I am hoping to bring more new traffic to my second Blogger website, Satire Und Theology, so I will be publishing second versions of articles from Dr. Russell Norman Murray, with bonus work I do not want to lead with.
The Gambler's Fallacy
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Preface
An entry in the Pirie book review. Originally published on 20170306, edited on Blogger for an entry on academia.edu, 20250105.
PIRIE, MADSEN (2006)(2015) How To Win Every Argument, Bloomsbury, London.
PIRIE, MADSEN (2006)(2015) How To Win Every Argument, Bloomsbury, London.
The Gambler's Fallacy
Cited
'Gamblers, and others, are led into this fallacy by confusing the odds against a whole sequence with the odds against any event in that sequence.' (113). The odds against a coin landing heads five times in a row are therefore: 1/2 x 1/2 x 1/2 x 1/2 x 1/2 or 1/32 (113).
Very importantly...
Cited
'If the first four tosses, despite the odds, come down to heads, the chance of the fifth toss being heads is not 1 in 32, but 1 in 2.' (113). The odds for each individual toss remain the same! The previous tosses do not somehow effect the next. (113).
Pirie correctly reasons that philosophically, the odds remain the same. Luck will not improve or get worse. (114). Luck will not 'even out'. (114). The coin toss is random and heads or tails occurs by chance.
Investpedia
Cited
'What is the 'Gambler's Fallacy'
The gambler's fallacy is when an individual erroneously believes that the onset of a certain random event is less likely to happen following an event or a series of events. This line of thinking is incorrect because past events do not change the probability that certain events will occur in the future.'
Cited
'Gamblers, and others, are led into this fallacy by confusing the odds against a whole sequence with the odds against any event in that sequence.' (113). The odds against a coin landing heads five times in a row are therefore: 1/2 x 1/2 x 1/2 x 1/2 x 1/2 or 1/32 (113).
Very importantly...
Cited
'If the first four tosses, despite the odds, come down to heads, the chance of the fifth toss being heads is not 1 in 32, but 1 in 2.' (113). The odds for each individual toss remain the same! The previous tosses do not somehow effect the next. (113).
Pirie correctly reasons that philosophically, the odds remain the same. Luck will not improve or get worse. (114). Luck will not 'even out'. (114). The coin toss is random and heads or tails occurs by chance.
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Cited
'What is the 'Gambler's Fallacy'
The gambler's fallacy is when an individual erroneously believes that the onset of a certain random event is less likely to happen following an event or a series of events. This line of thinking is incorrect because past events do not change the probability that certain events will occur in the future.'
Investpedia References
University of Wisconsin. "The Gambler's Fallacy: On the Danger of Misunderstanding Simple Probabilities," Page 1-2.
American Statistical Association, Chance. "The Mathematical Anatomy of the Gambler's Fallacy.
Online
My Example of this fallacy
'The Vancouver Canucks are likely to win the Stanley Cup in the next few years, because they have not won it since entering the League in 1970.'
Professional oddsmakers can create reasonable odds of a particular team winning the Stanley Cup in a given year. It has nothing to do with any concept that the odds will even out, or with fairness.
Pirie explains that in this context, the universe is not fair. (115).
Rather, from a Christian theological perspective, God has established laws of the universe and within that is mathematical chance which can be logically explained in equation. From a theological perspective, this is no way negates the concept of an infinite, eternal, sovereign, providential God that created and maintains natural laws and can interfere supernaturally within divine will as first and primary cause.
My Example of this fallacy
'The Vancouver Canucks are likely to win the Stanley Cup in the next few years, because they have not won it since entering the League in 1970.'
Professional oddsmakers can create reasonable odds of a particular team winning the Stanley Cup in a given year. It has nothing to do with any concept that the odds will even out, or with fairness.
Pirie explains that in this context, the universe is not fair. (115).
Rather, from a Christian theological perspective, God has established laws of the universe and within that is mathematical chance which can be logically explained in equation. From a theological perspective, this is no way negates the concept of an infinite, eternal, sovereign, providential God that created and maintains natural laws and can interfere supernaturally within divine will as first and primary cause.
From Science Direct
The gambler's fallacy and gender
Cited
'Abstract
The “gambler's fallacy” is the false belief that a random event is less likely to occur if the event has occurred recently. Such beliefs are false if the onset of events is in fact independent of previous events. We study gender differences in the gambler's fallacy using data from the Danish state lottery. Our data set is unique in that we track individual players over time which allows us to investigate how men and women react with their number picking to outcomes of recent lotto drawings. We find evidence of gambler's fallacy for men but not for women. On average, men are about 1% less likely to bet on numbers drawn in the previous week than on numbers not drawn. Women do not react significantly to the previous week's drawing outcome.'
Science Direct References
M. Bar-Hillel et al. The perception of randomness Advances in Applied Mathematics (1991)
T. Dohmen et al. Biased probability judgment. Evidence of incidence and relationship to economic outcomes from a representative sample, Journal of Economic Behavior & Organization (2009)
C. Eckel et al. Forecasting risk attitudes: an experimental study using actual and forecast gamble choices Journal of Economic Behavior & Organization (2008)
L. Farrell et al. The welfare effects of lotto: evidence from the UK Journal of Public Economics (1999)
M. Kearney State lotteries and consumer behavior Journal of Public Economics (2005)
K. Wärneryd Risk attitudes and risky behavior Journal of Economic Psychology (1996)
G. Charness et al. When optimal choices feel wrong: a laboratory study of Bayesian updating, complexity, and affect American Economic Review (2005)
C. Clotfelder et al. The “gambler's fallacy” in lottery play Management Science (1993)
R. Croson et al. Gender differences in preferences Journal of Economic Literature (2009)
R. Croson et al. The gambler's fallacy and the hot hand: empirical data from casinos Journal of Risk and Uncertainty (2005)
P. Delfabbro et al. It's not what you know, but how you use it: statistical knowledge and adolescent problem gambling Journal of Gambling Studies (2006)
M. Griffiths et al. The psychology of lottery gambling International Gambling Studies (2001)
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If gambling foolishness and the gambler's fallacy is more prevalent in males than females, I am glad I have no interest in gambling, as a male.
References
LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. (Philosophy).
PIRIE, MADSEN (2006)(2015) How To Win Every Argument, Bloomsbury, London.
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Bonus work
I pray that my life will not be tragic.
I pray that my death will not be tragic.
In the name of God the Father, God the Son and God the Holy Spirit
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