The Gambler's Fallacy, the Fallacy of the Maturity of Chances
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 everyday experiences with nonrandom events (such as when a scheduled train is late, where it can be expected that it has a greater chance of arriving the later it gets). This is an informal fallacy. It is also known colloquially as the law of averages. What is true instead are the law of large numbers – in the long term, averages of independent trials will tend to approach the expected value, even though individual trials are independent – and regression toward the mean, namely that following a rare extreme event (say, a run of 10 heads), the next event is likely to be less extreme (the next run of heads is likely to be less than 10), simply because extreme events are rare. The gambler's fallacy implicitly involves an assertion of negative correlation between trials of the random process and therefore involves a denial of the exchangeability of outcomes of the random process. In other words, one implicitly assigns a higher chance of occurrence to an event even though from the point of view of "nature" or the "experiment", all such events are equally probable (or distributed in a known way). The reversal is also a fallacy, in which a gambler may instead decide that tails are more likely out of some mystical preconception that fate
1
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 everyday experiences with nonrandom events (such as when a scheduled train is late, where it can be expected that it has a greater chance of arriving the later it gets). This is an informal fallacy. It is also known colloquially as the law of averages. What is true instead are the law of large numbers – in the long term, averages of independent trials will tend to approach the expected value, even though individual trials are independent – and regression toward the mean, namely that following a rare extreme event (say, a run of 10 heads), the next event is likely to be less extreme (the next run of heads is likely to be less than 10), simply because extreme events are rare. The gambler's fallacy implicitly involves an assertion of negative correlation between trials of the random process and therefore involves a denial of the exchangeability of outcomes of the random process. In other words, one implicitly assigns a higher chance of occurrence to an event even though from the point of view of "nature" or the "experiment", all such events are equally probable (or distributed in a known way). The reversal is also a fallacy, in which a gambler may instead decide that tails are more likely out of some mystical preconception that fate
References: [1] Lehrer, Jonah (2009). How We Decide. New York: Houghton Mifflin Harcourt. p. 66. ISBN 978-0-618-62011-1. [2] Colman, Andrew (2001). "Gambler 's Fallacy - Encyclopedia.com" (http:/ / www. encyclopedia. com/ doc/ 1O87-gamblersfallacy. html). A Dictionary of Psychology. Oxford University Press. . Retrieved 2007-11-26. [3] O 'Neill, B. and Puza, B.D. (2004) Dice have no memories but I do: A defence of the reverse gambler 's belief. (http:/ / cbe. anu. edu. au/ research/ papers/ pdf/ STAT0004WP. pdf). Reprinted in abridged form as O 'Neill, B. and Puza, B.D. (2005) In defence of the reverse gambler 's belief. The Mathematical Scientist 30(1), pp. 13–16. [4] Tversky, Amos; Daniel Kahneman (1974). "Judgment under uncertainty: Heuristics and biases". Science 185 (4157): 1124–1131. doi:10.1126/science.185.4157.1124. PMID 17835457. [5] Tversky, Amos; Daniel Kahneman (1971). "Belief in the law of small numbers". Psychological Bulletin 76 (2): 105–110. doi:10.1037/h0031322. [6] Tversky & Kahneman, 1974. [7] Tune, G.S. (1964). "Response preferences: A review of some relevant literature". Psychological Bulletin 61 (4): 286–302. doi:10.1037/h0048618. PMID 14140335. [8] Tversky & Kahneman, 1971. [9] Gilovich, Thomas (1991). How we know what isn 't so. New York: The Free Press. pp. 16–19. ISBN 0-02-911706-2. Article Sources and Contributors 6 Article Sources and Contributors Gambler 's fallacy Source: http://en.wikipedia.org/w/index.php?oldid=455892717 Contributors: 2004-12-29T22:45Z, 2005, AKGhetto, Aaron Kauppi, Alex W, Alksub, Aly89, Andeggs, Andyroo316, Aoxiang, Areldyb, Ashley Pomeroy, Aveekbh, Avirunes, AxelBoldt, Baccyak4H, Badger Drink, Barklund, Bender235, Bfinn, Bigturtle, Bkell, Blue Tie, Bryan Derksen, Bush6984, CSTAR, Calair, Camaj, Camw, Cgwaldman, Cjrcl, Cmglee, CobaltBlue, Constructive editor, Conversion script, Courcelles, Cyclist, D o m e, DanielCD, DavidDouthitt, DavidWBrooks, Day viewing, Dcoetzee, Den fjättrade ankan, Deor, DocWatson42, Doniago, Donnaidh sidhe, DragonHawk, E090, Edward, Electricbassguy, Emurphy42, Enric Naval, Eurosong, Evanreyes, Father Goose, FeatherPluma, Feezo, Fosterd2, Fr, Furrykef, GDstew4, GVnayR, Gayasri, Gazpacho, Giftlite, Gonzalo Diethelm, Grace Note, Graham87, GreenReaper, Gregbard, Grumpyyoungman01, HAGADAG, Headcase88, Heron, Horovits, Hyphz, Iceberg3k, Jaguar9a9, Jasperdoomen, Jimjam27, Jnestorius, Jokes Free4Me, Julesd, Karada, Kazvorpal, Labans, Lenoxus, Lifefeed, Liko81, LilHelpa, LukeH, Luqui, Magog the Ogre, Malcolm Farmer, MathHisSci, McGeddon, Melchoir, Melcombe, Meno25, Michaelbluejay, Mike Van Emmerik, Molinari, Musiphil, Navigatr85, Nbarth, Netsumdisc, Notoldyet, NykeYoung, O 'kelly, Orthologist, Ozkaplan, PAR, Pacomartin, Pakaran, PanagosTheOther, Pat Hayes, PatrikR, Pigman, Pimnl, Pratik.mallya, Quarl, Quiddity, Qwfp, Rbarreira, Reki, Roma emu, Ruzbehabbasi, S2000magician, SCF71, Sandebert, Sbyrnes321, Shantavira, Sietse Snel, Silence, Slicing, SmartGuy, Smjg, Snoyes, Sockatume, Spoon!, Statoman71, StuRat, Superm401, Taak, Takwish, Tamfang, Tarquin, The Anome, TheFix63, TheOtherStephan, Thumperward, Timo Honkasalo, Tomeasy, Tomisti, Torbad, UltimateHombre, Uvaphdman, Vbailo, Vicki Rosenzweig, Vonbontee, Waleswatcher, Wolfkeeper, Woodstone, Wotnow, Wrp103, 178 anonymous edits Image Sources, Licenses and Contributors File:Lawoflargenumbersanimation.gif Source: http://en.wikipedia.org/w/index.php?title=File:Lawoflargenumbersanimation.gif License: Public Domain Contributors: Sbyrnes321 License Creative Commons Attribution-Share Alike 3.0 Unported //creativecommons.org/licenses/by-sa/3.0/