Talk:Gambler's fallacy

message: What if I imagine I bet 0 unit on the first several game?
You cannot get it logically right  — Preceding unsigned comment added by 220.232.202.2 (talk) 07:43, 15 January 2015 (UTC)
thread_title: This Gambler's fallacy has a fallacy within itself

message: Before nominating again, fully source the article with references that comply with WP:MEDRS. --LauraHale (talk) 08:41, 27 April 2012 (UTC)
thread_title: Good article

message: In most jurisdictions, Slot Machines etc have Payout schedule / percentage required by law and predetermined by the manufacturer. http://en.wikipedia.org/wiki/Slot_machine#Payout_percentage. Perhaps modify the example in the second paragraph to Roulette or something?  — Preceding unsigned comment added by Billyoffland (talk • contribs) 15:14, 6 October 2011 (UTC)
thread_title:  Slot machine jackpots can in most cases be "due" 

message: Allow me to point out that euro coins don't have an equal distribution of weight hence the national side of the coin comes up more often. Try it for yourself and see.  —Preceding unsigned comment added by 86.45.154.157 (talk) 19:56, 8 September 2009 (UTC)
replies: text: I cannot find any verifiable evidence for this, but I can find verifiable evidence that coins, in general, are fair when flipped, regardless of the distribution of weight. You cannot "weight" a coin like you can "weight" dice, unless you are spinning, rolling, or otherwise allowing the coin to contact a surface before stopping it. Eebster the Great (talk) 02:06, 9 September 2009 (UTC)

text: The initial conditions that vary from one toss to the next, by the same person, are not just which coin face is initially pointing up. The precise direction of hand, thumb, and arm movement inevitably varies -- it's impossible for a person to make these identical on different tosses; also, the precise amount of energy imparted to the coin inevitably varies from toss to toss. And the nature of the coin toss is that the outcome is very sensitive to these slight variations in initial conditions. Duoduoduo (talk) 17:38, 27 August 2013 (UTC)
replies: text: I agree that the initial conditions are unlikely to be identical apart from the obvious state of which side of the coin is facing up as the toss starts, but I have never been sure that coin tosses are sufficiently sensitive to small variations in thrust and angle to affect the outcome. I may, of course, be entirely wrong; intuition is an exceedingly poor guide to probability and randomness, as this very discussion and the subject matter under discussion show. Coins being tossed tend  to be large, they tend to be fairly heavy and they tend not to be tossed with great force so I suspect the initial forcing conditions don't affect the result too much. Whether "too much" is "enough" to produce a chaotic system that is sufficiently sensitive to initial conditions to mimic a random "fair toss" or not is exactly what I would like to see tested. If it could be.
This intuitive feeling that coin tosses are sometimes forced by the tosser has bothered me sufficiently that I thought I would mention it. I would be exceptionally pleased if Science could put the notion to bed finally and forever someday. Qordil (talk) 17:56, 27 August 2013 (UTC)

text: You could test it yourself: flip a coin once, remembering how you flipped it and what the result was. (To make it fair, make sure it rotates at least three or four times.) Then do 100 more flips, each time trying to replicate your original flip. The null hypothesis is that the flips are independent, in which case the total number of heads is binomially distributed with probability parameter = 1/2. By Binomial distribution#Normal approximation, the number of heads is close to normally distributed under the null, with mean = 50 and standard deviation = 5. So there's a 95% probability under the null that the number of heads will be in the range 50 plus or minus 1.96 × 5, or between 41 and 59 inclusive. If you're trying for heads and you get more than 59 heads, that's unlikely to have happened with fair independent coin tosses. Duoduoduo (talk) 20:01, 27 August 2013 (UTC)
thread_title:  Coins 

message: The statement "This is how counting cards really works, when playing the game of blackjack." is erroneous. The (spurious) skill of card-counting for profit is not based on either remembering which individual card values have been previously dealt, or on calculating the ongoing probabilities of individual card values appearing. That this follows an example that uses a Jack (specifically, in lieu of a 10-value card generally), only serves to compound the error.
: I would ask former members of the MIT Blackjack Team whether the statistical advantage conferred by card counting is spurious. I do agree that it is difficult to beat the house, both because few people possess the required faculties and because casinos take effective countermeasures. It's also not true that individual card values are ignored by all types of card counters. In particular, ace tracking has been used successfully by some professional gamblers. Gerweck (talk) 14:21, 10 August 2013 (UTC)
thread_title:  Non-examples of the fallacy 

message: The first sentence of the article is "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] or the fallacy of the maturity of chances, is the belief that if deviations from expected behaviour are observed in repeated independent trials of some random process then these deviations are likely to be evened out by opposite deviations in the future."
I have a major problem with the way this is stated.  In a very specific and quantitative sense, it IS true that deviations from expected behavior are likely to be evened out  by future results - not by opposite deviations exactly, but simply by virtue of the fact that future results will average to the mean, and there will eventually be many more than them than the original deviation.  That's called the law of large numbers, and it lies at the base of all of statistics.  
So I suppose the article's first sentence isn't exactly wrong, but I think it's potentially very misleading.  It ought to be re-phrased to make it clear that the fallacy is believing that the future results are in any way influenced by those already obtained, or to highlight more clearly the fallacious part in the sentence as is (which is that the deviations will be evened out not simply by more data, but specifically by opposite deviations).
Unless someone else has any objection, I'll re-write the first sentence  to something like this: "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] or the fallacy of the maturity of chances, 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."  (Can anyone think of a better term than "direction"?)    Waleswatcher (talk) 03:01, 19 February 2011 (UTC)
replies: text: "it IS true that deviations from expected behavior are likely to be evened out by future results" Nope. They don't even out. Things only even out if you average them, but in many cases you're interested in (for example) the amount of money in your pocket, and that is not an average, it's a sum. That's not the same thing. The average converges, the sum diverges, it follows a drunkard's walk in fact, and gets further and further from the mean with repeated gambles.Rememberway (talk) 03:23, 19 February 2011 (UTC)
replies: text: "Nope. They don't even out. Things only even out if you average them"  Sorry, but the latter is *exactly* what I said.  You took part of the middle of a sentence from my comment, dropped the beginning and end, and then repeated the rest in your own words - so I'm not sure what your point was supposed to be.  My point is that someone reading the first sentence of the article as is now might well conclude that it's a fallacy to believe that the average will even out, when in fact it isn't.  Do you object to my proposed re-wording?  Waleswatcher (talk) 13:58, 19 February 2011 (UTC)

text: Sorry in advance for being a bit of a pedant, but that first sentence is still slightly incorrect.  Gambler's Fallacy is the belief that a past independent trial will affect a future independent trial.  The difference there being that many people falsely believe a streak will continue, not just that the opposite will happen.  Examples of this in a casino abound, from people who believe they are on a winning "streak", particularly in craps, to baccarat players that wait for "runs" of Player or Banker wins and then bet that side, assuming the streak is bound to continue.  It's not incorrect to the point that I'd edit it, but since you brought it up... AddBlue (talk) 06:52, 17 February 2012 (UTC)
thread_title:  Very first sentence false? 

message: I removed a link to the inverse gambler's fallacy. The article with that title describes it as drawing the conclusion that there must have been many trials from observing an unlikely outcome. The rather different concept this article was referring to was the belief that a long run of heads means that the next roll is outcome is likely to be heads. MathHisSci (talk) 16:38, 7 April 2011 (UTC)
replies: text: Yet let's have a look at the article content. "The probability of getting 20 heads then 1 tail, and the probability of getting 20 heads then another head are both 1 in 2,097,152." So, the probability of me getting heads that many times is ~ 1 in 2 million? Without ANY evidence to support either position, would the more rational assumption be the coin is not fair and heads is weighted? Since we talk about "fair coin" (no such thing, varying degrees of debris, weighting of the print, etc) and we didn't even consider fair toss, while it doesn't invalidate the fallacy, would you not agree it brings into question some of it's more common applications?  — Preceding unsigned comment added by 87.112.178.244 (talk) 15:39, 25 May 2011 (UTC)
replies: text:  Yes, the inverse gambler's fallacy, as this article defines it, can be seen as more rational than the usual version in practice, though not in the formal mathematical model. MathHisSci (talk) 21:39, 8 August 2011 (UTC)
thread_title:  Inverse gambler's fallacy 

message: Here are some sources that I'm considering for this page, and what they will contribute to the page:
Burns, B.D. and Corpus, B. (2004). Randomness and inductions from streaks: "Gambler's fallacy" versus "hot hand." Psychonomic Bulletin and Review. 11, 179-184. These researchers found that people are more likely to continue a streak when they are told that a non-random process is generating the results. The more likely it is that a process is non-random, the more likely people are to continue the streaks. Useful explanation of the types of processes that are more likely to induce gambler's fallacy.
Croson, R. and Sundali, J. (2005). The gambler's fallacy and the hot hand: Empirical data from casinos. The Journal of Risk and Uncertainty 30, 195-209. This is an observational study rather than an experiment, observing the behaviors of individuals in casinos. I found it interesting that they also observed the "hot hand" phenomenon in gamblers as well - and that it's not just restricted to basketball. 
Oppenheimer, D.M. and Monin, B. (2009). The retrospective gambler's fallacy: Unlikely events, constructing the past, and multiple universes. Judgment and Decision Making, 4, 326-334. This article introduces the retrospective gambler's fallacy (seemingly rare event comes from a longer streak than a seemingly common event) and ties it to real-world implications. The researchers tie it to the "belief in a just world" and perhaps even hindsight bias (the article talks about how memory is reconstructive). 
Rogers, P. (1998). The cognitive psychology of lottery gambling: A theoretical review. Journal of Gambling Studies, 14, 111-134. Ties the gambler's fallacy in with the representativeness and availability heuristic. Defines gambler's fallacy as the belief that chance is self-correcting and fair. 
Roney, C.J. and Trick, L.M. (2003). Grouping and gambling: A gestalt approach to understanding the gambler's fallacy. Canadian Journal of Experimental Psychology, 57, 69-75. Explains that simply telling people about the nature of randomness will not eliminate the gambler's fallacy. Instead, the grouping of events determines whether or not gambler's fallacy occurs. Very interesting, and possibly a good source for a possible "solutions" section.
Sundali, J. and Croson, R. (2006). Biases in casino betting: The hot hand and the gambler's fallacy. Judgment and Decision Making, 1, 1-12. Correlates hot hand and gambler's fallacy - people who exhibit one will also exhibit the other. Introduces the possibility of a construct underlying both of these. 
One idea I had for possibly altering the structure of this article: dividing the "psychology" section into subsections by each psychological concept - biases, grouping, etc. Songm (talk) 21:40, 7 March 2012 (UTC)
thread_title:  Psychology of Gambler's Fallacy 

message: It is entirely possible that the universe does have a 'memory' of events and that probability theory and the idea of randomness are not actually correct.
There is no way to prove probability theory.  You can't prove probability theory by, for example, tossing a coin and counting results and comparing to expected results because you would actually have to use the theory to do that comparison.  The argument becomes circular.  It is just one of the axioms we just accept in science.
I work with probabilities and stats so I'm not saying it is wrong.  I'm pretty sure it is right and it's a great tool.  But, I do find it fascinating that it may well be false and there is no way of knowing if it is or isn't.  There is, for example, no way to demonstrate or prove 'randomness'.  We must simply state that a coin toss is random and accept it.  There are tests for randomness, but there are many sets of numbers that pass randomness tests that are in fact not random, the famous example being the Mandelbrot set.  These sets exist in nature frequently.
So maybe the gambler's fallacy is not so false after all.
Still I think it *probably* is  :-p  — Preceding unsigned comment added by 129.78.32.22 (talk) 05:47, 7 August 2012 (UTC)
thread_title:  philosophical point of view 

message: "The probability of having a child of either gender is still regarded as 50/50."  The idea that the probability is 50/50 is a fallacy.  It is only roughly true, with respect to large populations. In human populations we see that there are slightly more male births than female ones, and it is believed that this difference is because more boy babies die before reaching reproductive age than girl babies.  Thus the population has reached some sort of equilibrium, but it is an equilibrium of 50/50 at reproductive age, not birth.  This is called Fisher's Principle.  http://en.wikipedia.org/wiki/Fisher%27s_principle  According to Fisher the roughly 50/50 outcome is entirely dependent on having some individuals in the population who are genetically predispositioned to produce boys as offspring, while others are genetically predispositioned to produce girls. The outcome for populations says nothing about the expected sex ratio of offspring of individuals.  Thus people who after having a series of children of the same sex who keep trying for the other, because they think in some sense 'they are owed one' are making the gamblers fallacy.  But people who keep trying because they think that 50/50 are good odds, may be making a different error.  They may be strongly biased to produce the sex they already have produced, and the odds of them getting the other one may be very small.  As of now we have no way to tell, because the mechanisms which determine the sex of offspring are largely unknown.  — Preceding unsigned comment added by 85.224.196.196 (talk) 13:49, 17 September 2012 (UTC)
thread_title:  Childbirth 

message: As far as I understand, this article is talking about the same concept as law of averages. Since the other article is shorter, would anyone be opposed to merging that article into this one? 173.181.83.109 (talk) 21:59, 24 June 2013 (UTC)
replies: text: As far as I understand it, the Gambler's Fallacy is a psychological phenomenon, it is a failure to understand and to correctly use the "laws" of probability. As a matter of human psychology, it is not identical to the law of averages so having one article for each would seem to be more appropriate. It is like the subject of risk and the inability of people to correctly assess risk which would fall under psychological failings.Qordil (talk) 18:10, 27 August 2013 (UTC)
thread_title:  Merge [[law of averages]] into this article 

message: I'm just now writing a response to someone who's brought up a difficult and fallacious argument. It's related to this topic, so I wanted to see if I could refer them here. I cannot. The problem is that the article is not written for the casual reader, but for the accomplished statistician. There needs to be extended text at the beginning that explains in simple and compelling language why this is a fallacy.
From the backtalk in the comments, there are a fair amount of people who are convinced they are still right. (For example Carl from Louisiana, on Jan 15, 2010.) Eebster the Great responded, but was more or less taking the (correct) and somewhat sterile party line. I don't feel that's effective explaining to Carl and people like him why he's in error. For Carl, one of four things is happening. Either the gambling object is not quite "fair" because of manufacture or wear, or the house is intentionally cheating in his favor, or he is observing patterns where none have statistical significance, or he is mis-remembering what happened. Naturally, the last argument isn't going to sway any reader, but the others should alert casual readers that what they see as compelling evidence may be flawed. Leptus Froggi (talk) 20:31, 11 October 2013 (UTC)
thread_title:  Preaching to the choir 

message: Suppose we have 6 heads in a row. What if the gambler bets not on what the next toss will be (with a resulting 50/50 probability), but on whether or not there will be a series of 7 heads in the game he plays (with the next toss completing the series)? Since the probability of 7 heads in a row is low, wouldn't it still be prudent to bet against it? And if not, why not? Try not to repeat the formulation of the fallacy or restate that the probability is still 50%. Explain, why a bet on the probability of 7 heads in a row is meaningless. What if we're talking about 69 previous heads (still assuming a fair coin) and the next toss is no. 70?89.12.84.0 (talk) 15:44, 12 October 2013 (UTC)
replies: text: I see you answered your own question, but the key issue is conditional probabilities. Even people who can do a decent job of estimating probilities can get tripped up when the issue is coonditional probablities.--S Philbrick(Talk) 16:44, 23 January 2018 (UTC)
thread_title:  What if... 

message: Another variety, known as the retrospective gambler's fallacy, occurs when individuals judge that a seemingly rare event must come from a longer sequence than a more common event does. For example, people believe that an imaginary sequence of die rolls is more than three times as long when a set of three 6's is observed as opposed to when there are only two 6's. This effect can be observed in isolated instances, or even sequentially. A real world example is that when a teenager becomes pregnant after having unprotected sex, people assume that she has been engaging in unprotected sex for longer than someone who has been engaging in unprotected sex and is not pregnant.[17]
The example is completely false. It compares looking at a dice roll and concluding something about previous dice rolls to pregnancy, but the analogy doesn't work at all. Being pregnant is instead analogous to "successfully" rolling 3 6's anytime in the sequence, not just as the very last roll. This is because having sex and not being impregnated that particular time doesn't undo being impregnated previously.  — Preceding unsigned comment added by 98.164.193.204 (talk) 23:57, 14 October 2013 (UTC)
thread_title:  False example for retrospective gambler's fallacy. 

message: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2627354
When you observe short sequences, the probability that a sequence will alternate is greater than 50%. Paraphrasing part of the paper, consider these coin flips (generated just now using a random generator at: http://www.mathgoodies.com/calculators/random_no_custom.html):  1001010101110
So we have: 6 zero's, and 6 one's. A perfect 50/50 as expected. But, the gambler's fallacy is not this probability, it is the probability that given a short sequence and a 1, what is the chance the the next value will also be a 1? In the above example, out of the 6 "ones", only 2 are followed by another "one". In the sequence above, two thirds of the time you will be better off switching, a predictive power of the next flip that is better than 50/50! If this sequence were extended out, then this probability would converge back to 50%. On the other hand, if you were to get more sequences of the same length, then these skewed probabilities would likely remain.  — Preceding unsigned comment added by Dvanatta (talk • contribs) 08:50, 26 October 2015 (UTC)
replies: text: Re this edit: the first problem is that the Social Science Research Network looks like one of the many places where people can publish research online with little if any peer review. Unless probability theory is badly wrong, the probability of a 50-50 bet being successful remains at 50-50 every time. People have often tried to convince themselves otherwise, but that's the way it goes.--♦IanMacM♦ (talk to me) 15:30, 23 January 2018 (UTC)

text: I've only read through page three, but the short answer is that your math is wrong. You aren't counting things corrrectly.--S Philbrick(Talk) 15:37, 23 January 2018 (UTC)

text: Very short sequences can be misleading. It takes a large amount of trials to approximate a normal distribution curve accurately. The authors of the paper don't seem to have taken this into account.--♦IanMacM♦ (talk to me) 16:07, 23 January 2018 (UTC)
thread_title:  Recent Paper Supports the Gambler's Fallacy as Fact 

message: Jonah Lehrer’s How We Decide is no longer available, as it was pulled by the publisher in March 2013. It has been removed from the article as a source. As for the Monte Carlo example, where black came up 26 times in a row in August 1913, some sources regard this as an anecdote with doubtful authenticity. At 1 in 136.8 million, it is very unlikely, but of course not outright impossible. Here is a roulette wheel that came up red ten times in a row, but at 1 in 1347 this is much more plausible.--♦IanMacM♦ (talk to me) 13:51, 6 February 2018 (UTC)
thread_title:  Monte Carlo Casino example  

message: The odds were stated to be 1:136.8 million. However, that is getting specifically black 26 times in a row. It's not relevant that it was black; it'd make no difference if it had been red 26 times in a row. The "first" time it landed on black wasn't actually the first time, unless it was opening day within the first few rolls (and everyone happened to bet on that one). Rather, the "first" black was completely insignificant to the gamblers, and only became the "first" by being followed by 25 more. Therefore, I've corrected the odds to a black happening 25 MORE times after the "first" as 18/37 chance per roll, so 1 / 0.486486486^25 = 66,564,294.2. Roguetech (talk) 12:38, 21 September 2018 (UTC)
replies: text: This is correct, but if a person was betting on black continuously, the probability would be 136.8 million as stated.--♦IanMacM♦ (talk to me) 13:12, 21 September 2018 (UTC)
replies: text: Re this edit: when betting on red or black on a single zero roulette wheel, the probability of success is 18 out of 37, or p = 0.486. Writing it as  implies that the fraction is 2.055, which seems obviously wrong.--♦IanMacM♦ (talk to me) 16:21, 22 September 2018 (UTC)
replies: text: I think we're getting confused because of the wording of the sentence. The probability is p = ()26-1 which is 1 in 66.6 million. I've adjusted the wording to be consistent with the other sentences in the article where the probability is given.--♦IanMacM♦ (talk to me) 16:38, 22 September 2018 (UTC)
replies: text:  Thanks for our hint concerning my edit, ianmacm, but I cannot agree:1. There are no other sentences in the article where the probability (of 26 blacks) is given.2. If the calculcation was to be consistent, it would have to be the same as in the coin example: The probability of 21 heads in a coin experiment is ()21. The probability of 26 blacks in a roulette experiment is ()26. As there is no first head only becoming first because of other heads following (if you start a coin toss sequence and get heads, it is the first, no matter which outcomes follow), there is no first black only becoming black because there are more blacks following. Even if a sequence has a length of 1, the first element remains the first.3. Roguetech's calculation of the probability of "a black happening 25 MORE times after the 'first'" is correct, but they should have adapted the sentence as well. As of now, it states that the probability of getting 26 blacks in a row is ()251:, which is false. It denotes the probability of getting 25 blacks after the first trial (no matter if the outcome of the first trial was black or red, by the way). So you'd either have to change the sentence or the probability. Guy Bukzi Montag (talk) 13:05, 11 August 2019 (UTC)
replies: text: It depends on the wording. The probability of specifically 26 blacks in a row is 1 in 136.8 million. However, the crowd at the Monte Carlo casino would have been just as happy with 26 reds in a row, and when this is taken into account, the probability is 1 in 66.6 million.--♦IanMacM♦ (talk to me) 13:23, 11 August 2019 (UTC)
replies: text: Of course it depends on the wording. But the wording, as it is in the article, is wrong. Or the probability. They don't fit together. Guy Bukzi Montag (talk) 10:18, 12 August 2019 (UTC)
replies: text: One way round this problem is to go back to the previous wording, which makes clear that the probability of black (and black only) 26 times in a row is 1 in 136.8 million. It starts to get more complicated when red or black is specified. However, I do believe that the current wording is correct, which is "the probability of a sequence of red or black occurring 26 times in a row is ()26-1 or around 1 in 66.6 million." After a red or black has occurred with p=1, the follow up is red or black 25 times in a row. Possibly it could be changed to "either red or black" to make this clearer.--♦IanMacM♦ (talk to me) 16:54, 12 August 2019 (UTC)
replies: text: To be clear, the argument of "it doesn't matter if black or red" is just an easy way to look at/explain it. It simply doesn't make sense to count the "first" spin. If a casino only did roulette once per day, and only continued spinning if it landed on black, then there would be a 1:137 million chance of spinning it 26 times on any specific day. (This is the same as saying "if you flip a coin X number of times".) But that doesn't reflect reality of the "Monte Carlo" example, where they continue rolling regardless. So which is the "first" spin...? You can pick any of them.! For the sake of figuring "odds", you can pick any one as the "first" spin, with the only caveat being that you ignore all prior spins. If the spin you picked as being the first were red (or green), then the odds of getting 25 more blacks in a row would be 0%.  So if you're measuring consecutive black spins, why pick red as the first one? There is no one specific set of 26 spins, rather for every 26 spins, there are 26 possible starting points. Another way to look at/explain it, there's no requirement for when the Monte Carlo players placed their bets. If caught in the "gambler's fallacy", you wouldn't bet on black if the prior spin was anything other than black. Ergo, the first spin must be black for the "gambler's fallacy" to apply. So in context of either a continuously operating casino, or any "gambler's fallacy", you would not count the first spin. I don't oppose it saying "red or black" (or "either red or black"), but only as a means to avoid arguments. @@Guy Bukzi Montag Note that the same argument doesn't apply to the "Example" of flipping coins, since it addresses specifically "a single toss", which must be a specific single toss. However, for the "Non-example" example of flipping coins, I agree that the odds should be computed on the standard of "more flips" rather than "total flips". Roguetech (talk) 18:41, 19 August 2019 (UTC)
thread_title:  Monte Carlo Casino Odds 

message: This was added on my talk page by :
Hello, regarding the change I made suggesting that the probability of a sequence of either red or black occurring 26 times in a row is , since the probability of the first occurrence of a red or a black is not 1, but 36/37, then the probability of 26 occurrences in a row is not 1 x  , it's (36/37) x  , which is .
As 2A02:2F04:A001:C400:450:9681:1692:82EE points out, the current wording assumes that the probability of red or black on the first spin is 1 (completely certain) when it is actually  on a single zero roulette wheel. I think this is the more correct wording. This makes the probability of red or black appearing 26 times in a row in any given 26 spins 1 in 68.4 million rather than 1 in 66.6 million.--♦IanMacM♦ (talk to me) 19:19, 17 May 2024 (UTC)
thread_title: Different formulation for the probability

message: A of systems in the physical world are stochastic but not truly random; e.g. economic growth, the stock market, sex ratios (I noticed that did get a mention), etc.  Processes that seem random in the short and even the medium term will still converge back to a mean eventually, usually in no more than 10-20 years.  I think the article should acknowledge this more.  Is there really such a thing as true randomness outside of contrived human games and particle physics? Heck, I've read papers on random number generators that make truly random sequences, and it's not easy.  — Preceding unsigned comment added by Joeedh (talk • contribs) 20:17, 13 November 2018 (UTC)
replies: text: John von Neumann famously said that "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." For the purposes of everyday probability theory, events like the toss of a coin, the throw of dice and the spin of a roulette wheel are considered to be random. It's never quite that simple, but events like the ups and downs of the stock market cannot be examined with basic probability theory.--♦IanMacM♦ (talk to me) 05:21, 14 November 2018 (UTC)
thread_title:  What About Stochastic But Not Truly Random Phenomena? 

message: Re this edit: there is a large amount of philosophy and very little mathematics in this addition. As far as mathematicians are concerned, the fallacy is real and occurs when a person falsely believes that non-dependent random events will even out in some way, which they are under no obligation to do. This is similar to previous attempts to undermine the fallacy with philosophical reasoning that has little to do with the underlying mathematics. I'm also worried by the use of Social Science Research Network as a source, because this is a preprint service, where people can upload anything they like without any effective peer review. Is this really suitable for the article?--♦IanMacM♦ (talk to me) 17:47, 14 January 2019 (UTC)
replies: text: Don't even bother engaging, this is a continuation of the editor's attempts from a year ago to "to determine how long it takes for an anarchic experiment in democratic knowledge accumulation to become, as eventually they always do, a cult of a few restricting knowledge to acceptable forms". Toohool (talk) 18:10, 14 January 2019 (UTC)
thread_title:  January 2019 

message: Referring to this revert.  are you saying you're going to get the book? Because as I've indicated, I have read the book. I don't remember the precise numbers - for example it could be 6 championships in 8 years instead of 5 championships in 7 - but I remember the essence of what was written. Banedon (talk) 06:46, 8 June 2019 (UTC)
replies: text: Going from memory obviously isn't ideal. I had hoped it would be on Google Books; it is  but you can't look inside it.  The book can be purchased on Amazon  but I don't have a copy.--♦IanMacM♦ (talk to me) 06:52, 8 June 2019 (UTC)
replies: text: Like I said, I do. The puzzle in question was about how one guy was attempting to impress a woman by boasting about how his team had won X championships in Y years. The woman sarcastically congratulated the guy for winning in year Y and commented that the guy must've been so happy after his team failed to win in year Y+1. The guy apologized for not recognizing an "expert" at the game. The woman said she knew nothing about it. Puzzle asked for how it's possible. The solution gives the explanation in the text, and said the same thing about politicians & unemployment. Banedon (talk) 08:01, 8 June 2019 (UTC)
replies: text:  If you have a copy of the book, then why are you going by memory? It looks like you are the editor who introduced the example of unemployment statistics to the article, and now you're saying that the same Guinness Book of Mindbenders you originally cited gives a better example of something not being an example of the gambler's fallacy? Toohool (talk) 01:23, 11 June 2019 (UTC)
replies: text:  Because I don't have the book anymore. I inserted the original section, then figured perhaps the other example is better and so changed it. Now tell me: why are you questioning my motivations? Why aren't you looking at the text and commenting on which is better? Banedon (talk) 01:58, 11 June 2019 (UTC)
replies: text: Because I'm skeptical about the whole paragraph. A half-remembered passage from a book that doesn't look like a very reliable source for any particular topic, about an example that it's not entirely clear is relevant to the article. Toohool (talk) 02:24, 11 June 2019 (UTC)
replies: text: I've ordered a copy of the book. Then we'll have a look at what it says. As a general rule, you should not use a book as a source unless you can lay your hands on it and quote from it directly.--♦IanMacM♦ (talk to me) 05:05, 11 June 2019 (UTC)

text: The book does not call it "gambler's fallacy" (neither does the Martin Gardner book also cited in the section, by the way). But I am 100% certain the puzzle described above is there. As I remember it was in the first half of the book. If you can't find it, I'll find it myself in about two months. Banedon (talk) 21:32, 13 June 2019 (UTC)
replies: text: Sorry, but this now needs a direct quote from the book. I've removed it from the article.--♦IanMacM♦ (talk to me) 05:17, 14 June 2019 (UTC)
replies: text: What kind of direct quote are you looking for? Like, the entire text of the puzzle? Banedon (talk) 05:18, 14 June 2019 (UTC)
replies: text: There are 109 puzzles. Which one is it? If you cannot say, it is because you do not have a copy of the book to hand.--♦IanMacM♦ (talk to me) 05:22, 14 June 2019 (UTC)
replies: text: You've proven to be sufficiently annoying that I went and acquired the book myself. It is puzzle 2. The fact that the puzzle is literally on the first page of the main text makes me question if you made a good faith attempt to find it. Banedon (talk) 05:38, 14 June 2019 (UTC)
replies: text: It's in the solution of Cricket for Americans. So apologies if I missed this. The Guinness Book of Mindbenders is a book of puzzles and their solutions, it isn't really a mathematics textbook. Looking at the exact quote, it is not strictly an example of the gambler's fallacy because it is not based on probability theory. It is more about selective citing of statistics or cherry picking to make them look good.--♦IanMacM♦ (talk to me) 05:53, 14 June 2019 (UTC)
replies: text: That's why the text was in a section on non-examples of the Gambler's fallacy. Banedon (talk) 05:54, 14 June 2019 (UTC)
replies: text: There are WP:TOPIC problems because it isn't an example of gambler's fallacy. It doesn't give specific probabilities for the events. If these remain constant, it is an example of the fallacy if a person believes that they are influenced by past results. Cherry picking is something different.--♦IanMacM♦ (talk to me) 06:02, 14 June 2019 (UTC)

text: Yes, that's why it is a non-example. Consider this example since it's more direct. Suppose there are two teams, Oxford and Cambridge, who are equally skilled. They play each other every year. I tell you that Cambridge has won the last eight years from 2012-2019. What are the odds that Cambridge will win in 2020? That would be 50% - it's the essence of the Gambler's fallacy. What are the odds that Cambridge won in 2011? As this source shows, that probability is not 50%. Banedon (talk) 06:05, 14 June 2019 (UTC)
replies: text: Sports betting is not the same as probability theory. The toss of a fair coin is always p = 0.5. If Cambridge has a better team than Oxford, they are more likely to win. In the 2018 men's boat race, Cambridge were quoted at 4/11, while Oxford were quoted at 2-1. 4/11 is an implied probability of 73.3%, while 2-1 is an implied probability of 33.3%. This might seem counterintuitive when there are only two teams, but sports betting works like this. The figures do not add up to 100% because the bookmakers always make a profit regardless of who wins, this is because the odds are over-round.--♦IanMacM♦ (talk to me) 06:34, 14 June 2019 (UTC)
replies: text: I don't see how that's related. The example I gave isn't about sports betting, and it explicitly assumes that the two teams are equally skilled. Banedon (talk) 06:39, 14 June 2019 (UTC)
replies: text: Gambler's fallacy is based on probability theory, such as red and black on a single zero roulette wheel always being p = 0.486. In real world situations like football matches and tennis matches, it is never quite that simple. Laying odds on a single event is not the same thing as gambling in a casino all day long, as the 2018 Boat Race can happen only once.--♦IanMacM♦ (talk to me) 06:54, 14 June 2019 (UTC)
replies: text: At that I think we're at an impasse which can only be settled by the participation of more editors. Banedon (talk) 10:38, 14 June 2019 (UTC)
thread_title:  Selective reporting section 

message: OK, I have now got a copy of the book. There are 109 puzzles in it, and I can't find anything that refers to the Gambler's fallacy. So I have added  and will remove it unless a specific reference can be found.--♦IanMacM♦ (talk to me) 17:16, 13 June 2019 (UTC)
replies: text: The book does not call it "gambler's fallacy" (neither does the Martin Gardner book also cited in the section, by the way). But I am 100% certain the puzzle described above is there. As I remember it was in the first half of the book. If you can't find it, I'll find it myself in about two months. Banedon (talk) 21:32, 13 June 2019 (UTC)
replies: text: Sorry, but this now needs a direct quote from the book. I've removed it from the article.--♦IanMacM♦ (talk to me) 05:17, 14 June 2019 (UTC)
replies: text: What kind of direct quote are you looking for? Like, the entire text of the puzzle? Banedon (talk) 05:18, 14 June 2019 (UTC)
replies: text: There are 109 puzzles. Which one is it? If you cannot say, it is because you do not have a copy of the book to hand.--♦IanMacM♦ (talk to me) 05:22, 14 June 2019 (UTC)
replies: text: You've proven to be sufficiently annoying that I went and acquired the book myself. It is puzzle 2. The fact that the puzzle is literally on the first page of the main text makes me question if you made a good faith attempt to find it. Banedon (talk) 05:38, 14 June 2019 (UTC)
replies: text: It's in the solution of Cricket for Americans. So apologies if I missed this. The Guinness Book of Mindbenders is a book of puzzles and their solutions, it isn't really a mathematics textbook. Looking at the exact quote, it is not strictly an example of the gambler's fallacy because it is not based on probability theory. It is more about selective citing of statistics or cherry picking to make them look good.--♦IanMacM♦ (talk to me) 05:53, 14 June 2019 (UTC)
replies: text: That's why the text was in a section on non-examples of the Gambler's fallacy. Banedon (talk) 05:54, 14 June 2019 (UTC)
replies: text: There are WP:TOPIC problems because it isn't an example of gambler's fallacy. It doesn't give specific probabilities for the events. If these remain constant, it is an example of the fallacy if a person believes that they are influenced by past results. Cherry picking is something different.--♦IanMacM♦ (talk to me) 06:02, 14 June 2019 (UTC)

text: Yes, that's why it is a non-example. Consider this example since it's more direct. Suppose there are two teams, Oxford and Cambridge, who are equally skilled. They play each other every year. I tell you that Cambridge has won the last eight years from 2012-2019. What are the odds that Cambridge will win in 2020? That would be 50% - it's the essence of the Gambler's fallacy. What are the odds that Cambridge won in 2011? As this source shows, that probability is not 50%. Banedon (talk) 06:05, 14 June 2019 (UTC)
replies: text: Sports betting is not the same as probability theory. The toss of a fair coin is always p = 0.5. If Cambridge has a better team than Oxford, they are more likely to win. In the 2018 men's boat race, Cambridge were quoted at 4/11, while Oxford were quoted at 2-1. 4/11 is an implied probability of 73.3%, while 2-1 is an implied probability of 33.3%. This might seem counterintuitive when there are only two teams, but sports betting works like this. The figures do not add up to 100% because the bookmakers always make a profit regardless of who wins, this is because the odds are over-round.--♦IanMacM♦ (talk to me) 06:34, 14 June 2019 (UTC)
replies: text: I don't see how that's related. The example I gave isn't about sports betting, and it explicitly assumes that the two teams are equally skilled. Banedon (talk) 06:39, 14 June 2019 (UTC)
replies: text: Gambler's fallacy is based on probability theory, such as red and black on a single zero roulette wheel always being p = 0.486. In real world situations like football matches and tennis matches, it is never quite that simple. Laying odds on a single event is not the same thing as gambling in a casino all day long, as the 2018 Boat Race can happen only once.--♦IanMacM♦ (talk to me) 06:54, 14 June 2019 (UTC)
replies: text: At that I think we're at an impasse which can only be settled by the participation of more editors. Banedon (talk) 10:38, 14 June 2019 (UTC)
thread_title: The book says...

message: In the context of "runs" it is not required to have a 20-item run of the same outcome in order to be considered a run for gambling purposes:
Yes, it's true that the 21st coin flip has a 50/50 chance of being heads even if it was heads the last 20 times.  However, the chances of generating 21 heads in a row is NOT equally likely as having 20 heads and a tails in terms of gambling.  There is only 1 way you can have 21 heads in a row, but there are 21 different ways you can have 20 heads and a tails in the run.  The traditional notion of "the chance of getting a tails is going up" after a long run containing mostly heads is actually a correct notion, not a fallacy, because truly-random game outcomes do eventually approach a normal distribution of outcomes and you need to compare your current run to a theoretical normal run in order to visualize the likelihood of future outcomes.
IN reality, the majority of gamblers consider a lucky run to potentially include some losses as long as the wins highly-outweigh those losses.  The real "gambler's fallacy" is not that "The next one will be tails" but rather "I should be seeing *more* tails soon" because runs in gambling are most often mixtures of results, not straight runs of perfectly uniform outcomes.  A "run" in gambling can be a mixture of wins and loses that leans heavily toward wins, and in a chance-based game the longer you play the more likely your outcomes will approach a normal distribution.
The real-world "gambler's fallacy" is the assumption that a string of random events will eventually achieve a normal distribution of outcomes - that's not a fallacy at all. 50.239.107.122 (talk) 18:33, 3 October 2019 (UTC)
replies: text: The key word here is "eventually". There is no fixed amount of time that would guarantee a 50-50 split of heads and tails. The probability on each individual toss is always p = 0.5.--♦IanMacM♦ (talk to me) 05:40, 4 October 2019 (UTC)
thread_title:  Coil-Toss analogy not accurately applied to Gambler's Fallacy; real-life Gambler's Fallacy is not accurately depicted, anyways, and not really a  fallacy 

message: Re this edit: the simple answer to the question "Is the gambler's fallacy really a fallacy?" is "yes". As the coin toss example in the article says, "When flipping a fair coin 21 times, the outcome is equally likely to be 21 heads as 20 heads and then 1 tail. These two outcomes are equally as likely as any of the other combinations that can be obtained from 21 flips of a coin. All of the 21-flip combinations will have probabilities equal to 0.521, or 1 in 2,097,152. Assuming that a change in the probability will occur as a result of the outcome of prior flips is incorrect because every outcome of a 21-flip sequence is as likely as the other outcomes." Considering a series of events does not alter the probability of individual random events. I'm also concerned about a potential conflict of interest here. This section is giving way too much prominence to a single paper, which leads to problems with WP:DUE.--♦IanMacM♦ (talk to me) 19:18, 1 September 2020 (UTC)
thread_title:  "Is the gambler's fallacy really a fallacy?" 

message: because good shooters can increase the probability of hitting a desired number significantly by training. This skill is a part of their profession, to defeat systematic big bettors.--2400:4050:95C3:2B00:207A:3830:B1F7:3D98 (talk) 01:02, 1 March 2021 (UTC)
replies: text: Modern casinos go to considerable trouble to ensure that roulette wheels are random, while the croupiers are instructed to spin the wheel and throw the ball with a different amount of strength each time. This suggestion also implies that the croupiers are acting in bad faith, and would require a reliable source.--♦IanMacM♦ (talk to me) 08:04, 1 March 2021 (UTC)
thread_title:  Roulette is not a good example 

message: This section refers to Laplace having published A Philosophical Essay on Probabilities in 1796. The article Pierre-Simon Laplace (under Inductive probability) gives a date of 1814 for this work. In Chapter 1 - Introduction - of this edition, Laplace refers to the essay as a development of a lecture he had given in 1795. It looks like this reference may have conflated the lecture and the essay. How should we handle this? Autarch (talk) 01:39, 9 April 2021 (UTC)
thread_title:  Childbirth section 

message: Wikipedia "d'Alembert's system" redirects to this page. I think that that is a bad mistake. d'Alembert's system is not such a bad system. It does not really have anything to do with the gambler's fallacy, as far as I know. I mean: I'm not sure that d'Alembert himself believed in that fallacy. Richard Gill (talk) 12:00, 15 April 2021 (UTC)
replies: text: This source says (correctly in my view) that d'Alembert's betting system is "a prime example of the Gambler’s Fallacy". It is based on the assumption that 50-50 bets should even out over a period of time, but there is no guarantee that they will. In practice, the system has no memory and the probability remains at 0.5 every time the event occurs.--♦IanMacM♦ (talk to me) 16:17, 15 April 2021 (UTC)
replies: text:  I've now discovered that the d'Alembert system is *erroneously* attributed to d'Alembert. It should not be called "d'Alembert's system" at all. Richard Gill (talk) 17:51, 16 April 2021 (UTC)

text:  Also, d'Alembert comes out very well in a comparison with other gambling systems. If you must gamble, it is not a bad choice. "Table 3 thus reveals the magic of the d’Alembert. Though it lags behind in terms of mean upside return for small goals, it matches Labouchere in terms of martingaling ratio and requires fewer rounds of play on average to achieve the goal. But the d’Alembert improves consistently as the goal becomes more ambitious. For a desired gain of at least 5% of the initial capital, d’Alembert requires more time to reach the goal, but does so with higher frequency and by requiring the gambler to take less money out of his pocket. d’Alembert also competes with le tiers et le tout on mean upside return, even though TT is designed to produce large gains." https://www.researchers.one/article/2020-08-32 "Risk is random: The magic of the d'Alembert", Harry Crane, Glenn Shafer Richard Gill (talk) 18:00, 16 April 2021 (UTC)

text: The d'Alembert betting system may be an example of Stigler's law of eponymy. In Croix ou Pile d'Alembert wrote that in two tosses of a fair coin,  the probability that heads will appear at least once is . This isn't correct, as there are four possible outcomes, making the answer . The betting system is also known as Martingale, and people are advised not to try this in real life because they can lose money very quickly.--♦IanMacM♦ (talk to me) 20:52, 16 April 2021 (UTC)
replies: text:  ah, interesting. The d’Alembert is sometimes grouped with other systems called collectively martingale systems, but only one of them is “the” classic martingale system. With *the* martingale people rapidly do lose a lot of money. But not so much with d’Alembert. See Crane and Shafer. Richard Gill (talk) 03:20, 17 April 2021 (UTC)
thread_title: d'Alembert's system

message: Relevant to several discussions I'm seeing here, and in anticipation of future discussions, there are a few points that may need clarification:
First, "probability" is about *future* or *hypothetical* events. It is the mathematical likelihood that an event (or combination of events grouped together) will happen in the future or in a hypothetical situation. After an event has happened, by definition the probability then equals 100%, and equations for probability no longer apply.  In non-mathematical terms, probability is the degree of certainty that a future/hypothetical event will happen. 100% equals complete certainty. For an event that has already happened, the degree of certainty is 100%. The probability of an observed past event/outcome is automatically set to 100%. 
Also, please note that probability equations will often state conditions (e.g.; "assume a fair coin"). For a real-life situation, this doesn't mean you should always assume the condition is true. It means that if the condition has been met (e.g.; a "fair coin" has been confirmed to be true), then the probability equation applies. If the condition has not been met (or is not certain) then the equation provides an estimate at best. 
Additionally: As with all things mathematical, adding a human variable makes things messy. People are not machines. Physical tasks (e.g., a coin flip) depend on human physical mechanics which is often inconsistent. This type of variability becomes less significant if the task is repeated numerous times and/or by numerous subjects. Also, the stated assumptions for a mathematical equation (such as "fair coin") can only be met if the human is able/willing to meet the condition. In this example with gambling, ethically questionable behavior is a variable that can render a mathematical calculation useless. Basically, humans ruin everything. You're welcome. :-)
Hope that helps clarify probability equations and how/when they're applied. Betsy Rogers (talk) 22:37, 21 November 2022 (UTC)
thread_title:  Clarification on "probability" definition & calculations