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KontobestГ¤tigung Gamblers Fallacy Der Denkfehler bei der Gambler’s Fallacy Video
People who fall prey to the gambler's fallacy think that a streak should end, but people who believe in the hot hand think it should continue.
Edward Damer: Consider the parents who already have three sons and are quite satisfied with the size of their family.
However, they both would really like to have a daughter. They commit the gambler's fallacy when they infer that their chances of having a girl are better, because they have already had three boys.
They are wrong. The sex of the fourth child is causally unrelated to any preceding chance events or series of such events. Tails one chance. Over time, as the total number of chances rises, so the probability of repeated outcomes seems to diminish.
Over subsequent tosses, the chances are progressively multiplied to shape probability. So, when the coin comes up heads for the fourth time in a row, why would the canny gambler not calculate that there was only a one in thirty-two probability that it would do so again — and bet the ranch on tails?
After all, the law of large numbers dictates that the more tosses and outcomes are tracked, the closer the actual distribution of results will approach their theoretical proportions according to basic odds.
Thus over a million coin tosses, this law would ensure that the number of tails would more or balance the number of heads and the higher the number, the closer the balance would become.
But — and this is a Very Big 'But'— the difference between head and tails outcomes do not decrease to zero in any linear way. Over tosses, for instance, there is no reason why the first 50 should not all come up heads while the remaining tosses all land on tails.
Random distribution is the first flaw in the reasoning that drives the Gambler's Fallacy. Now let us return to the gambler awaiting the fifth toss of the coin and betting that it will not complete that run of five successive heads with its theoretical probability of only 1 in 32 3.
What that gambler might not understand is that this probability only operated before the coin was tossed for the first time.
Once the fourth flip has taken place, all previous outcomes four heads now effectively become one known outcome, a unitary quantity that we can think of as 1.
So the fallacy is the false reasoning that it is more likely that the next toss will be a tail than a head due to the past tosses and that a run of luck in the past can somehow influence the odds in the future.
This video, produced as part of the TechNyou critical thinking resource, illustrates what we have discussed so far. The corollary to this is the equally fallacious notion of the 'hot hand', derived from basketball, in which it is thought that the last scorer is most likely to score the next one as well.
The academic name for this is 'positive recency' - that people tend to predict outcomes based on the most recent event. Of course planning for the next war based on the last one another manifestation of positive recency invariably delivers military catastrophe, suggesting hot hand theory is equally flawed.
Indeed there is evidence that those guided by the gambler's fallacy that something that has kept on happening will not reoccur negative recency , are equally persuaded by the notion that something that has repeatedly occurred will carry on happening.
However, what is actually observed is that, there is an unequal ratio of heads and tails. Now, if one were to flip the same coin 4, or 40, times, the ratio of heads and tails would seem equal with minor deviations.
The more number of coin flips one does, the closer the ratio reaches to equality. Hence, in a large sample size, the coin shows a ratio of heads and tails in accordance to its actual probability.
This is because, despite the short-term repetition of the outcome, it does not influence future outcomes, and the probability of the outcome is independent of all the previous instances.
In other words, if the coin is flipped 5 times, and all 5 times it shows heads, then if one were to assume that the sixth toss would yield a tails, one would be guilty of a fallacy.
An example of this would be a tennis player. Here, the prediction of drawing a black card is logical and not a fallacy. Therefore, it should be understood and remembered that assumption of future outcomes are a fallacy only in case of unrelated independent events.
Just because a number has won previously, it does not mean that it may not win yet again. The conceit makes the player believe that he will be able to control a risky behavior while still engaging in it, i.
However, this does not always work in the favor of the player, as every win will cause him to bet larger sums, till eventually a loss will occur, making him go broke.
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