"As an instrument for selecting at random, I have found nothing superior to dice. It is most tedious to shuffle cards thoroughly be- tween each successive draw, and the method of mixing and stirring up marked balls in a bag is more tedious still. A teetotum or some form of roulette is preferable to these, but dice are better than all. When they are shaken and tossed in a basket, they hurtle so variously against one another and against the ribs of the basket-work that they tumble wildly about, and their positions at the outset afford no perceptible clue to what they will be after even a single good shake and toss." (Francis Galton, Nature vol. 42, 1890)
"In no subject is there a rule, compliance with which will lead to new knowledge or better understanding. Skillful observations, ingenious ideas, cunning tricks, daring suggestions, laborious calculations, all these may be required to advance a subject. Occasionally the conventional approach in a subject has to be studiously followed; on other occasions it has to be ruthlessly disregarded. Which of these methods, or in what order they should be employed is generally unpredictable. Analogies drawn from the history of science are frequently claimed to be a guide; but, as with forecasting the next game of roulette, the existence of the best analogy to the present is no guide whatever to the future. The most valuable lesson to be learnt from the history of scientific progress is how misleading and strangling such analogies have been, and how success has come to those who ignored them." (Thomas Gold, "Cosmology", 1956)
“[In statistics] you have the fact that the concepts are not very clean. The idea of probability, of randomness, is not a clean mathematical idea. You cannot produce random numbers mathematically. They can only be produced by things like tossing dice or spinning a roulette wheel. With a formula, any formula, the number you get would be predictable and therefore not random. So as a statistician you have to rely on some conception of a world where things happen in some way at random, a conception which mathematicians don’t have.” (Lucien LeCam, [interview] 1988)
"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)
"The dice and the roulette wheel, along with the stock market and the bond market, are natural laboratories for the study of risk because they lend themselves so readily to quantification; their language is the language of numbers." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)
"The theory of probability can define the probabilities at the gaming casino or in a lottery - there is no need to spin the roulette wheel or count the lottery tickets to estimate the nature of the outcome - but in real life relevant information is essential. And the bother is that we never have all the information we would like. Nature has established patterns, but only for the most part. Theory, which abstracts from nature, is kinder: we either have the information we need or else we have no need for information." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)
“Sequences of random numbers also inevitably display certain regularities. […] The trouble is, just as no real die, coin, or roulette wheel is ever likely to be perfectly fair, no numerical recipe produces truly random numbers. The mere existence of a formula suggests some sort of predictability or pattern.” (Ivars Peterson, “The Jungles of Randomness: A Mathematical Safari”, 1998)
"The chance events due to deterministic chaos, on the other hand, occur even within a closed system determined by immutable laws. Our most cherished examples of chance - dice, roulette, coin-tossing – seem closer to chaos than to the whims of outside events. So, in this revised sense, dice are a good metaphor for chance after all. It's just that we've refined our concept of randomness. Indeed, the deterministic but possibly chaotic stripes of phase space may be the true source of probability." (Ian Stewart, "Does God Play Dice: The New Mathematics of Chaos", 2002)
"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)
"A very different - and very incorrect - argument is that successes must be balanced by failures (and failures by successes) so that things average out. Every coin flip that lands heads makes tails more likely. Every red at roulette makes black more likely. […] These beliefs are all incorrect. Good luck will certainly not continue indefinitely, but do not assume that good luck makes bad luck more likely, or vice versa."
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