University of Calgary PRISM: University of Calgary's Digital Repository Alberta Gambling Research Institute Alberta Gambling Research Institute 1963 Chance, luck and statistics : the science of chance Levinson, Horace C. Dover Publications, Inc. http://hdl.handle.net/1880/41334 book Downloaded from PRISM: https://prism.ucalgary.ca Chance, Luck and Statistics THE SCIENCE OF CHANCE (formerly titled: The Science of Chance) BY Horace C. Levinson, Ph. D. Dover Publications, Inc., New York Copyright @ 1939, 1950, 1963 by Horace C. Levinson All rights reserved under Pan American and International Copyright Conventions. Published in Canada by General Publishing Company, Ltd., 30 Lesmill Road, Don Mills, Toronto, Ontario. Published in the United Kingdom by Constable and Company, Ltd., 10 Orange Street, London, W.C. 2. This new Dover edition, first published in 1963. is a revised and enlarged version ot the work pub- lished by Rinehart & Company in 1950 under the former title: The Science of Chance. The first edi- tion of this work, published in 1939, was called Your Chance to Win. International Standard Rook Number: 0-486-21007-3 Libraiy of Congress Catalog Card Number: 63-3453 Manufactured in the United States of America Dover Publications, Inc. 180 Varick Street New York, N.Y. 10014 PREFACE TO DOVER EDITION THE present edition is essentially unchanged from that of 1950. There are only a few revisions that call for comment. On the other hand, the edition of 1950 contained far more extensive revisions of the first edition, which appeared in 1939 under the title Your Chance to Win. One major revision was required by the appearance in 1953 of a very important work, a life of Cardan,* a brief account of whom is given in Chapter 11. This book explodes two or three ficticious anecdotes of his life which had somehow found their way into the histories of science. Far more important, however, is the discovery that in his book Liber de Ludo Aleae (The Book on Games of Chance), Cardan succeeded in reach- ing certain fundamental ideas in the theory of probability, thus anticipating Galileo, Pascal and Fermat by some hundred years. Further details will be found in Appendix I. In Chapter XVII there is an illustration from the field of sports, the world records for the mile run since 1865 and the current records for other distances. It seemed advisable to bring these records up to date, and this has been done in Appendix 11. Since nothing is said in the text about the much-discussed four-minute mile, a few pages on that sub- ject will also be found in Appendix 11. Since 1939, even since 1950, there has been considerable progress in both the theory of probability and the science of statistics, just as there has been in other fields of science. But such progress has very naturally been at a far higher technical level than that of this book, so that no account of it has been taken. On the philosophical side, we would like to emphasize Vardano, the Gambling Scholar, by Oystein Ore: Princeton University Press. 'V PREFACE TO DOVER EDITION again, as is done on page 47, that properly speaking the theory of probability is a mathematical theory, or rather a set of such theories, so contrived as to be applicable to a wide variety of physical situations, in physics, in the social sciences, in insurance, in games of chance, and in a large number of other fields. The point is that the validity of a given applica- tion depends on how closely the physical situation conforms 1 to the demands of the theory. For example, in the applica- 5 tions to throwing coins and rolling dice, it must be assumed that the coins and dice are perfectly symmetrically constructed of homogeneous material. But no real coins or dice fully 1 meet these requirements. We are therefore talking about ! idealized coins and dice, and the problem arises: how closely can we expect the imperfect coins and dice that we use to conform to the laws of chance derived from the abstract d theory? The fact that dice show small discrepancies from I I these laws, if enough thousands of rolls are made, is shown by the classical experiments of Weldon, discussed on pages I 232-33 and on page 239. Perhaps the most important matter to which I must refer in this brief Preface is the revisions that are not made in this edition. In Chapter XVII, beginning on page 276, there I is a discussion of the field known as operations research (or operational research, as it is called in Britain). It is defined there as the application of scientific method to operational military problems. As such it was developed in EnglandL dur- ing the Battle of Britain, as indicated in the text, and this remained its meaning on both sides of the Atlantic through- out World War 11. At the end of the war the scientists of both countries recognized its great potential for other than military uses (pages 317-18). To further such uses there was *For background material on operational research and on the relation- ship of government to the scientific effort in Britain, both during and preceding World War 11, the reader can consult C. P. Snow's interesting book: Science and Government, Harvard University Press, 1961. PREFACE TO DOVER EDITION formed in England an Operational Research Club, later changed to a Society. In the United States in 1948 the Na- tional Academy of Sciences-National Research Council formed a Committee on Operations Research, with the same purpose of furthering the non-military applications, while certain universities, notably Massachusetts Institute of Tech- nology and Case Institute of Technology, organized courses in the new field. Scientific American and Fortune magazines were the first to feature articles on the subject. As a result of these and other endeavors, operations research (and some- what later its sister discipline, management science) has achieved a growth and an acceptance far beyond the hopes of those of us who were involved in its expansion. There can be little doubt that a major reason for this happy circum- stance is the fact that operations research, in its broadest sense, received the official stamp of approval of science and scientists, at a time in history when science was held in high popular esteem. In the 1939 edition of this book the author, perhaps rather timidly, expressed the hope and the conviction that at some future time the application of scientific method to the opera- tional problems of business and to statistically complex situa- tions in general, would come into its own. In the edition of 1950 much more space was devoted to an analysis of the difficulties involved, as they appeared to the author at that time (1948). These pages have been left unchanged in the present edition (pages 314-23). The fact is that the expansion and the development of the field of operations research have been so great that to bring our remarks on the subject up to date would require a separate volume. Although the subject matter of this book is the elementary theories of probability and statistics and some of their simpler applications, wide segments of operations research are so intimately related to these theories that it properly vii 1 PREFACE TO DOVER EDITION I finds a place in these pages. The examples of military opera- I tions research given in Chapter XVII were necessarily taken I from work done during World War I1 from which, for one reason or another, security restrictions had been lifted. As to non-military work, the bulk of the two final chapters, which appear here unchanged from the 1950 edition, is in fact de- voted to such applications. The majority of the illustrative I examples were based on the author's personal experience in the field. As implied on page 31 7, these examples were selected on the basis of their close relationship to the subject of this book. At that time (1948) what was urgently needed was an appropriate and descriptive term for the application of sci- entific method to the broad field of operations involving men and machines. In addition to being too restrictive, the term "business research," as used in the text, is a poor one. For there has long been intensive research in business and industry directed toward improving products and discovering new ones, and in some cases even extending into the area of basic research, none of which comes under the heading of operations research. The term "science of management" is highly descriptive, provided that it is confined to the functions of management, as usually understood. But opera- tions research is not so confined. It is strange that the English-speaking world should use the two equivalent terms "operational research" and "oper- ations research." Since the British developed the field, at least in its military bearing, and since they coined the expres- sion "operational research," it would seem that the fault lies on this side of the Atlantic. Where and how this schism de- veloped I have never been able to learn. I do know that when the Committee on Operations Research was formed in 1948, the proposal to adopt the British designation was rejected on the ground that the term "operations research" was already too entrenched in the military establishments of viii PREFACE TO DOVER EDITION this country. And so the schism will have to be perpetuated. All this is perhaps a counterexample to the usual implications of the phrase: "What's in a name?" I would like to express my appreciation of the manner in which Dover Publications, and in particular Mr.