# Chapter 7: Proportional Play and the Kelly Betting System

Save this PDF as:

Size: px
Start display at page:

Download "Chapter 7: Proportional Play and the Kelly Betting System"

## Transcription

2 X 0 ( f) (what you did not bet) plus fx 0 (your original bet) plus γfx 0 (your gain). So we have { { X0 + γfx X 0 if you win X0 ( + γf) with probability p X 0 fx 0 if you lose X 0 ( f) with probability q p So at each step your fortune is multiplied by a random factor either + γf or f, so we define the random variable Q ( + γf) with probability p and Q ( f) with probability q. To find our fortune at time N we take Q, Q 2, Q N independent identically distributed random variables all with the same distribution as Q. Then we have Fortune after N bets is X N Q N Q N Q 2 Q X 0 Since we make a series of super fair bets we expect that our fortune to fluctuate but to increase exponentially X N X 0 exp αn. and so α represents the rate at which our fortune increases. We can compute the long run value of α by using the law of large numbers. Indeed we have and so by Chebyshev α N log(x N/X 0 ) N [log(q ) + log(q 2 ) + log(q N )] N [log(q ) + log(q 2 ) + log(q N )] E[log(Q)] α and we have P ( X 0 e N(α ɛ) X N X 0 e N(α+ɛ)) var(log(q)) Nɛ 2 To find the best asset allocation we seek to imize α E[log(Q)]. 2

3 Optimal proportional play imize E[log(Q)] We have E[log(Q)] p log( + γf) + q log( f) Differentiating with respect to f we find 0 d df E[log(Q)] and so we have Finally we obtain d p log( + γf) + q log( f) df pγ + γf q f pγ( f) q( + γf) pγ q fγ(p + q) fγ () Optimal f : f pγ q γ Expected gain gain Kelly s formula For example if your bet results in a payout of \$0 with probability /4 you should bet f of your fortune on each bet. Your fortune, on the long run, will grow at the rate of α 4 log( ) log( 7 40 ) Horse races: In the same spirit we can wonder what is the optimal strategy if we are betting on a horse race. We suppose there are m horses, and the betting odds are such that if we pay \$ on on horse i then we earn γ i of horse i wins. How should we bet to imize our fortune in the long run? In order not to ever lose all our money it makes sense to split your money and bet on every horse. That is 3

4 Proportional Play Bet a proportion b i of your fortune on horse i. In order to find the optimal proportion we assume that horse i has probability p i to win. How do we find p i is the interesting part of the problem. One possible way to estimate p i is to trust the wisdom of the crowd and to use as p i the proportion of players which bets on horse i. This is the idea behind betting markets where one assume that if many people bet real money on a certain outcome, then their collective knowledge will produce the true probability. This is a version of the efficient market hypothesis which asserts that stock always trade at their fair values. Or in the context of sport betting you may want to believe that a knowledgeable bettor will be able to find the right value of p i by the virtue of his accumulated knowledge. In any case, as in the Kelly betting system above we try to imize the growth rate. If we bet b i on horse i and wins we earn γ i b i so if we start with a fortune X after betting our fortune will be Q b X where Q b is a random variable with and we need to find b i : E[ln(Q b )] b i P {Q b b i γ i } p i b i : b i This can be done using Lagrange multiplier. We set F (b, λ) p i ln(b i γ i ) + λ p i ln(b i γ i ) b i. and differentiating with respect to b i we find that the imum should satisfy p i b i + λ 0 Using that i b i we find λ and thus or b i p i λ Optimal strategy is to bet a proportion b i p i of your fortune. Asset allocation in the stock market: A similar situation occurs in the stock market. We suppose there are m stocks and the i th stock rate of return is described by the random variable Z i Z i ratio of the value of stock i tomorrow and the value of stock i today 4

5 that is Z i.98 it means the stock i lost two percent today. To invest our money we decide to invest a proportion b i of our fortune in stock i with m b i. With this allocation our fortune after N days will be where Q i are IID copies of Q X N Q N Q X 0 Q b i Z i and X 0 is the initial fortune. In order to imize the rate of growth of the fortune, we need to find b i 0 E[log( m b i Z i )] b i 5

### Week 4: Gambler s ruin and bold play

Week 4: Gambler s ruin and bold play Random walk and Gambler s ruin. Imagine a walker moving along a line. At every unit of time, he makes a step left or right of exactly one of unit. So we can think that

### The Kelly criterion for spread bets

IMA Journal of Applied Mathematics 2007 72,43 51 doi:10.1093/imamat/hxl027 Advance Access publication on December 5, 2006 The Kelly criterion for spread bets S. J. CHAPMAN Oxford Centre for Industrial

### Week 5: Expected value and Betting systems

Week 5: Expected value and Betting systems Random variable A random variable represents a measurement in a random experiment. We usually denote random variable with capital letter X, Y,. If S is the sample

### Betting with the Kelly Criterion

Betting with the Kelly Criterion Jane June 2, 2010 Contents 1 Introduction 2 2 Kelly Criterion 2 3 The Stock Market 3 4 Simulations 5 5 Conclusion 8 1 Page 2 of 9 1 Introduction Gambling in all forms,

### Goal Problems in Gambling and Game Theory. Bill Sudderth. School of Statistics University of Minnesota

Goal Problems in Gambling and Game Theory Bill Sudderth School of Statistics University of Minnesota 1 Three problems Maximizing the probability of reaching a goal. Maximizing the probability of reaching

### Part I. Gambling and Information Theory. Information Theory and Networks. Section 1. Horse Racing. Lecture 16: Gambling and Information Theory

and Networks Lecture 16: Gambling and Paul Tune http://www.maths.adelaide.edu.au/matthew.roughan/ Lecture_notes/InformationTheory/ Part I Gambling and School of Mathematical

### National Sun Yat-Sen University CSE Course: Information Theory. Gambling And Entropy

Gambling And Entropy 1 Outline There is a strong relationship between the growth rate of investment in a horse race and the entropy of the horse race. The value of side information is related to the mutual

### Expected Value. 24 February 2014. Expected Value 24 February 2014 1/19

Expected Value 24 February 2014 Expected Value 24 February 2014 1/19 This week we discuss the notion of expected value and how it applies to probability situations, including the various New Mexico Lottery

### Prediction Markets, Fair Games and Martingales

Chapter 3 Prediction Markets, Fair Games and Martingales Prediction markets...... are speculative markets created for the purpose of making predictions. The current market prices can then be interpreted

### Review Horse Race Gambling and Side Information Dependent horse races and the entropy rate. Gambling. Besma Smida. ES250: Lecture 9.

Gambling Besma Smida ES250: Lecture 9 Fall 2008-09 B. Smida (ES250) Gambling Fall 2008-09 1 / 23 Today s outline Review of Huffman Code and Arithmetic Coding Horse Race Gambling and Side Information Dependent

### פרויקט מסכם לתואר בוגר במדעים )B.Sc( במתמטיקה שימושית

המחלקה למתמטיקה Department of Mathematics פרויקט מסכם לתואר בוגר במדעים )B.Sc( במתמטיקה שימושית הימורים אופטימליים ע"י שימוש בקריטריון קלי אלון תושיה Optimal betting using the Kelly Criterion Alon Tushia

### SOME ASPECTS OF GAMBLING WITH THE KELLY CRITERION. School of Mathematical Sciences. Monash University, Clayton, Victoria, Australia 3168

SOME ASPECTS OF GAMBLING WITH THE KELLY CRITERION Ravi PHATARFOD School of Mathematical Sciences Monash University, Clayton, Victoria, Australia 3168 In this paper we consider the problem of gambling with

### Betting systems: how not to lose your money gambling

Betting systems: how not to lose your money gambling G. Berkolaiko Department of Mathematics Texas A&M University 28 April 2007 / Mini Fair, Math Awareness Month 2007 Gambling and Games of Chance Simple

### The Kelly Betting System for Favorable Games.

The Kelly Betting System for Favorable Games. Thomas Ferguson, Statistics Department, UCLA A Simple Example. Suppose that each day you are offered a gamble with probability 2/3 of winning and probability

### A New Interpretation of Information Rate

A New Interpretation of Information Rate reproduced with permission of AT&T By J. L. Kelly, jr. (Manuscript received March 2, 956) If the input symbols to a communication channel represent the outcomes

### Lecture 25: Money Management Steven Skiena. http://www.cs.sunysb.edu/ skiena

Lecture 25: Money Management Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 4400 http://www.cs.sunysb.edu/ skiena Money Management Techniques The trading

### Probability and Expected Value

Probability and Expected Value This handout provides an introduction to probability and expected value. Some of you may already be familiar with some of these topics. Probability and expected value are

### Gambling and Data Compression

Gambling and Data Compression Gambling. Horse Race Definition The wealth relative S(X) = b(x)o(x) is the factor by which the gambler s wealth grows if horse X wins the race, where b(x) is the fraction

### Section 7C: The Law of Large Numbers

Section 7C: The Law of Large Numbers Example. You flip a coin 00 times. Suppose the coin is fair. How many times would you expect to get heads? tails? One would expect a fair coin to come up heads half

### Lecture 2: The Kelly criterion for favorable games: stock market investing for individuals

Lecture 2: The Kelly criterion for favorable games: stock market investing for individuals David Aldous September 8, 2014 Most adults drive/own a car Few adults work in the auto industry. By analogy Most

### Term Project: Roulette

Term Project: Roulette DCY Student January 13, 2006 1. Introduction The roulette is a popular gambling game found in all major casinos. In contrast to many other gambling games such as black jack, poker,

### Elementary Statistics and Inference. Elementary Statistics and Inference. 17 Expected Value and Standard Error. 22S:025 or 7P:025.

Elementary Statistics and Inference S:05 or 7P:05 Lecture Elementary Statistics and Inference S:05 or 7P:05 Chapter 7 A. The Expected Value In a chance process (probability experiment) the outcomes of

### Gambling with Information Theory

Gambling with Information Theory Govert Verkes University of Amsterdam January 27, 2016 1 / 22 How do you bet? Private noisy channel transmitting results while you can still bet, correct transmission(p)

α α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =

### The Mathematics of Gambling

The Mathematics of Gambling with Related Applications Madhu Advani Stanford University April 12, 2014 Madhu Advani (Stanford University) Mathematics of Gambling April 12, 2014 1 / 23 Gambling Gambling:

### THE WINNING ROULETTE SYSTEM by http://www.webgoldminer.com/

THE WINNING ROULETTE SYSTEM by http://www.webgoldminer.com/ Is it possible to earn money from online gambling? Are there any 100% sure winning roulette systems? Are there actually people who make a living

### Enriching Tradition Through Technology

WYOMING PARI-MUTUEL COMMISSION Enriching Tradition Through Technology Historic Racing is an effort by racing interests to present traditional horse racing with a new and electronic look! WYOMING S TRADITION

### A Simple Parrondo Paradox. Michael Stutzer, Professor of Finance. 419 UCB, University of Colorado, Boulder, CO 80309-0419

A Simple Parrondo Paradox Michael Stutzer, Professor of Finance 419 UCB, University of Colorado, Boulder, CO 80309-0419 michael.stutzer@colorado.edu Abstract The Parrondo Paradox is a counterintuitive

### Expected Value and the Game of Craps

Expected Value and the Game of Craps Blake Thornton Craps is a gambling game found in most casinos based on rolling two six sided dice. Most players who walk into a casino and try to play craps for the

### Can I hold a race night, casino night or poker night? Click here for printer-friendly version

Can I hold a race night, casino night or poker night? Click here for printer-friendly version Can I hold a race night or casino night to raise funds for charity? You should read all of the information

### Published in 2003 by High Stakes Publishing, 21 Great Ormond Street, London, WC1N 3JB www.highstakes.co.uk. Copyright Joseph Buchdahl

Published in 2003 by High Stakes Publishing, 21 Great Ormond Street, London, WC1N 3JB www.highstakes.co.uk Copyright Joseph Buchdahl The right of Joseph Buchdahl to be identified as author of this work

### Elementary Statistics and Inference. Elementary Statistics and Inference. 16 The Law of Averages (cont.) 22S:025 or 7P:025.

Elementary Statistics and Inference 22S:025 or 7P:025 Lecture 20 1 Elementary Statistics and Inference 22S:025 or 7P:025 Chapter 16 (cont.) 2 D. Making a Box Model Key Questions regarding box What numbers

### Unit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.)

Unit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.) Logistic regression generalizes methods for 2-way tables Adds capability studying several predictors, but Limited to

### Applying the Kelly criterion to lawsuits

Law, Probability and Risk (2010) 9, 139 147 Advance Access publication on April 27, 2010 doi:10.1093/lpr/mgq002 Applying the Kelly criterion to lawsuits TRISTAN BARNETT Faculty of Business and Law, Victoria

### Gambling Systems and Multiplication-Invariant Measures

Gambling Systems and Multiplication-Invariant Measures by Jeffrey S. Rosenthal* and Peter O. Schwartz** (May 28, 997.. Introduction. This short paper describes a surprising connection between two previously

### Guide to Spread Betting

www.footballbettingdata.co.uk Guide to Spread Betting Part One: How to get a 9/2 payout from a 5/6 shot Are you interested in boosting your profits? Of course you are. Who isn t? There is more to making

### DEVELOPING A MODEL THAT REFLECTS OUTCOMES OF TENNIS MATCHES

DEVELOPING A MODEL THAT REFLECTS OUTCOMES OF TENNIS MATCHES Barnett T., Brown A., and Clarke S. Faculty of Life and Social Sciences, Swinburne University, Melbourne, VIC, Australia ABSTRACT Many tennis

### Decision Theory. 36.1 Rational prospecting

36 Decision Theory Decision theory is trivial, apart from computational details (just like playing chess!). You have a choice of various actions, a. The world may be in one of many states x; which one

### Who is behind The Betting Lion?

Who is behind The Betting Lion? My name is Mike Walker and I am the man behind the succesful sports handicapping service The Betting Lion. I turned \$2000 into \$460 000 for 5 years before I discovered my

### Finite Horizon Investment Risk Management

History Collaborative research with Ralph Vince, LSP Partners, LLC, and Marcos Lopez de Prado, Guggenheim Partners. Qiji Zhu Western Michigan University Workshop on Optimization, Nonlinear Analysis, Randomness

### Betting on Excel to enliven the teaching of probability

Betting on Excel to enliven the teaching of probability Stephen R. Clarke School of Mathematical Sciences Swinburne University of Technology Abstract The study of probability has its roots in gambling

### Probability Models.S1 Introduction to Probability

Probability Models.S1 Introduction to Probability Operations Research Models and Methods Paul A. Jensen and Jonathan F. Bard The stochastic chapters of this book involve random variability. Decisions are

### In the situations that we will encounter, we may generally calculate the probability of an event

What does it mean for something to be random? An event is called random if the process which produces the outcome is sufficiently complicated that we are unable to predict the precise result and are instead

### We have put together this beginners guide to sports betting to help you through your first foray into the betting world.

If there is one thing about sports betting that is an absolute certainty, it s that the game is infinitely more exciting when there is money on the outcome. Most people like you are new to this concept

### 1. Overconfidence {health care discussion at JD s} 2. Biased Judgments. 3. Herding. 4. Loss Aversion

In conditions of laissez-faire the avoidance of wide fluctuations in employment may, therefore, prove impossible without a far-reaching change in the psychology of investment markets such as there is no

### Kelly s Criterion for Option Investment. Ron Shonkwiler (shonkwiler@math.gatech.edu)

Kelly s Criterion for Option Investment Ron Shonkwiler (shonkwiler@math.gatech.edu) 1 1 Kelly s Criterion for Option Investment Ron Shonkwiler (shonkwiler@math.gatech.edu) Outline: Review Kelly s Problem

### You can place bets on the Roulette table until the dealer announces, No more bets.

Roulette Roulette is one of the oldest and most famous casino games. Every Roulette table has its own set of distinctive chips that can only be used at that particular table. These chips are purchased

### Fair Price. Math 5 Crew. Department of Mathematics Dartmouth College. Fair Price p.1/??

Fair Price p.1/?? Fair Price Math 5 Crew Department of Mathematics Dartmouth College Fair Price p.2/?? Historical Perspective We are about ready to explore probability form the point of view of a free

### Advice on non-commercial and private gaming and betting

Advice on non-commercial and private gaming and betting November 2012 Contents 1 Introduction 3 2 Defining non-commercial and private gaming and betting 3 3 Non-commercial prize gaming 4 4 Non-commercial

### Comparing & Contrasting. - mathematically. Ways of comparing mathematical and scientific quantities...

Comparing & Contrasting - mathematically Ways of comparing mathematical and scientific quantities... Comparison by Division: using RATIOS, PERCENTAGES, ODDS, and PROPORTIONS Definition of Probability:

### MA 1125 Lecture 14 - Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values.

MA 5 Lecture 4 - Expected Values Friday, February 2, 24. Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the

### A Range Trading System

A Range Trading System Daniel Herlemont email:dherlemont@yats.com - YATS Finances & Technologies - tel:+33 (0) 5 62 71 22 84 This trading system addresses some questions like: ˆ probability of hitting

### Chapter 22. Markets and Information

From the book Networks, Crowds, and Markets: Reasoning about a Highly Connected World. By David Easley and Jon Kleinberg. Cambridge University Press, 2010. Complete preprint on-line at http://www.cs.cornell.edu/home/kleinber/networks-book/

### If You Think Investing is Gambling, You re Doing it Wrong!

If You Think Investing is Gambling, You re Doing it Wrong! Warren Buffet Jennifer Arthur, M.Sc. PhD Candidate, University of Adelaide Supervisor: Dr. Paul Delfabbro 10th European Conference on Gambling

### Instant Earnings. Long-term Earnings

Partner Programme Earn a piece of the turnover from Lopoca s games! Casino, Sportsbetting, Poker, Nugget Game and IQ-Game The Lopoca Difference! Your ability to Earn CashBack AND a piece of the gaming

### MOVIES, GAMBLING, SECRET CODES, JUST MATRIX MAGIC

MOVIES, GAMBLING, SECRET CODES, JUST MATRIX MAGIC DR. LESZEK GAWARECKI 1. The Cartesian Coordinate System In the Cartesian system points are defined by giving their coordinates. Plot the following points:

### NAPCS Product List for NAICS 7132: Gambling Industries

NAPCS List for NAICS 7132: Gambling Industries 7132 1 Gambling services Providing games of chance and making/taking wagers on such games, including the outcome of sporting events or on other future events

### Math 425 (Fall 08) Solutions Midterm 2 November 6, 2008

Math 425 (Fall 8) Solutions Midterm 2 November 6, 28 (5 pts) Compute E[X] and Var[X] for i) X a random variable that takes the values, 2, 3 with probabilities.2,.5,.3; ii) X a random variable with the

### How to bet and win: and why not to trust a winner. Niall MacKay. Department of Mathematics

How to bet and win: and why not to trust a winner Niall MacKay Department of Mathematics Two ways to win Arbitrage: exploit market imperfections to make a profit, with certainty Two ways to win Arbitrage:

### On Directed Information and Gambling

On Directed Information and Gambling Haim H. Permuter Stanford University Stanford, CA, USA haim@stanford.edu Young-Han Kim University of California, San Diego La Jolla, CA, USA yhk@ucsd.edu Tsachy Weissman

### Automatic Bet Tracker!

Russell Hunter Street Smart Roulette Automatic Bet Tracker! Russell Hunter Publishing, Inc. Street Smart Roulette Automatic Bet Tracker 2015 Russell Hunter and Russell Hunter Publishing, Inc. All Rights

### We rst consider the game from the player's point of view: Suppose you have picked a number and placed your bet. The probability of winning is

Roulette: On an American roulette wheel here are 38 compartments where the ball can land. They are numbered 1-36, and there are two compartments labeled 0 and 00. Half of the compartments numbered 1-36

### Spaceball7. Manual Outlet Version 1

Spaceball7 Manual Outlet Version 1 Table of contents 1 Spaceball7 Main View...3 2 Bingo-Mode... 4 3 Spaceball7 special bets ("Super7")...5 4 Bet slip... 6 5 Spaceball7 draw...7 6 Display of past drawing

### Betting rules and information theory

Betting rules and information theory Giulio Bottazzi LEM and CAFED Scuola Superiore Sant Anna September, 2013 Outline Simple betting in favorable games The Central Limit Theorem Optimal rules The Game

### arxiv:math/0412362v1 [math.pr] 18 Dec 2004

Improving on bold play when the gambler is restricted arxiv:math/0412362v1 [math.pr] 18 Dec 2004 by Jason Schweinsberg February 1, 2008 Abstract Suppose a gambler starts with a fortune in (0, 1) and wishes

### Betting Terms Explained www.sportsbettingxtra.com

Betting Terms Explained www.sportsbettingxtra.com To most people betting has a language of its own, so to help, we have explained the main terms you will come across when betting. STAKE The stake is the

### Introduction to Hypothesis Testing. Point estimation and confidence intervals are useful statistical inference procedures.

Introduction to Hypothesis Testing Point estimation and confidence intervals are useful statistical inference procedures. Another type of inference is used frequently used concerns tests of hypotheses.

### During the course of our research on NBA basketball, we found out a couple of interesting principles.

After mining all the available NBA data for the last 15 years, we found the keys to a successful basketball betting system: If you follow this system exactly, you can expect to hit 90% of your NBA bets.

### Remote gambling taxation reform

Remote gambling taxation reform Who is likely to be affected? This measure will affect all gambling operators who supply remote gambling to UK customers. Some terrestrial gambling operators will also be

### Stat 134 Fall 2011: Gambler s ruin

Stat 134 Fall 2011: Gambler s ruin Michael Lugo Setember 12, 2011 In class today I talked about the roblem of gambler s ruin but there wasn t enough time to do it roerly. I fear I may have confused some

### John Kerrich s coin-tossing Experiment. Law of Averages - pg. 294 Moore s Text

Law of Averages - pg. 294 Moore s Text When tossing a fair coin the chances of tails and heads are the same: 50% and 50%. So, if the coin is tossed a large number of times, the number of heads and the

### Chapter 4 Lecture Notes

Chapter 4 Lecture Notes Random Variables October 27, 2015 1 Section 4.1 Random Variables A random variable is typically a real-valued function defined on the sample space of some experiment. For instance,

### To begin, I want to introduce to you the primary rule upon which our success is based. It s a rule that you can never forget.

Welcome to the casino secret to profitable options trading. I am very excited that we re going to get the chance to discuss this topic today. That s because, in this video course, I am going to teach you

### The New Mexico Lottery

The New Mexico Lottery 26 February 2014 Lotteries 26 February 2014 1/27 Today we will discuss the various New Mexico Lottery games and look at odds of winning and the expected value of playing the various

### Standard 12: The student will explain and evaluate the financial impact and consequences of gambling.

STUDENT MODULE 12.1 GAMBLING PAGE 1 Standard 12: The student will explain and evaluate the financial impact and consequences of gambling. Risky Business Simone, Paula, and Randy meet in the library every

### Intoduction to the Fifth Workshop Game-Theoretic Probability and Related Topics

Intoduction to the Fifth Workshop Game-Theoretic Probability and Related Topics Glenn Shafer 13 November 2014 1. Basics of game-theoretic probability 2. Probability-free finance 3. Prediction Glenn Shafer

### National Gambling Statistics Casinos, Bingo, Limited Pay-out Machines and Fixed Odds and Totalisator Betting

National Gambling Statistics Casinos, Bingo, Limited Pay-out Machines and Fixed Odds and Totalisator Betting 2013/2014 Financial Year (FY14) 1 April 2013 31 March 2014 Quarter 1 = 1 April 2013 30 June

### Estimating the Frequency Distribution of the. Numbers Bet on the California Lottery

Estimating the Frequency Distribution of the Numbers Bet on the California Lottery Mark Finkelstein November 15, 1993 Department of Mathematics, University of California, Irvine, CA 92717. Running head:

### Easy Surefire Guaranteed System To Win Every Time At Online Blackjack (only system in the world based on human greed)

Easy Surefire Guaranteed System To Win Every Time At Online Blackjack (only system in the world based on human greed) Brought to you by advantagegamingtools.com Page 1 WWW.DEALPLAYWIN.COM Hello fellow

### You Are What You Bet: Eliciting Risk Attitudes from Horse Races

You Are What You Bet: Eliciting Risk Attitudes from Horse Races Pierre-André Chiappori, Amit Gandhi, Bernard Salanié and Francois Salanié March 14, 2008 What Do We Know About Risk Preferences? Not that

### Learn How to Use The Roulette Layout To Calculate Winning Payoffs For All Straight-up Winning Bets

Learn How to Use The Roulette Layout To Calculate Winning Payoffs For All Straight-up Winning Bets Understand that every square on every street on every roulette layout has a value depending on the bet

### ECE 316 Probability Theory and Random Processes

ECE 316 Probability Theory and Random Processes Chapter 4 Solutions (Part 2) Xinxin Fan Problems 20. A gambling book recommends the following winning strategy for the game of roulette. It recommends that

### TABLE OF CONTENTS. ROULETTE FREE System #1 ------------------------- 2 ROULETTE FREE System #2 ------------------------- 4 ------------------------- 5

IMPORTANT: This document contains 100% FREE gambling systems designed specifically for ROULETTE, and any casino game that involves even money bets such as BLACKJACK, CRAPS & POKER. Please note although

### A THEORETICAL ANALYSIS OF THE MECHANISMS OF COMPETITION IN THE GAMBLING MARKET

A THEORETICAL ANALYSIS OF THE MECHANISMS OF COMPETITION IN THE GAMBLING MARKET RORY MCSTAY Senior Freshman In this essay, Rory McStay describes the the effects of information asymmetries in the gambling

### ! Insurance and Gambling

2009-8-18 0 Insurance and Gambling Eric Hehner Gambling works as follows. You pay some money to the house. Then a random event is observed; it may be the roll of some dice, the draw of some cards, or the

### Sin City. In poker, the facility to buy additional chips in tournaments. Total payout liability of a casino during any one game.

gambling glossary Words & phrases to help you out with your dealings at The Paramount Casino A Action: Active Player: Added Game: Add-on: Aggregate Limit: A bet or wager. In poker, one who is still in

### Risk Formulæ for Proportional Betting

Risk Formulæ for Proportional Betting William Chin DePaul University, Chicago, Illinois Marc Ingenoso Conger Asset Management LLC, Chicago, Illinois September 9, 2006 Introduction A canon of the theory

### Random Fibonacci-type Sequences in Online Gambling

Random Fibonacci-type Sequences in Online Gambling Adam Biello, CJ Cacciatore, Logan Thomas Department of Mathematics CSUMS Advisor: Alfa Heryudono Department of Mathematics University of Massachusetts

### Chance and Uncertainty: Probability Theory

Chance and Uncertainty: Probability Theory Formally, we begin with a set of elementary events, precisely one of which will eventually occur. Each elementary event has associated with it a probability,

### Is betting on horse racing legal in south carolina, horse racing betting statistics, horse racing betting made easy, betting on horse racing online.

Is betting on horse racing legal in south carolina, horse racing betting statistics, horse racing betting made easy, betting on horse racing online. > GET IT HERE < Lowprice horse race betting in france

### Virtual Sports Betting Secrets

Virtual Sports Betting Secrets How to make a fortune betting on virtual football by using these revolutionary new betting systems A step-by-step blueprint for beginners or experts! By: Frank Belanger www.virtualsportscash.com

### Percent, Sales Tax, & Discounts

Percent, Sales Tax, & Discounts Many applications involving percent are based on the following formula: Note that of implies multiplication. Suppose that the local sales tax rate is 7.5% and you purchase

### The following words and terms, when used in this subchapter, shall have the following meanings unless the context clearly indicates otherwise.

CHAPTER 69E GAMING EQUIPMENT 13:69E-1.10 (a) (u) No Change (v) If a casino licensee offers bet the set blackjack pursuant to N.J.A.C. 13:69F- 2.29, the layout otherwise required by this section shall also

### 5-10 - 20-40 -80-160 - 320-640 - 1280-2560 - 5120-10,240-20,480-40,960-81,920

Progression Betting With horse betting, or any kind of betting, anything other than flat betting is in fact a kind of progression... but the subject in this article is (as it should be) a bit controversial:

### Sport Hedge Millionaire s Guide to a growing portfolio. Sports Hedge

Sports Hedge Sport Hedging for the millionaire inside us, a manual for hedging and profiting for a growing portfolio Congratulations, you are about to have access to the techniques sports books do not

### Risk Adjustment for Poker Players

Risk Ajustment for Poker Players William Chin DePaul University, Chicago, Illinois Marc Ingenoso Conger Asset Management LLC, Chicago, Illinois September, 2006 Introuction In this article we consier risk

### 5. FIXED ODDS BETS. 5.1 Fixed Odds Betting

5. FIXED ODDS BETS 5.1 Fixed Odds Betting (c) (d) (e) (f) The Operator may decide from time to time to offer the types of Fixed Odds Bets in relation to any race, races or race meeting. The Operator may,