- Title Pages
- Dedication
- Foreword
- Preface
- Notation
-
Chapter One A Quick Introduction to Benfordʼs Law -
Chapter Two A Short Introduction to the Mathematical Theory of Benfordʼs Law -
Chapter Three Fourier Analysis and Benfordʼs Law -
Chapter Four Benfordʼs Law Geometry -
Chapter Five Explicit Error Bounds via Total Variation -
Chapter Six Lévy Processes and Benfordʼs Law -
Chapter Seven Benfordʼs Law as a Bridge between Statistics and Accounting -
Chapter Eight Detecting Fraud and Errors Using Benfordʼs Law Mark Nigrini -
Chapter Nine Can Vote Countsʼ Digits and Benfordʼs Law Diagnose Elections? -
Chapter Ten Complementing Benfordʼs Law for Small N: A Local Bootstrap -
Chapter Eleven Measuring the Quality of European Statistics -
Chapter Twelve Benfordʼs Law and Fraud in Economic Research -
Chapter Thirteen Testing for Strategic Manipulation of Economic and Financial Data -
Chapter Fourteen Psychology and Benfordʼs Law -
Chapter Fifteen Managing Risk in Numbers Games -
Chapter Sixteen Benfordʼs Law in the Natural Sciences -
Chapter Seventeen Generalizing Benfordʼs Law -
Chapter Eighteen PV Modeling of Medical Imaging Systems -
Chapter Nineteen Application of Benfordʼs Law to Images -
Chapter Twenty Exercises - Bibliography
- Index
Managing Risk in Numbers Games
Managing Risk in Numbers Games
- Chapter:
- (p.276) Chapter Fifteen Managing Risk in Numbers Games
- Source:
- Benford's Law
- Author(s):
Mabel C. Chou
Qingxia Kong
Chung-Piaw Teo
Huan Zheng
- Publisher:
- Princeton University Press
This chapter applies Benford's law to study how players choose numbers in fixed-odds number lottery games. Empirical data suggests that not all players choose numbers with equal probability in lottery games. Some of them tend to bet on (smaller) numbers that are closely related to events around them (e.g., birthdays, anniversaries, addresses, etc.). In a fixed-odds lottery game, this small-number phenomenon imposes a serious risk on the game operator of a big payout if a very popular number is chosen as the winning number. The chapter quantifies this phenomenon and develops a choice model incorporating a modified Benford's law for lottery players to capture the magnitude of the small-number phenomenon observed in the empirical data.
Keywords: fixed odds, number lottery games, small number, gambling, lottery, managing risk, numbers games
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- Title Pages
- Dedication
- Foreword
- Preface
- Notation
-
Chapter One A Quick Introduction to Benfordʼs Law -
Chapter Two A Short Introduction to the Mathematical Theory of Benfordʼs Law -
Chapter Three Fourier Analysis and Benfordʼs Law -
Chapter Four Benfordʼs Law Geometry -
Chapter Five Explicit Error Bounds via Total Variation -
Chapter Six Lévy Processes and Benfordʼs Law -
Chapter Seven Benfordʼs Law as a Bridge between Statistics and Accounting -
Chapter Eight Detecting Fraud and Errors Using Benfordʼs Law Mark Nigrini -
Chapter Nine Can Vote Countsʼ Digits and Benfordʼs Law Diagnose Elections? -
Chapter Ten Complementing Benfordʼs Law for Small N: A Local Bootstrap -
Chapter Eleven Measuring the Quality of European Statistics -
Chapter Twelve Benfordʼs Law and Fraud in Economic Research -
Chapter Thirteen Testing for Strategic Manipulation of Economic and Financial Data -
Chapter Fourteen Psychology and Benfordʼs Law -
Chapter Fifteen Managing Risk in Numbers Games -
Chapter Sixteen Benfordʼs Law in the Natural Sciences -
Chapter Seventeen Generalizing Benfordʼs Law -
Chapter Eighteen PV Modeling of Medical Imaging Systems -
Chapter Nineteen Application of Benfordʼs Law to Images -
Chapter Twenty Exercises - Bibliography
- Index
