On Chance: Gamblers III

"Behavioural research shows that we tend to use simplifying heuristics when making judgements about uncertain events. These are prone to biases and systematic errors, such as stereotyping, disregard of sample size, disregard for regression to the mean, deriving estimates based on the ease of retrieving instances of the event, anchoring to the initial frame, the gambler’s fallacy, and wishful thinking, which are all affected by our inability to consider more than a few aspects or dimensions of any phenomenon or situation at the same time." (Hans G Daellenbach & Donald C McNickle, "Management Science: Decision making through systems thinking", 2005)

"People sometimes appeal to the ‘law of averages’ to justify their faith in the gambler’s fallacy. They may reason that, since all outcomes are equally likely, in the long run they will come out roughly equal in frequency. However, the next throw is very much in the short run and the coin, die or roulette wheel has no memory of what went before." (Alan Graham, "Developing Thinking in Statistics", 2006)

"Another kind of error possibly related to the use of the representativeness heuristic is the gambler’s fallacy, otherwise known as the law of averages. If you are playing roulette and the last four spins of the wheel have led to the ball’s landing on black, you may think that the next ball is more likely than otherwise to land on red. This cannot be. The roulette wheel has no memory. The chance of black is just what it always is. The reason people tend to think otherwise may be that they expect the sequence of events to be representative of random sequences, and the typical random sequence at roulette does not have five blacks in a row." (Jonathan Baron, "Thinking and Deciding" 4th Ed, 2008)

"The theory of randomness is fundamentally a codification of common sense. But it is also a field of subtlety, a field in which great experts have been famously wrong and expert gamblers infamously correct. What it takes to understand randomness and overcome our misconceptions is both experience and a lot of careful thinking." (Leonard Mlodinow, "The Drunkard’s Walk: How Randomness Rules Our Lives", 2008)

"Finding patterns is easy in any kind of data-rich environment; that's what mediocre gamblers do. The key is in determining whether the patterns represent signal or noise." (Nate Silver, "The Signal and the Noise: Why So Many Predictions Fail-but Some Don't", 2012)

"[…] many gamblers believe in the fallacious law of averages because they are eager to find a profitable pattern in the chaos created by random chance." (Gary Smith, "Standard Deviations", 2014)

On Chance: Gamblers II

"Pure mathematics is the world's best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It's free. It can be played anywhere - Archimedes did it in a bathtub." (Richard J Trudeau, "Dots and Lines", 1976)

"Probability does pervade the universe, and in this sense, the old chestnut about baseball imitating life really has validity. The statistics of streaks and slumps, properly understood, do teach an important lesson about epistemology, and life in general. The history of a species, or any natural phenomenon, that requires unbroken continuity in a world of trouble, works like a batting streak. All are games of a gambler playing with a limited stake against a house with infinite resources. The gambler must eventually go bust. His aim can only be to stick around as long as possible, to have some fun while he's at it, and, if he happens to be a moral agent as well, to worry about staying the course with honor!" (Stephen J Gould, 1991)

"Gambling was the place where statistics and profound human consequences met most nakedly, after all, and cards, even more than dice or the numbers on a roulette wheel, seemed able to define and perhaps even dictate a player's... luck." (Tim Powers, "Last Call", 1992)

"Probability theory has a right and a left hand. On the right is the rigorous foundational work using the tools of measure theory. The left hand 'thinks probabilistically', reduces problems to gambling situations, coin-tossing, motions of a physical particle." (Leo Breiman, "Probability", 1992)

"Losing streaks and winning streaks occur frequently in games of chance, as they do in real life. Gamblers respond to these events in asymmetric fashion: they appeal to the law of averages to bring losing streaks to a speedy end. And they appeal to that same law of averages to suspend itself so that winning streaks will go on and on. The law of averages hears neither appeal. The last sequence of throws of the dice conveys absolutely no information about what the next throw will bring. Cards, coins, dice, and roulette wheels have no memory." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"Time is the dominant factor in gambling. Risk and time are opposite sides of the same coin, for if there were no tomorrow there would be no risk. Time transforms risk, and the nature of risk is shaped by the time horizon: the future is the playing field." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"A random walk is one in which future steps or directions cannot be predicted on the basis of past history. When the term is applied to the stock market, it means that short-run changes in stock prices are unpredictable. Investment advisory services, earnings forecasts, and chart patterns are useless. [...] What are often called 'persistent patterns' in the stock market occur no more frequently than the runs of luck in the fortunes of any gambler playing a game of chance. This is what economists mean when they say that stock prices behave very much like a random walk." (Burton G Malkiel, "A Random Walk Down Wall Street", 1999)

"All this, though, is to miss the point of gambling, which is to accept the imbalance of chance in general yet deny it for the here and now. Individually we know, with absolute certainty, that 'the way things hap pen' and what actually happens to us are as different as sociology and poetry." (John Haigh," Taking Chances: Winning With Probability", 1999)

"The psychology of gambling includes both a conviction that the unusual must happen and a refusal to believe in it when it does. We are caught by the confusing nature of the long run; just as the imperturbable ocean seen from space will actually combine hurricanes and dead calms, so the same action, repeated over time, can show wide deviations from its normal expected results - deviations that do not themselves break the laws of probability. In fact, they have probabilities of their own." (John Haigh," Taking Chances: Winning With Probability", 1999)

"This notion of 'being due' - what is sometimes called the gambler’s fallacy - is a mistake we make because we cannot help it. The problem with life is that we have to live it from the beginning, but it makes sense only when seen from the end. As a result, our whole experience is one of coming to provisional conclusions based on insufficient evidence: read ing the signs, gauging the odds." (John Haigh," Taking Chances: Winning With Probability", 1999)

On Chance: Gamblers I

"The gambling reasoner is incorrigible; if he would but take to the squaring of the circle, what a load of misery would be saved." (Augustus De Morgan, "A Budget of Paradoxes", 1872)

"In moderation, gambling possesses undeniable virtues. Yet it presents a curious spectacle replete with contradictions. While indulgence in its pleasures has always lain beyond the pale of fear of Hell’s fires, the great laboratories and respectable insurance palaces stand as monuments to a science originally born of the dice cup." (Edward Kasner & James R Newman, "Mathematics and the Imagination", 1940)

"A misunderstanding of Bernoulli’s theorem is responsible for one of the commonest fallacies in the estimation of probabilities, the fallacy of the maturity of chances. When a coin has come down heads twice in succession, gamblers sometimes say that it is more likely to come down tails next time because ‘by the law of averages’ (whatever that may mean) the proportion of tails must be brought right some time." (William Kneale, "Probability and Induction", 1949)

"The classical theory of probability was devoted mainly to a study of the gamble's gain, which is again a random variable; in fact, every random variable can be interpreted as the gain of a real or imaginary gambler in a suitable game." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"The painful experience of many gamblers has taught us the lesson that no system of betting is successful in improving the gambler's chances. If the theory of probability is true to life, this experience must correspond to a provable statement." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"The picture of scientific method drafted by modern philosophy is very different from traditional conceptions. Gone is the ideal of a universe whose course follows strict rules, a predetermined cosmos that unwinds itself like an unwinding clock. Gone is the ideal of the scientist who knows the absolute truth. The happenings of nature are like rolling dice rather than like revolving stars; they are controlled by probability laws, not by causality, and the scientist resembles a gambler more than a prophet. He can tell you only his best posits - he never knows beforehand whether they will come true. He is a better gambler, though, than the man at the green table, because his statistical methods are superior. And his goal is staked higher - the goal of foretelling the rolling dice of the cosmos. If he is asked why he follows his methods, with what title he makes his predictions, he cannot answer that he has an irrefutable knowledge of the future; he can only lay his best bets. But he can prove that they are best bets, that making them is the best he can do - and if a man does his best, what else can you ask of him?" (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)

"Control is an attribute of a system. This word is not used in the way in which either an office manager or a gambler might use it; it is used as a name for connectiveness. That is, anything that consists of parts connected together will be called a system." (Stafford Beer, "Cybernetics and Management", 1959)

"There always remains an orbit that to the limited knowledge of man appears as an orbit of pure chance and marks life as a gamble. Man and his works are always exposed to the impact of unforeseen and uncontrollable events." (Ludwig von Mises, "The Ultimate Foundation of Economic Science: An Essay on Method", 1962)