Talk:Gambler's fallacy

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 (talk • contribs) 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 (talk • contribs) 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)

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)

circular logic

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

consider "Explaining why the probability is $\scriptstyle {\frac {1}{2}}$ 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 (talk • contribs) 07:21, 24 March 2012 (UTC)

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)

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.

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)

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)