Monty Hall problem Concepts

Rationality: What It Is, Why It Seems Scarce, Why It Matters

by Steven Pinker · 14 Oct 2021 · 533pp · 125,495 words

bet doesn’t sound so crazy.42 In Let’s Make a Deal, Monty Hall is God. The godlike host reminds us how exotic the Monty Hall problem is. It requires an omniscient being who defies the usual goal of a conversation—to share what the hearer needs to know (in this case

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) Maria Klawe. 38. To be fair, normative analyses of the Monty Hall dilemma have inspired voluminous commentary and disagreement; see https://en.wikipedia.org/wiki/Monty_Hall_problem. 39. Try it: Math Warehouse, “Monty Hall Simulation Online,” https://www.mathwarehouse.com/monty-hall-simulation-online/. 40. Such as Late Night with David Letterman

Everything Is Predictable: How Bayesian Statistics Explain Our World

by Tom Chivers · 6 May 2024 · 283pp · 102,484 words

would assume that the other is a girl (why not say, “They’re both boys?”). The math of this is entirely the same as the Monty Hall problem above. But for some reason I find it far more counterintuitive, and I wanted to share the frustration with you all. And I’m not

The Mathematics of Banking and Finance

by Dennis W. Cox and Michael A. A. Cox · 30 Apr 2006 · 312pp · 35,664 words

insurance 4.12 Tree Diagram 4.12.1 An example of prediction of success 4.12.2 An example from an American game show: The Monty Hall Problem 4.13 Conclusion 26 27 27 28 29 29 30 30 34 35 5 Standard Terms in Statistics 5.1 Introduction 5.2 Maximum and

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203 167 170 203 205 x Contents 22.4 22.5 22.6 22.7 Queuing Problem The Bank Cashier Problem Monte Carlo for the Monty Hall Problem Conclusion 208 209 212 214 23 Reliability: Obsolescence 23.1 Introduction 23.2 Replacement at a Fixed Age 23.3 Replacement at Fixed Times 215

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, corresponds to the line x + y = 1. 34 The Mathematics of Banking and Finance 4.12.2 An example from an American game show: The Monty Hall problem The set of Monty Hall’s game show Let’s Make a Deal has three closed doors (A, B and C). Behind one of these

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.5 B 0.5 A 0.3333 C 1.0 C 0.5 C Figure 4.9 Tree diagram for the Monty Hall problem. Probability Theory 35 Table 4.2 Summary probabilities for Monty Hall problem Change No change Win Lose 0.3333 0.1667 0.1667 0.3333 Therefore in order to maximise the chance

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receiving an instantaneous service. These results are remarkably close to those obtained from the very brief simulation conducted earlier. 22.6 MONTE CARLO FOR THE MONTY HALL PROBLEM This problem was introduced at the conclusion of the probability section, within Chapter 4. The set of Monty Hall’s game show Let’s Make

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probability of winning the car if the contestant stays with his first choice? What if the contestant decides to switch? The winning letter in the Monty Hall problem will represent a door, the position of which is always known to Monty. Let us assume it is A. The participant’s initial choice is

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C or B. These options are set out in Table 22.8. Simulation: Monte Carlo Methods 213 Table 22.7 Cumulative initial probabilities for the Monty Hall problem Choice Cumulative probability Probability A B C 0.3333 0.3333 0.3333 0 0.3333 0.6666 1 Table 22.8 Second event probabilities

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for the Monty Hall problem Initial choice Shown Probability Stick Switch B C C B 0.5 0.5 1 ! A A A A C B B C A A

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B C Table 22.9 Simulation of the Monty Hall problem Random variable 0.8444 0.1011 0.5444 0.9736 0.4440 0.2745 0.9083 0.6326 0.5568 0.6940 Initial choice Random

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C B B C lose win lose lose lose win lose lose lose lose Table 22.10 Summary of a Monte Carlo simulation of the Monty Hall problem Switch Stick Win Lose 1,320 680 680 1,320 Ratio 0.66 0.34 The player may either stick with the original choice or

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action 191–2 definition 21 delegation 189–90 empowerment 189–90 guesswork 191 lethargy pitfalls 189 minimax regret rule 192–4 modelling problems 189–91 Monty Hall problem 34–5, 212–13 pitfalls 189–94 probability theory 21–35, 53–66, 189–94, 215–18 problem definition 129, 190–2 project analysis guidelines

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272–4 Monte Carlo simulation bank cashier problem 209–12 concepts 203–14, 234 examples 203–8 Monty Hall problem 212–13 queuing problems 208–10 random numbers 207–8 stock control 203–8 uses 203, 234 Monty Hall problem 34–5, 212–13 moving averages concepts 241–7 even numbers/observations 244–5 moving totals

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, 75–81 event types 22–4 examples 25–35, 53–5 frequentist approach 22, 25–6 independent events 22–4, 35, 58, 60, 92–5 Monty Hall problem 34–5, 212–13 multiplication rule 26–7 mutually exclusive events 22–4, 58 notation 21–2, 24–30, 54–5, 68–9, 75–6

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training needs, communications 189 transport problems concepts 171–7 ghost costs 172–7 ‘travelling salesman’ problem, dynamic programming 185–7 tree diagrams examples 30–4 Monty Hall problem 34–5 probability theory 30–5 trends analysis 235–47 concepts 235–47 cyclical variations 238–47 graphical presentational approaches 5, 10, 235–47 identification

Radical Uncertainty: Decision-Making for an Unknowable Future

by Mervyn King and John Kay · 5 Mar 2020 · 807pp · 154,435 words

win overall conditional on A having won the first game, but B having won the second , and so on as the evening progresses. Hall The Monty Hall problem 15 is a famous illustration of the power of Bayes’ theorem, loosely based on the 1960s American quiz show Let’s Make a Deal , in

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win each of the remaining games, and perhaps there was a frequency distribution of past results of similar games to guide our conjecture. In the Monty Hall problem, we judged that if there were three identical boxes the probability that the keys were in any one of them was one third. 17 John

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interest? Can the viewers be confident that the original rules are still being applied? Real worlds are always complex. Many commentators and teachers use the Monty Hall problem to emphasise that a puzzle, or model, can only be ‘solved’ if the assumptions made are completely specified. And this observation is correct. But in

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probabilities? In subsequent chapters, we will show how significant this problem is for the wide application of probabilistic thinking. Bayes in the consulting room The Monty Hall problem is light entertainment, but the diagnosis of cancer is a matter of life and death. Campaigning organisations urge screening for breast and prostate cancer. These

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who are not. In games of chance, such as the wagers that prompted the Chevalier de Méré to contemplate the problem of points or the Monty Hall problem, everything is either known or unknown, deterministic or random. But that dichotomy does not exist in most real worlds. We know something, but never enough

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numerical – even though they agree about the known facts of that situation, the formalised description fails to add to our knowledge. In contrast to the Monty Hall problem, in which you can verify the ‘correct’ answer by repeating the game many times – and derive an objective, frequentist, probability – there is no means of

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. Vagueness and ambiguity may be observed not just in the terms used in describing a problem, but in the connection between actions and outcomes. The Monty Hall problem has a definite solution which can be identified clearly once the implicit as well as the explicit rules of the game have been spelt out

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was careful not to claim that his analysis could be applied outside the narrow confines of his ‘small worlds’. The problem of points and the Monty Hall problem both relate to small worlds – games of chance which are repeatable and repeated. Savage’s caution over the scope of his analysis was not shared

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remained at the stop after learning this, they would be irrational. Yet even in small worlds, subjects are often slow to rethink their positions. The Monty Hall problem continues to perplex; debate over the ‘correct’ answer to the two-child problem remains unresolved. Martin Gardner and others have made careers out of devising

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exclusive claims – on the one hand, that the prosecution or claimant’s submission is true, on the other, that the defence submission is true. The Monty Hall problem has that exhaustive and exclusive structure. The keys are in one box or the other, and the contestant, with or without the aid of Bayes

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know enough to be able to sensibly frame such a discussion in probabilistic terms. But at least these are the kinds of question, like the Monty Hall problem, in which a knowledge of Bayes’ theorem is helpful. The decision is presented as a ‘small world’ problem to which there is a definite solution

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, scissors, which game theorists explain requires a solution in mixed strategies, is within the capacity of chimpanzees. 16 Pigeons can solve a version of the Monty Hall problem. 17 In some respects, intelligent non-human creatures correspond better than do humans to the representations of rational behaviour proposed by economists. And pigeons can

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the host Monte (sic ) Hall. But the real Monty participated enthusiastically in the subsequent correspondence and ever since the game has been known as the Monty Hall problem. It was popularised in an article in Parade magazine in 1990 by the American columnist calling herself Marilyn vos Savant and claiming to have the

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, 96–7 , 206–7 , 403 ; the ‘Linda problem’, 90–1 , 98 ; and markets in risk, 55–7 ; models as contingent and transitory, 235–6 ; the Monty Hall problem, 62–3 , 64–6 , 98 , 100 , 113 , 139 , 203 , 204 ; mortality tables and life insurance, 56–7 , 69 , 232–3 ; non-stationary nature of social

Are You Smart Enough to Work at Google?: Trick Questions, Zen-Like Riddles, Insanely Difficult Puzzles, and Other Devious Interviewing Techniques You ... Know to Get a Job Anywhere in the New Economy

by William Poundstone · 4 Jan 2012 · 260pp · 77,007 words

Most Creative Thinkers. New York: Little, Brown, 2003. Selvin, Steve. “A Problem in Probability.” Letter to the editor. American Statistician 29 (1975): 67. ———. “On the Monty Hall Problem.” Letter to the editor. American Statistician 29 (1975): 134. Stone, Dianna L., and Gwen E. Jones. “Perceived Fairness of Biodata as a Function of the

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Diego. Selvin argued that you should switch boxes: Selvin, “A Problem in Probability.” had to defend it in a follow-up letter: Selvin, “On the Monty Hall Problem.” “has been debated in the halls of the Central Intelligence Agency”: Tierney, “Behind Monty Hall’s Doors.” only 12 percent of those questioned: Granberg and

The Book of Why: The New Science of Cause and Effect

by Judea Pearl and Dana Mackenzie · 1 Mar 2018

that they whiffed rather badly—it’s a warning sign that something might be amiss with viewing the world without a causal lens. THE PERPLEXING MONTY HALL PROBLEM In the late 1980s, a writer named Marilyn vos Savant started a regular column in Parade magazine, a weekly supplement to the Sunday newspaper in

Why Machines Learn: The Elegant Math Behind Modern AI

by Anil Ananthaswamy · 15 Jul 2024 · 416pp · 118,522 words

very high chance you have the disease if you tested positive. With this whirlwind introduction to Bayes’s theorem, we are ready to tackle the Monty Hall problem. (This is a bit involved. Feel free to skip to the end of this section if you think it’s too much, though it’s

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objected”: “Paul Erdős, Hungarian Mathematician.” GO TO NOTE REFERENCE IN TEXT Data scientist Paul van der Laken: “The Monty Hall Problem: Simulating and Visualizing the Monty Hall Problem in Python & R,” paulvanderlaken.com/2020/04/14/simulating-visualizing-monty-hall-problem-python-r/. GO TO NOTE REFERENCE IN TEXT “born in 1701 with probability 0.8”: Stephen M. Stigler

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…etc.,” PDF, The Royal Society, royalsocietypublishing.org/doi/10.1098/rstl.1764.0050. GO TO NOTE REFERENCE IN TEXT we are ready to tackle the Monty Hall problem: Steven Tijms, “Monty Hall and the ‘Leibniz Illusion,’ ” Chance, American Statistical Association, 2022, https://chance.amstat.org/2022/11/monty-hall/; and Christopher D. Long

Statistics hacks

by Bruce Frey · 9 May 2006 · 755pp · 121,290 words

the right path. Crazy, are you? Suffering from white-line fever? No, you've just applied the statistical solution to what is known as the Monty Hall problem and chosen the road among the three that has the greatest chance of being correct. Hard to believe? Read on, my friend, and prepare to

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downright weird that the world's smartest people have disagreed aggressively about whether it even really is the best strategy. But believe meit is. The Monty Hall Problem and Game Show Strategy In our example with the three roads and the prospector, there is, in fact, a two-thirds (about 67 percent) chance

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one curtain for both the other two curtains, you'd switch in a second wouldn't you? That's essentially what is offered in the Monty Hall problem. Some figures might be necessary to persuade your inner skeptic. Look at Table 5-1, which shows the probability breakdown for the three options at

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each curtain. The host reveals one of the unchosen curtains and the prize is not behind it. Your original choice was random. The Controversy The Monty Hall problem and the general game show strategy that resulted was first introduced to the masses in 1991 by Marilyn Vos Savant, a columnist for Parade Magazine

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people as wise as the old prospector you met out in Tonganoxie that started our discussion don't always know the right answer to the Monty Hall problem. How do you think he won that burro? Hack 51. Pass Go, Collect $200, Win the Game Monopoly is a game of chance (and Chance

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central tendency and 2nd defined normal curve and models building 2nd defined goodness-of-fit statistic and money casinos and 2nd infinite doubling of Monopoly Monty Hall problem multiple choice questions analysis of answer options writing good 2nd 3rd multiple regression criterion variables and defined multiple predictor variables predicting football games multiple regression

The Drunkard's Walk: How Randomness Rules Our Lives

by Leonard Mlodinow · 12 May 2008 · 266pp · 86,324 words

other people’s work is a good way to end up untenured and plying our math skills as a checker at Home Depot. But the Monty Hall problem is one of those that can be solved without any specialized mathematical knowledge. You don’t need calculus, geometry, algebra, or even amphetamines, which Erdös

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to decomposing a problem into lists of possibilities, we are ready to employ the law of the sample space to tackle the Monty Hall problem. AS I SAID EARLIER, understanding the Monty Hall problem requires no mathematical training. But it does require some careful logical thought, so if you are reading this while watching Simpsons reruns

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, you might want to postpone one activity or the other. The good news is it goes on for only a few pages. In the Monty Hall problem you are facing three doors: behind one door is something valuable, say a shiny red Maserati; behind the other two, an item of far less

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who found themselves in the situation described in the problem and switched their choice won about twice as often as those who did not. The Monty Hall problem is hard to grasp because unless you think about it carefully, the role of the host, like that of your mother, goes unappreciated. But the

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all 99 of those other doors, and so the probability that the Maserati is behind that remaining door is 99 out of 100! Had the Monty Hall problem been around in Cardano’s day, would he have been a Marilyn vos Savant or a Paul Erdös? The law of the sample space handles

When Einstein Walked With Gödel: Excursions to the Edge of Thought

by Jim Holt · 14 May 2018 · 436pp · 127,642 words

of inconsistency, let me (overconfidently?) express the conviction that the “Copernican principle,” “Gödel’s incompleteness theorems,” “Heisenberg’s uncertainty principle,” “Newcomb’s problem,” and “the Monty Hall problem” are all exceptions to Stigler’s law of eponymy (vide p. 292). J.H. New York City, 2017 PART I The Moving Image of Eternity

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you see between your incompleteness theorem and Heisenberg’s uncertainty principle?’ And Gödel got angry and threw me out of his office.” Overconfidence and the Monty Hall Problem Can you spot a liar? Most people think they are rather good at this, but they are mistaken. In study after study, subjects asked to

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his name synonymous with probability. In 1991, Erdős found himself befuddled when the Parade magazine columnist Marilyn vos Savant published a probability puzzle called the Monty Hall problem, named after the original emcee of the TV game show Let’s Make a Deal. It goes like this. There are three doors onstage, labeled

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Mishima, Yukio Miyake, Issey Modalities (Marcus) “Modalities and Intensional Languages” (Marcus) modal logic modus ponens, law of Moivre, Abraham de Monde, Le Montaigne, Michel de Monty Hall problem Monty Python Moore Doris Langley Moore, G. E. Moore, Michael moral philosophy moral sainthood More, Henry Morgenbesser, Sidney Morgenstern, Oskar Moscow Institute of Oil and

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• Is Logic Coercive? • Newcomb’s Problem and the Paradox of Choice • The Right Not to Exist • Can’t Anyone Get Heisenberg Right? • Overconfidence and the Monty Hall Problem • The Cruel Law of Eponymy • The Mind of a Rock Part IX: God, Sainthood, Truth, and Bullshit 21. Dawkins and the Deity 22. On Moral