Gambler's fallacy
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Gambler's fallacy
The Gambler's fallacy, also known as the Monte Carlo fallacy (because its most famous example happened in a Monte Carlo Casino in 1913)[1] . Also referred to as the fallacy of the maturity of chances, which is the belief that if deviations from expected behaviour are observed in repeated independent trials of some random process, future deviations in the opposite direction are then more likely. For example, if a fair coin is tossed repeatedly and tails comes up a larger number of times than is expected, a gambler may incorrectly believe that this means that heads is more likely in future tosses.[2] . Such an expectation could be mistakenly referred to as being due, and it probably arises from
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However, this is not correct, and is a manifestation of the gambler's fallacy; the event of 5 heads in a row and the event of "first 4 heads, then a tails" are equally likely, each having probability 1⁄32. Given the first four rolls turn up heads, the probability that the next toss is a head is in fact, . While a run of five heads is only 1⁄32 = 0.03125, it is only that before the coin is first tossed. After the first four tosses the results are no longer unknown, so their probabilities are 1. Reasoning that it is more likely that the next toss will be a tail than a head due to the past tosses, that a run of luck in the past somehow influences the odds in the future, is the fallacy.
Gambler's fallacy
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Explaining why the probability is 1/2 for a fair coin
We can see from the above that, if one flips a fair coin 21 times, then the probability of 21 heads is 1 in 2,097,152. However, the probability of flipping a head after having already flipped 20 heads in a row is simply 1⁄2. This is an application of Bayes' theorem. This can also be seen without knowing that 20 heads have occurred for certain (without applying of Bayes' theorem). Consider the following two probabilities, assuming a fair coin: • probability of 20 heads, then 1 tail = 0.520 × 0.5 = 0.521 • probability of 20 heads, then 1 head = 0.520 × 0.5 = 0.521 The probability
In the article, Elaine Young talks about the concept of probability. This concept correlates to CCSS.Math.Content.7.SP.C.5 “Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.” In the article, a third grade teacher, Mrs. Alvarado, enforce this concept through literature arts. She read the book, Dear Mr. Blue, out loud then have a class discussion over the probability of a whale living in one of the character’s backyard pond. Afterwards, the teacher introduces the probability terms such as impossible, unlikely, equally, likely, unlikely, or certain. Another activity that enforces this standard is when the third grade teacher have students post appropriate vocabulary words on a line chart. CCSS.Math.Content.7.SP.C.6 “Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the
Although two different stories, with multiple differences in conflict and setting, “The Lottery” by Shirley Jackson and “The Most Dangerous Game” by Richard Connell bear multiple similarities as well. Both stories demonstrate how humans are portrayed as evil vs. good. Each story depicts a protagonist exhibiting conflict with another human or humans. One ends on a dark gloomy path for the protagonist while the other results in a victory for the protagonist.
Pascal’s Wager has been argued to be impractical because our beliefs are often not in our control. This argument is
Donnelly begins his presentation with a thought experiment involving the tossing of a coin and predicts the possibility of a certain series of results. When predicting the possibility of heads, tails, heads (HTH) or heads, tails, tails (HTT), I, like most of the audience, believed that the chance of either possibility was equal. However, I did not take into account the possibility of overlap and how HTH was more like to be achieved in an overlap. I also did not catch that the HTH could appear in clumps because of the overlapping (the third "H" in HTH is also the first "H" in the next HTH). There was also the
The above example does not preserve the truth, for instance, the premise does not provide truth in that, it a certain probability that all cups will be yellow in
To test just exactly how E.S.P. worked, he created an experiment with Zener cards, which had one of a total 5 pictures on each of them. Rhine would draw a card form the deck and ask the subject to guess what picture was on the card. Out of the many subjects tested, most guessed only about 20% of the cards correct, but one young man averaged about 50% correct. This young man, Adam Linzmayer, would even guess up to 9 cards in a row, which was almost a one in a million chance—he did it three times. Rhine became overly excited of his findings on his belief in E.S.P. and wanted to publish the results. But upon his replication of the experiment, Linzmayer’s success rate of guessing the drawn cards greatly decreased (Lehrer, para. 12-13). This decline effect could possible be due to regressive fallacy, which is the inability to account natural and unavoidable fluctuations in experiments. For example, things like stock market prices and chronic back pain unavoidably fluctuate between prosperous and well-feeling times to poor and pain-filled times. By setting aside the idea of natural and unavoidable fluctuations, one can ultimately fall into self-deception and into post hoc
In this essay I will discuss the ontological problem of the existence of God and discuss Pascal’s Wager and how it solves the issue. The problem with the proof of the existence of God is that it is not something we will know for sure until our dying day. We can speculate and bet on his existence and “feel” his presence but at this point it is just that, only a bet. This wager is famous for opening up minds to look at the problem in a bigger picture. The problem with the existence of God is not in the answer but instead in the question. Pascal is responsible for refocusing this discussion on God to the bigger problem of the existential context of human life. In a way this can all be broken down to very black and white terms “Either God is or he is not.” But upon looking further we realize that this is a much bigger issue with many grey areas than something as simple as ‘is or is not’.
In Shirley Jackson’s “The Lottery,” the story begins on a sunny day that imposes gossip and frenzy around the town. In this location, they conduct a “lottery” that involves the families of the town to go into a drawing. Once the drawing is done, the family that is chosen is forced to commence into another lottery between themselves. The winner of the lottery is used as a sacrifice for the town and is pelted by stones thrown from the community, including children. Furthermore, the basis of “The Lottery” has to do with psychological problems and influence. Psychoanalysis is built upon Sigmund Freud’s theories of psychology, which asserts that the human mind is affected by their “unconscious that is driven by their desires and fears”
Kerr’s observation on “The folly of rewarding A while hoping for B is true today, simply illustrates the sometimes fouled up rewards systems that most companies have in place. Fouled up in the sense that most companies wrongly reward not so positive behaviours while hoping and expecting for better ones.
Chance is a very interesting concept. The belief things happen unknowingly and by mere luck. In the play chance is over shadowed by fate, a pre-determined destiny. A prime example of
Let’s begin with the basics: for starters what is roulette? What are outside bets for that matter? Roulette is a game in which a small ball is thrown into a revolving wheel with around 37 to 38 colored sections. The players of course bet where the ball will halt when the wheel ceases to spin. Now there are many ways to win when acting as a participant in this somewhat risky past time, to win big on outside bets you have to know the game well. Now outside bets are simply bets in which you risk very little, earning small payouts for each bet as you continue to spin. Real winnings come from playing steadily and carefully and avoiding such bets, which are based more on probability only and not the wheel itself.
But what media outlets have failed to acknowledge is that not all people are problem gamblers. Its as if a study on alcoholism has been completed yet neglecting the effect of fine wines.
Human gambling often involves the decision to choose a low probability pay off, with the illusion of gaining quick and easy money, over a high probability pay off. This reflects a form of suboptimal choice behaviour. Suboptimal choice refers to the choice that does not result in the highest overall reinforcement one could achieve. The probability of actually winning is slim to none when gambling, but these behaviours are significantly popular. One of the most insidious behaviour humans engage in is compulsive gambling, which had been associated with several negative outcomes for the compulsive gambler and their loved ones. Thus, it is important to understand why humans make suboptimal choices and ultimately know how to reduce the probability of such choices to occur (Fantino, Navarro, & O’daly, 2005). Research on this topic aims to investigate the underlying mechanisms involved such as the environmental factors influencing suboptimal behaviour, and the behavioural process in making decisions.
When discussing probability, a text of my previous reading came to mind. Within the lecture Physics II, much of Aristotle’s work is concerned with providing a definition for various events and subjects, and as such, identifying the types of causes for each event is an important step in accomplishing this goal. Aristotle specifically investigates the role of luck and chance as causes of change. Although we commonly speak of luck or chance as being a cause, Aristotle purposefully refrains from including them in his explanation of causes. When giving an account of our observable world, I agree with Aristotle in that there is no place for luck and chance as causes of events, yet I believe they do have a role, namely in predicting future events.
Objective probability refers to the long-run relative frequency of an event based on the assumption of an infinite number of observations and no change in the underlying conditions. Subjective probability is the individual’s personal estimate of the chance of loss.