Investment Betting Algorithm

121 Pages·2009·4.21 MB·English

by  Long, Jarrod

To my parents, name and name, in gratitude for their encouragement and
support.

v
Abstract
All bettors, including the ”House,” experience losing streaks and winning
streaks. The House typically has a ”bankroll” that is orders of magnitude
larger than that of any individual bettor, and so can survive losing streaks
without going bankrupt, thus remaining solvent long enough to win. Online
wagering provides a new twist to this age-old scenario. We use elementary
mathematical principles together with the idea of a virtual infinite sample
sizeandtheeliminationoftimeasaconstrainttodevelopafail-proofsystem
that generates the greatest possible exponential growth of capital.
Let σ (stake) be the amount you wish to invest or wager each time and
ρ (return) be your return or odds on a proposition. Let n (number) be the
sum of consecutive loosing investments or number of times you can loose on
an identical proposition before depleting a specified amount of investment
capital called β ( bankroll). The resultant equation, which I call the :
n
i
Investment Betters Algorithm (IBA) β = 2σ (ρ )
Xi=0
provides the answer to remaining solvent long enough to outlast the irra-
tionalityofthesimulatedonline”wagersopenmarket”throughageometric
progression. The augmented bankroll β , calculated slightly higher than the
typical sum of the Geometric Series, can serve as a safeguard to capital ruin
by it extreme disproportion to. Consider further the expected value of even
money propositions, a virtual infinite sample size, and the elimination of
time as a constraint and you have a no fail system to generate the greatest
progressive exponential growth of capital.
Current problems associated with financial return optimization algo-
rithms are identified and discussed. Probable solutions to those problems
are also prescribed along with improvements to diversified portfolio design.
vii
Contents
Acknowledgements iv
Abstract v
1 Introduction 1
1.1 Motivation for Experiment . . . . . . . . . . . . . . . . . . . 1
1.2 Turning Point . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Statement Summary . . . . . . . . . . . . . . . . . . . . . . 13
2 Philosophy 14
2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Empirical Mathematical Basis . . . . . . . . . . . . . . . . . 22
2.3 The next worse thing . . . . . . . . . . . . . . . . . . . . . . 32
3 What’s at stake ? 40
3.1 Which Wager . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 How much to Wager . . . . . . . . . . . . . . . . . . . . . . 43
3.3 How much bankroll do you need . . . . . . . . . . . . . . . . 46
4 Advantages 50
4.1 Better off with IBA . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 Advantages to Kelly . . . . . . . . . . . . . . . . . . . . . . 57
4.3 Advantages to Martingale . . . . . . . . . . . . . . . . . . . 63
4.4 General Advantages . . . . . . . . . . . . . . . . . . . . . . . 70
5 Results 86
5.1 Outcome of Algorithm Implementation . . . . . . . . . . . . 86
5.2 Earning Capabilities of IBA . . . . . . . . . . . . . . . . . . 90
5.3 DataSet Wagering of Activity . . . . . . . . . . . . . . . . . 94
5.4 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6 References 109
6.1 Links and Resources . . . . . . . . . . . . . . . . . . . . . . 109
Bibliography 111
1
Chapter 1
Introduction
1.1 Motivation for Experiment
There are several mathematical strategies behind picking an optimal win-
ning wagering schema that many professional players use constantly to get
a slightly higher wining percentage than what is expected. This is similar
to the approach many investors take in attempting to beat the open mar-
ket by finding the next winning stock that will have a runaway winning
season, so to speak, in the largest international legal casino on the planet,
which happens to be the stock market. It’s widely accepted in the economic
universe that the market cannot be beat; but what about the Casinos and
Sports books ?
In an analytical work for Fortune and CNN Money published in 2002
titled ’Is The Market Rational? No, say the experts . . .’ Justin Fox [9]
summarizes the underlying message of Chicago professor Eugene Fama’s
address to the American Finance Association in 1969[7] as: In an efficient