# Talk:Gambler's fallacy

Gambler's fallacy was a Social sciences and society good articles nominee, but did not meet the good article criteria at the time. There are suggestions below for improving the article. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.
 April 27, 2012 Good article nominee Not listed

## This Gambler's fallacy has a fallacy within itself

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)

## Good article

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

## Slot machine jackpots can in most cases be "due"

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 (talkcontribs) 15:14, 6 October 2011 (UTC)

Pim says: Totally agree! This sentence suggests slotmachines make random choices, while all modern slotmachines are programmed to be predictable.. — Preceding unsigned comment added by Pimnl (talkcontribs) 19:32, 16 October 2011 (UTC)

Whoa, with respect, the above two comments are absolutely incorrect. Slots do in fact have a payback percentage set but this does not ever mean a machine can be "due". The payback percentage reflects what will statistically happen given the chance of each reel stop and the payback set to particular combinations of stops. This payback percentage is in no way guaranteed to occur in any set period of time. A slot machine might be set with a 95% payback schedule but may payback 50% one day and 150% the next. It could even payback well above or below its payback percentage for years, however statistically unlikely. The only guarantee is that in an infinite number of spins the machine will average its set payback percentage. The random number generators in slots are independent trials and do not have "memories" and the computer inside will not, and cannot, influence the RNG to try and match the payback. This is based on 15 years of experience as a casino employee. I've worked with game manufacturers and have read plenty of PAR sheets. For another source see: http://www.casinocenter.com/?p=846 AlmtyBob (talk) 06:24, 17 February 2012 (UTC)

To put all that another way: If a slot machine fails to pay out for a whole year, it is not the case that some agent of government will knock on the casino's door to talk about it, nor will the casino be expected to do anything in particular. They might generally be require to demonstrate the machine's fairness ante facto, but not post facto. (If it were the latter than it might make some sense to consider a result "due", especially if it's the last day within a year during which the machine is officially required to pay out 1% of earnings, and it hasn't paid out all year.) 141.158.199.150 (talk) 20:30, 18 May 2013 (UTC)

## Coins

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)

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)

I have always been unconvinced of the lack of bias in coin-tossing. Any coin is of a finite size. When tossed, finite energy is pumped into the flick that gives it lift and spin. The coin, on any trial, will then rotate a certain finite number of half-spins while falling upwards, and a possibly larger number when it pauses and falls downwards towards the landing surface. Humans have a tendency to flick coins with a roughly similar thrust on each toss and each human is, of course, the same height and has the same arm length (roughly) on every toss. That leads to the anecdotal conclusion that all tossings of the same coin will have roughly the same number of half spins. The only "random" factor in the process is then the starting condition; whether the coin is heads-up or not just prior to the toss. I have the feeling, completely unsubstantiated by any evidence save personal observations of my own behaviour on a very few occasions when I remembered to note it, that an human tossing a coin repeatedly will force a seemingly random selection of heads-up positions before tossing the coin "just for fairness' sake". In short, people fiddle the game to produce expected results. While this cooking of the books may not invalidate a single toss I suspect it biases experiments in repeated coin-tossing in favour of "randomness". I would really like to know if I'm right but I see absolutely no way of unequivocally proving the point either way. Qordil (talk) 17:11, 27 August 2013 (UTC)

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)
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)

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)

## circular logic

The offered proof in the article is fallacious itself, because it is Begging_the_question

consider "Explaining why the probability is ${\displaystyle \scriptstyle {\frac {1}{2}}}$ for a fair coin":

The fallacious gambler works under the assumption that probability is ever-changing, depending on the previous outcomes. Thus he would not assume

• probability of 20 heads = 0.520

but rather something like

• probability of 20 heads = [(1-x)*(0.5)]20

since for the fallacious gambler the probability of Heads decreases with every Heads.

The corrolary is that for the fallacious gambler a fair coin does not exist unless it has previously produced perfectly even results and even then it becomes biased again after the very next toss. The fallacious gambler cannot within his logic calculate 2 or more coin tosses using the same probability for each.

Hence the fallacy cannot be disproved using the toss of a fair coin, since the existence of such a coin is already contradicting the gambler's fallacy and it is rather unsurprising that any subsequent reasoning would do the same.

BharatKulamarva (talk) 11:12, 29 November 2009 (UTC)

It seems like your argument is that the "fallacious gambler" uses "fallacious logic".....which is evidently true and is the basis of the Gambler's fallacy.
Certainly you must admit that fair coins exist. You can test it yourself by flipping coins and recording the number of heads/tails. So indeed, as you said, the existence of such a coin contradicts the fallacious gambler's logic. This does not mean such coins do not exist, rather it means that the gambler's fallacy is exactly just that, a fallacy. Paul Laroque (talk) 01:21, 21 December 2009 (UTC)
Agreed. As I said: a fair coin does not exist for the fallacious gambler. Thus if a fair coin exists, the fallacious gambler is proven to be - well - fallacious.
My point though was: If I was a fallacious gambler, the paragraph in question would not be a proof to me, since it assumes the existence of a fair coin, which - being a fallacious gambler - I would deny.
Herein lies the heart of the problem of proving the fallacy. The existence of a fair coin is technically just an assumption, albeit an assumption that most reasonable people (including me) agree to be true and that the whole of classical probability theory builds upon.
Thus my reasoning that you cannot - strictly speaking - prove the fallacy, just illustrate its insanity. For example it would follow that - since all coins are biased - you could prepare dice for a competition by purchasing a lot of them and rolling them beforehand at home. You would then keep the dice that are "due" (e.g. had very little sixes) and take them to a competition. This absurd example should illustrate the fallacy especially since it exactly contradicts the concept of "lucky dice" which many gamblers believe in as well. --BharatKulamarva (talk) 11:58, 22 December 2009 (UTC)

Ok, so it is very obvious that if we have a set of fair coin flips of TTT that the next flip has a .5 chance of being tails. But among the next two flips we have a more complex set of possible outcomes, i.e. TT, TH, HT, HH. So, the odds of getting a single heads in the two flips is 3/4, while the odds of getting only tails is 1/4. Am I missing something about the gamblers fallacy or does it only really apply to expectations of the initial or next result? If I'm not horribly misunderstanding the argument here, it should be clarified by linking to other articles, etc. And, I'm perfectly willing to help with clean up. — Preceding unsigned comment added by Andwats (talkcontribs) 07:21, 24 March 2012 (UTC)

BharatKulamarva is correct, the logic is circular, the thing being proved "the next toss has 50/50 chance" and the assumption "a fair coin exists and has a 50/50 chance on each toss" are the same, therefore it is question begging. Paul Laroque's example of how you can test for yourself if there exists "a fair coin" actually favours the gambler's fallacy because if you tossed a coin n times, and the result was 50/50, it doesn't need to show that each toss was 50/50 it could show that the nth toss was "due" as the gambler's fallacy tells us, and brought things back into balance. The fallacy doesn't lie in the math, but in the creation of the observed set but this is OR. The fact remains that the "proof" offered is circular and therefore worthless.

## From a gambler point of view.

The theory is true, the math its accurate but in the real world and from a gambler point of view it doesn't work exactly like that. No physical system is 100% random, A coin or dice will have infinitesimal variations in the distribution of mass, shape... A roulette table would have hundreds if not thousands of variables affecting the odds, a poker slot machine has a pseudo random number generator.... The list goes on

For instance, a very well know method to bit the odds in roulette is to expend days or even weeks on a given table writing down the numbers, after you have obtained a significant sample its only a matter of entering the data on a computer and run an statistical analysis. You will always find a deviation, the ball has a slightly bigger tendency to fall on certain area of the wheel, then you calculate your playing strategy according to those statistics, if you play smart and long enough the house looses.

Casinos of course hate this kind of thing, they will ban you if they find out what you are doing. Roulette makers spend a great deal of time fine tunning the tables in order to minimize the effect and make the system as random as possible, random generators on gambling machines use huge base lists, dices are manufactured as uniformly as possible, shapes with tolerances on the 100s of millimeters... No matter how hard they try, Physical tolerances will cause a deviation from the mathematical odds. The goal is to make those variations small enough to prevent anybody from taking advantage of them, but they will always be there. Its an intrinsic characteristics of any real physical system.

I've been banned from casinos in Europe for playing black jack in the way they like less (Never cheated) and for using this tactic playing roulette, takes time and self discipline, They've got so good at building those devices that the money earned is in the best possible scenario just enough to make a living, because all the precautions taken the deviations are really small, a mistake will set you a long way back. Roulette is not a good game for a professional gambler but the method does work if done properly.

--70.186.170.117 (talk) 13:23, 15 January 2010 (UTC) Carl - Louisiana

I don't believe you have won money on roulette using this strategy. The idea that you could find the extremely marginal tendencies of a decent roulette wheel even with years of daily study seems very unlikely, but even if you could, this tendency would not begin to approach the house advantage. The house has a 5.3% edge in roulette--this is quite significant. Obviously the wheel is not so skewed that it is six percent more likely that the ball fall into a given pocket than it should. That would be one seriously warped wheel. Besides, the amount of time you would need to invest into studying it would be enormous to get a statistically significant sample. No, if you really have won money playing roulette, you are just very lucky.
Blackjack is different, because the house edge is very small if the player makes all the right bets (as determined by computers), only about 1% for a normal pack. By counting cards, one can theoretically wait to play until the pack is rich with aces, tens, and face cards, making blackjack likely enough that the odds are actually, temporarily, in the player's favor if the player bets correctly. So in principle, one can make only extremely low bets when the deck is not in her favor, and then bet enormous sums of money when it is, therefore making money overall. However, this is not usually a viable strategy for a number of reasons. For one thing, all casinos have table maximums and minimums, so you usually cannot vary your betting enough to overcome the house edge. Furthermore, casinos that suspect players of counting cards usually kick them out, so it must be very surreptitious, meaning one cannot simply sit there betting the minimum and then suddenly start betting thousands of dollars when the deck is good. That said, a few MIT kids did manage to pull it off a few times, and they are not the only ones. So it is impossible, but rare and difficult, and not viable in many casinos.
But neither of these has anything to do with the gambler's fallacy. That fallacy has to do with the belief that, say, a roulette wheel that has spun red five times in a row is bound to spin black next, whereas what you are describing is actually the opposite (since the roulette wheel spins red so much, it must be skewed toward red), and not significant enough to affect practical betting anyway. Eebster the Great (talk) 06:27, 16 January 2010 (UTC)
I don't agree with the article. Yes, while each time you get red, it was 50% chance, but consider that for you to get 6 reds in a row, is much smaller chance, than getting 5 reds and 1 black. If you know statistics, it would be smart of you to pick black, even though the events are unrelated, the chance of getting 6 reds in a row is still much smaller. This doesn't mean that you cannot get 6 reds in a row, there is a 50% chance, so you could very well lose. It's not logical at all to assume 100% that the next one will be black, but it is more likely. Things like 20 heads in a row, are more rare than 10 heads and 10 tails interlaced. 96.231.249.80 (talk) 20:42, 15 June 2011 (UTC)
It is true that 5 reds and 1 black in some order is more likely than six reds, but that's because 5+1 can be RRRRRB, RRRRBR, RRRBRR, RRBRRR, RBRRRR, BRRRRR — each of these is exactly as likely as RRRRRR but collectively they are six times as likely. Given RRRRR_, the final sequence is either RRRRRR or RRRRRB, equally likely, and your belief to the contrary is the gambler's fallacy. —Tamfang (talk) 21:59, 15 June 2011 (UTC)
Why is it a fallacy? RRRRRB is simply more likely, than RRRRRR... There is still a 50% chance that R or B will be the 6th. But usually, objects and physics being random, and R and B having equal chance of getting picked, it seems likely that eventually a B should come up, or something is broken with the roulette table. 96.231.249.80 (talk) 04:34, 20 July 2011 (UTC)
It is not a fallacy to say that after five Rs, a B is likely to eventually come up. Actually, it's not just likely for B to eventually come up, it's 100% certain. Doesn't matter if the wheel is biased, doesn't matter what the previous spins were. The key however is the word "eventually". If you spin it ten thousand times you can bet your life that you'll get at least one B! The "gambler's fallacy" concerns whether or not B is more likely than R on a particular spin, not just "eventually". Because when a gambler bets, he is betting on a particular spin. I mean, you can't go into a casino and make a bet that "at least one of the next ten thousand spins will be B"! :-) --Steve (talk) 06:48, 20 July 2011 (UTC)
RRRRRB is not more likely than RRRRRR. To suggest otherwise is the very essence of the fallacy. It's easier to think in terms of flipping a coin: how would the coin know that heads came up five times in a row so that it should spin toward tails this time? It simply doesn't. If anything, RRRRRR is more likely than RRRRRB because a string of identical outcomes may indicate that the apparatus is not actually statistically unbiased. (However, a string of five even-chance events is not enough to suspect bias for a real coin or a professionally produced roulette wheel.) Probability is difficult to learn, and even those of us who have studied it for years have to actively suppress our cognitive biases at times. Evolution has wired the human brain to misestimate the probabilities of certain types of events. Understanding probability offers substantial benefits in our lives, so it is smart to learn from to the experts rather than saying they're wrong. The truth is sometimes unintuitive, but it's still the truth. (BTW, @Steve: I think it's fairly safe to say that nothing in the real world is actually 100% certain. However, I completely agree that it would be prudent to bet your life against the chance of 10 k sequential lands on red—provided you know that the wheel is fair and that it will remain fair. :) Gerweck (talk) 13:56, 10 August 2013 (UTC)
I think this is actually a very good point that is being raised. Gamblers do indeed practice this strategy, and it is also documented thoroughly in the statistical/mathematical literature on the subject. There are several tests for bias documented in the statistical literature. This prediction method is dealt with in the article in the section entitled "Non-example: Unknown probability of event", though this section could certainly be expanded with some more work. The paper referenced in that section explains why betting on the most common outcome is the optimal prediction method under the assumption that biases may exist in the process (and certain other plausible assumptions about this bias). SCF71 (talk) 8:26, 7 August 2010 (UTC)
This is not a good point. Roulette wheels are very precisely machined to have the least bias possible. I'll admit that it is impossible to make a wheel completely without bias. The miniscule default bias would exploitable if not for the casino edge. Beating the 2.7% edge of a single-zero wheel would require a very large bias and a very large number of trials. Wheels do gain even more bias over time, which is why casinos balance them on a daily or weekly basis. Even if the wheel is only balanced monthly and the game is dealt at a reasonable speed (40 spins/hour) for 24 hours a day AND every single spin was tracked, that's still only 28,800 spins to detect a bias. It's incredibly unlikely, even in those ideal circumstance, to detect a bias large enough to overcome the house edge. AddBlue (talk) 06:44, 17 February 2012 (UTC)

## Non-examples of the fallacy

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)

## Very first sentence false?

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)

"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)
"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)
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)

The story of the events at Monte Carlo Casino in 1913 is itself questionable. Something of this nature would surely have been reported in the press at the time, yet I have searched several online newspaper archives without finding any references to the event. — Preceding unsigned comment added by StylusGuru (talkcontribs) 15:24, 10 December 2016 (UTC)

## Inverse gambler's fallacy

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)

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)
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)

## Psychology of Gambler's Fallacy

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)

If any of you would like to see some of the edits I'm planning for this page, you can check out my sandbox here. —Preceding undated comment added 01:11, 28 March 2012 (UTC).

## GA Review

This review is transcluded from Talk:Gambler's fallacy/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: LauraHale (talk · contribs) 08:39, 27 April 2012 (UTC)

This article was correctly assessed as a start. Huge tracts of it are not cited. The sources violate WP:MEDRS. The nominator made only four edits to the article, which did NOT address the GA criteria and violated WP:MEDRS. See this edit. It is clear the nominator was not familiar with or concerned with criteria at time of nomination and subsequently has not been interested because no work towards those criteria. Demonstrated they are not interested in meeting criteria but meeting criteria. See Template:Did you know nominations/Gambler's fallacy where they failed to respond to issues. Suggest no one will bother to bring it up to GAN and I can't see this being done in a week. --LauraHale (talk) 08:39, 27 April 2012 (UTC)

## philosophical point of view

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)

## Childbirth

"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)

## Merge law of averages into this article

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)

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)

## Preaching to the choir

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)

## What if...

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)

OK, after a bit of thinking I got where I went wrong. The "unlikely" part has already happened. And while it could in principle get even unlikelier, it is divided from that further improbability by a small step of 1/2. Ignore the previous stuff :-)89.12.84.0 (talk) 16:20, 12 October 2013 (UTC)

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)

## False example for retrospective gambler's fallacy.

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)

I'm not sure how pregnancy is relevant to the fallacy either. From what the article is describing, the fallacy occurs when a previous event is perceived to have an impact on the outcome of the next event. Pregnancy doesn't work this way. Having unprotected sex multiple times increases chances of pregnancy because 'you're buying more tickets' but also increases the chances of each individual attempt. Recalling from old lecture slides in university, the chance of pregnancy from an isolated case of unprotected sex is around 10%, however if you have unprotected sex each day for 30 days for example, the chances for each individual case goes up to 40% at least — Preceding unsigned comment added by Etceteralol (talkcontribs) 23:44, 3 August 2014 (UTC)

## Recent Paper Supports the Gambler's Fallacy as Fact

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 (talkcontribs) 08:50, 26 October 2015 (UTC)

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)
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)

────────────────────────────────────────────────────────────────────────────────────────────────────While an interesting way to summarize the experiment, you are correct to say the possible proportions are: {0, ½, 1}

But the probabilities are: {3/8, 2/8, 2/8}

not {3/6, 1/6, 2/6}

The expected value, of course, is:

0*3/8+ .5*2/8+1 *2/8= 0+.25+.25= .50

Exactly as one might expect.--S Philbrick(Talk) 15:48, 23 January 2018 (UTC)

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)

## Monte Carlo Casino example

Jonah Lehrer’s How We Decide is no longer available, as it was pulled by the publisher in March 2013.[1] 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)