strategies for increasing a lottery win /
Norbert Henze, Hans Riedwyl.
p. cm.
Includes bibliographical references and index.
ISBN 1-56881-078-4
1. Lotteries - Statistical methods - Handbooks,
manuals, etc. 2. Lotto - Statistical methods - Handbooks,
manuals, etc.
I. Riedwyl, Hans. II. Title.
HG6111.H46 1998
795.3’8-dc21 97-48846
CIP
Contents
1 The History of Lotteries 1
2 The Rules 7
2.1 r/s Lotteries.......................................................................... 7
2.2 Prize Structures................................................................... 11
3 The Odds 14
3.1 Chances, Odds, and Probabilities.............................. 14
3.2 How Many Years Will It Take to W in?................... 18
3.3 You Can’t Beat the O dds!............................................. 20
4 Learning from Prize Payouts 22
4.1 The Parimutuel Payout System .................................. 22
4.2 Examples of Extreme Payouts..................................... 24
4.3 Seeing Through Scatterplots......................................... 31
5 Foolish Styles of Play 36
5.1 Choosing Arithmetic Progressions.............................. 37
5.2 Choosing Winning Combinations of Previous Draws 42
5.3 Choosing “Hot” and “Cold” Numbers...................... 45
5.4 Choosing Outstanding Numbers.................................. 47
5.5 Choosing Winning Numbers
from Other Countries or States ................................. 49
5.6 Choosing Geometric Patterns ..................................... 52
5.7 Modifying Previous Winning Combinations . . . . 55
5.8 Playing with N um bers.................................................... 59
5.9 The Too-Large-Numbers Dilemma.............................. 62
5.10 Foolish Play and Arithmetic Complexity............... 65
v
Contents
VI
6 Quick Pick: A Sensible Style of Play 69
7 Intelligent Styles of Play 79
7.1 Arithmetic Complexity.................................................... 81
7.2 Sums of Numbers............................................................... 82
7.3 Edge Numbers....................................................................... 86
7.4 Cluster Numbers ................................................................ 89
7.5 Played Numbers.................................................................... 93
7.6 Played Number Combinations...................................... 97
7.7 A Quick Strategy for Intelligent P lay ...................... 100
7.8 A Regression Strategy for Intelligent Play . . . . 102
7.9 Answers to Frequently Asked Questions................... 104
8 Mathematical Appendix 106
8.1 Probabilities of W inning................................................ 106
8.2 Frequencies of Winning N um bers.............................. 110
8.3 Testing Equiprobability of Lotto Numbers . . . . 114
8.4 First Repetition of a Winning Combination . . . . 116
8.5 Waiting Tune to Exhaust Lotto Numbers............... 118
8.6 Record Waiting T im es..................................................... 122
8.7 The Distribution of Spaces on Lottery Tickets . . 125
8.8 The Sum of Winning Numbers..................................... 127
8.9 A Measure of Arithmetic Complexity...................... 128
8.10 The Correlation Coefficient............................................. 130
8.11 Multiple Linear Regression............................................. 131
8.12 Some Standard Distributions......................................... 132
8.13 Mathematical Aspects of Quick-Pick Play . . . . 135
8.14 The Natural Logarithm.................................................... 137
8.15 An Urn Model Reflecting Number Popularity . . 138
8.16 A Lotto Random Number G enerator...................... 140
References 142
Index 145
Preface
The main purpose of How to Win More is to give you valuable
insights into how to improve your long-term return on investment
when playing lotto. You shouldn’t mistake the title, however. It
doesn’t mean “win more often” ; that will happen only if you
buy more tickets. Rather, the title means that your winnings
will usually be larger when your numbers do come up.
In addition, reading this book might prevent you from having
a great disappointment—perhaps your greatest disappointment
ever. Imagine that your dream of a lifetime—winning a jackpot
of, let’s say, $50,000,000—has come true for you. (That’s why
you play lotto, isn’t it?) However, imagine your disappointment
when the lottery company tells you that you have to split that
jackpot with more than 10,000 other players, resulting in a share
of less than $5,000 for you.
Could this really happen? Yes it could, if, for example, the
winning combination was 8, 15, 22, 29, 36, 43. If this combina
tion ever comes up in any number lottery, it will likely produce
thousands of very disappointed winners. (The reason for this is
explained in Chapter 5.) By the way, 14,697 entries selected this
combination in the New York State Lotto of June 7, 1986.
If you are open minded, reading this book will make you an
informed lotto player who knows the following:
•The most popular number combinations are also the most
foolish. (Many are given in Chapter 5.)
vii
Preface
Vlll
•It is impossible to improve the odds of winning any legiti
mate lottery (for example, by charting numbers).
•The notion of picking so-called hot or cold numbers is non
sense. (You might as well throw your money away.)
•Although nice-looking tickets may be popular, they are also
unprofitable.
•Never copy suggested numbers from “Nighthawks,” lottery
horoscopes (“Zodiac Best Bets”), or “Dr. X’s Computer
Generated Lotto Picks” (to name only a few supposed con
sulting experts).
•It is extremely important to avoid picking the winning com
binations of past drawings (although each has the same
odds of winning as any other combination for future draw
ings).
Certainly, these maxims, along with other information in this
book, will not be confirmed by some agents who profit from lin
gering lottery myths. Nonetheless, they are only too true.
As you probably know, there are many different number lotter
ies. To date, Illinois plays a 6/54 (that is, each participant picks
six numbers between 1 and 54), California has a 6/51, Canada
runs a 6/49, Sweden has a 7/35, and Switzerland plays a 6/45, to
name only a few. This book doesn’t concentrate on any specific
number lottery, for two reasons:
1. All number lotteries are basically the same, so if you under
stand one, you understand them all.
2. States like to change the types of their lotto games fairly
often. For example, California switched from a 6/49 to a 6/53
lotto in June 1990 and to a 6/51 lotto in December 1991, and
Arizona changed from a 6/39 to a 6/42 in 1989. The only reason
for these changes (and many similar changes in other states) is
t.o keep ticket sales at a high level, which makes the lotto odds
Preface
IX
more difficult. As a rule of thumb, the odds for winning a jackpot
must be seen in comparison with the population base in the given
state. If the odds are too low, there will usually be a jackpot win
ner. Consequently, jackpots won’t get big and ticket sales won’t
increase. On the other hand, if the odds against winning the jack
pot are too high, few grand-prize winners will be presented to the
public and ticket sales might taper off. With the right odds, there
will sometimes be a string of jackpots with no winners, leading to
a huge carryover of money and thus much publicity and greater
participation. Moreover, the right odds will also entail enough
winning of small prizes for player reinforcement.
Although you will learn about the odds (and much more) for
any lottery, don’t be afraid. The discussion of mathematics will
be kept to an absolute minimum, and formulae for computing
odds or expectations have been “banned” into a separate unit
(Chapter 8).
Acknowledgements
We are indebted to David R. Bellhouse (University of Western
Ontario, Canada), Henri Carnal (University of Bern, Switzer
land), Persi Diaconis (Harvard University, Boston), Harry Joe
(University of British Columbia, Canada), Pekka Kangas (Uni
versity of Oulu, Finland), Mike Orkin (California State Univer
sity, Hayward), Hal Stern (Iowa State University), and Donald
Ylvisaker (University of California, Los Angeles) for providing
many valuable comments on early drafts of this book.
Special thanks go to the following lottery corporations for
providing us with valuable information and data: California State
Lottery, Colorado Lottery, Connecticut Lottery, Florida State
Lottery, Maryland State Lottery, Massachusetts State Lottery,
New Zealand Lottery, Ontario Lottery Corporation, Queensland
