Basketball and Gambling

A basketball player's chance of making his shot is based on his athletic skill. His percentages increase with his advantage but has nothing to do with the results of his or her previous shots. Randomness-challenged minds give real-world errors of judgment that lead to the widespread belief that a basketball player has a hot hand when he makes a random number of consecutive shots yet the frequency or duration of the streaks never exceed chance fluctuations. Of course, give a large enough sample size it is likely that some unspecified player somewhere does have an inordinately lengthy lucky streak via a chance manifestation of regression to the mean. In any case, an inference engine such as one's mind does not necessarily result in the most acurate results. Man has a number of misleading beliefs about random events that are applicable to his assumptions of randomness. Randomness is neither clearly defined nor understood. Even random number generators merely use some belief system to create an array of events random. People take incredible amounts of risk in the stock market full of uncertainties and cheating opportunities but call it investing but consider gambling risk. Mathematically speaking, gambling should be easier to tolerate as risk numbers are known within a high degree of confidence and losses correspond to a well-defined chance where skill actually matters. An allusion is to treat small samples of information drawn at random from a large population similar to one another and representative of the entire population. Statistically significant relationships between two variables that emerge from 20 individuals may not reappear from an additional 10 individuals, as the odds of this happening are less than 50-50. A mind thinks on a small random sequence where extended runs of one value or another inevitably cancels each other out. The gambler's fallacy reveals one will assume that a run of heads in a sequence of random coin flips will give way to a corrective series of tails to result in roughly equal numbers of heads and tails overall. Random sequences of two values alternate frequently from one value to another may contain extended runs of a single value. A sequence of "HHTTHTHTTH" as no better example of randomness than "THHHHHHHT," as the chances of observing either sequence is the same as any other of equal length.