1160:, in which people tend to predict the same outcome as the previous event - known as positive recency - resulting in a belief that a high scorer will continue to score. In the gambler's fallacy, people predict the opposite outcome of the previous event - negative recency - believing that since the roulette wheel has landed on black on the previous six occasions, it is due to land on red the next. Ayton and Fischer have theorized that people display positive recency for the hot-hand fallacy because the fallacy deals with human performance, and that people do not believe that an inanimate object can become "hot." Human performance is not perceived as random, and people are more likely to continue streaks when they believe that the process generating the results is nonrandom. When a person exhibits the gambler's fallacy, they are more likely to exhibit the hot-hand fallacy as well, suggesting that one construct is responsible for the two fallacies.
1111:, which states that people evaluate the probability of a certain event by assessing how similar it is to events they have experienced before, and how similar the events surrounding those two processes are. According to this view, "after observing a long run of red on the roulette wheel, for example, most people erroneously believe that black will result in a more representative sequence than the occurrence of an additional red", so people expect that a short run of random outcomes should share properties of a longer run, specifically in that deviations from average should balance out. When people are asked to make up a random-looking sequence of coin tosses, they tend to make sequences where the proportion of heads to tails stays closer to 0.5 in any short segment than would be predicted by chance, a phenomenon known as
1164:
outcome of a series of coin tosses, use an expert opinion to sway their decision, or choose a risk-free alternative instead for a smaller financial reward. Participants turned to the expert opinion to make their decision 24% of the time based on their past experience of success, which exemplifies the hot-hand. If the expert was correct, 78% of the participants chose the expert's opinion again, as opposed to 57% doing so when the expert was wrong. The participants also exhibited the gambler's fallacy, with their selection of either heads or tails decreasing after noticing a streak of either outcome. This experiment helped bolster Ayton and
Fischer's theory that people put more faith in human performance than they do in seemingly random processes.
1254:
prior education regarding probability. The question asked was: "Ronni flipped a coin three times and in all cases heads came up. Ronni intends to flip the coin again. What is the chance of getting heads the fourth time?" The results indicated that as the students got older, the less likely they were to answer with "smaller than the chance of getting tails", which would indicate a negative recency effect. 35% of the 5th graders, 35% of the 7th graders, and 20% of the 9th graders exhibited the negative recency effect. Only 10% of the 11th graders answered this way, and none of the college students did. Fischbein and
Schnarch theorized that an individual's tendency to rely on the
1139:
as defined by Gideon Keren and
Charles Lewis, occurs when a gambler underestimates how many observations are needed to detect a favorable outcome, such as watching a roulette wheel for a length of time and then betting on the numbers that appear most often. For events with a high degree of randomness, detecting a bias that will lead to a favorable outcome takes an impractically large amount of time and is very difficult, if not impossible, to do. The two types differ in that type one wrongly assumes that gambling conditions are fair and perfect, while type two assumes that the conditions are biased, and that this bias can be detected after a certain amount of time.
1270:
end of one block, or the beginning of the next block. Participants exhibited the strongest gambler's fallacy when the seventh trial was part of the first block, directly after the sequence of three heads or tails. The researchers pointed out that the participants that did not show the gambler's fallacy showed less confidence in their bets and bet fewer times than the participants who picked with the gambler's fallacy. When the seventh trial was grouped with the second block, and was perceived as not being part of a streak, the gambler's fallacy did not occur.
879:
same at the end of each month, they judged that the boys already born would render more probable the births next of girls." The expectant fathers feared that if more sons were born in the surrounding community, then they themselves would be more likely to have a daughter. This essay by
Laplace is regarded as one of the earliest descriptions of the fallacy. Likewise, after having multiple children of the same sex, some parents may erroneously believe that they are due to have a child of the opposite sex.
1338:
479:. After the first four tosses in this example, the results are no longer unknown, so their probabilities are at that point equal to 1 (100%). The probability of a run of coin tosses of any length continuing for one more toss is always 0.5. The reasoning that a fifth toss is more likely to be tails because the previous four tosses were heads, with a run of luck in the past influencing the odds in the future, forms the basis of the fallacy.
855:
arguing that the occurrence of our universe says nothing about the existence of other universes or trials of universes. Three studies involving
Stanford University students tested the existence of a retrospective gamblers' fallacy. All three studies concluded that people have a gamblers' fallacy retrospectively as well as to future events. The authors of all three studies concluded their findings have significant "
3740:
741:
515:
other combinations that can be obtained from 21 flips of a coin. All of the 21-flip combinations will have probabilities equal to 0.5, 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. In accordance with
1329:, it can be argued that monetary incentives are a key factor in biased decision making, rendering it harder to examine the gambler's fallacy effect. However, research shows that loan officers who are not incentivised by monetary gain are 8% less likely to approve a loan if they approved one for the previous client.
1043:(meaning that the random process from which the outcomes are generated may be biased but is equally likely to be biased in any direction) and that previous observations demonstrate the likely direction of the bias, the outcome which has occurred the most in the observed data is the most likely to occur again.
1592:
high-rarity item, subsequent loot boxes will improve the odds of a higher-rate item drop. This is considered to feed into the gambler's fallacy since it reinforces the idea that a player will eventually obtain a high-rarity item (a win) after only receiving common items from a string of previous loot boxes.
305:(one in thirty-two), a person might believe that the next flip would be more likely to come up tails rather than heads again. This is incorrect and is an example of the gambler's fallacy. The event "5 heads in a row" and the event "first 4 heads, then a tails" are equally likely, each having probability
1249:
was not given this information. The response styles of the two groups were similar, indicating that the experimental group still based their choices on the length of the run sequence. This led to the conclusion that instructing individuals about randomness is not sufficient in lessening the gambler's
878:
the ways in which men calculated their probability of having sons: "I have seen men, ardently desirous of having a son, who could learn only with anxiety of the births of boys in the month when they expected to become fathers. Imagining that the ratio of these births to those of girls ought to be the
1360:
lottery in which, a number selected with lower total wagers placed on it will result in a higher pay-out. While this examination did conclude that players in both types of lotteries exhibited behaviour in-line with the gambler's fallacy theory, those who took part in pari-mutuel betting seemed to be
1341:
The effect of gambler's fallacy on lottery selections, based on studies by Dek
Terrell. After winning numbers are drawn, lottery players respond by reducing the number of times they select those numbers in following draws. This effect slowly corrects over time, as players become less affected by the
1273:
Roney and Trick argued that instead of teaching individuals about the nature of randomness, the fallacy could be avoided by training people to treat each event as if it is a beginning and not a continuation of previous events. They suggested that this would prevent people from gambling when they are
1240:
The gambler's fallacy is a deep-seated cognitive bias and can be very hard to overcome. Educating individuals about the nature of randomness has not always proven effective in reducing or eliminating any manifestation of the fallacy. Participants in a study by Beach and
Swensson in 1967 were shown a
1163:
The difference between the two fallacies is also found in economic decision-making. A study by Huber, Kirchler, and Stockl in 2010 examined how the hot hand and the gambler's fallacy are exhibited in the financial market. The researchers gave their participants a choice: they could either bet on the
1591:
scheme. Since around 2018, loot boxes have come under scrutiny from governments and advocates on the basis they are akin to gambling, particularly for games aimed at youth. Some games use a special "pity-timer" mechanism, that if the player has opened several loot boxes in a row without obtaining a
1355:
investigated this effect in 1991, where they concluded bettors would cease to select numbers immediately after they were selected, ultimately recovering selection popularity within three months. Soon after, a 1994 study was constructed by Dek
Terrell to test the findings of Clotfelter and Cook. The
1138:
Some researchers believe that it is possible to define two types of gambler's fallacy: type one and type two. Type one is the classic gambler's fallacy, where individuals believe that a particular outcome is due after a long streak of another outcome. Type two gambler's fallacy,
1026:
In most illustrations of the gambler's fallacy and the reverse gambler's fallacy, the trial (e.g. flipping a coin) is assumed to be fair. In practice, this assumption may not hold. For example, if a coin is flipped 21 times, the probability of 21 heads with a fair coin is 1 in 2,097,152. Since this
805:
conclusion, bearing in mind the possibility that the coin may not be fair; it is not a fallacy. Believing the odds to favor tails, the gambler sees no reason to change to heads. However it is a fallacy that a sequence of trials carries a memory of past results which tend to favor or disfavor future
1269:
Roney and Trick told participants in their experiment that they were betting on either two blocks of six coin tosses, or on two blocks of seven coin tosses. The fourth, fifth, and sixth tosses all had the same outcome, either three heads or three tails. The seventh toss was grouped with either the
1253:
An individual's susceptibility to the gambler's fallacy may decrease with age. A study by
Fischbein and Schnarch in 1997 administered a questionnaire to five groups: students in grades 5, 7, 9, 11, and college students specializing in teaching mathematics. None of the participants had received any
1073:
If external factors are allowed to change the probability of the events, the gambler's fallacy may not hold. For example, a change in the game rules might favour one player over the other, improving his or her win percentage. Similarly, an inexperienced player's success may decrease after opposing
1142:
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. The belief that an imaginary sequence of die rolls is more than three times as long when a set of three sixes is
854:
and Benoît Monin argue that "In other words, the 'best explanation' for a low-probability event is that it is only one in a multiple of trials, which is the core intuition of the reverse gambler's fallacy." Philosophical arguments are ongoing about whether such arguments are or are not a fallacy,
1265:
psychologists who suggest that the fallacy may be eliminated as a result of grouping. When a future event such as a coin toss is described as part of a sequence, no matter how arbitrarily, a person will automatically consider the event as it relates to the past events, resulting in the gambler's
833:
An example of a retrospective gambler's fallacy would be to observe multiple successive "heads" on a coin toss and conclude from this that the previously unknown flip was "tails". Real world examples of retrospective gambler's fallacy have been argued to exist in events such as the origin of the
514:
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. 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
1346:
Lottery play and jackpots entice gamblers around the globe, with the biggest decision for hopeful winners being what numbers to pick. While most people will have their own strategy, evidence shows that after a number is selected as a winner in the current draw, the same number will experience a
1570:
The effect the of gambler's fallacy can be observed as numbers are chosen far less frequently soon after they are selected as winners, recovering slowly over a two-month period. For example, on the 11th of April 1988, 41 players selected 244 as the winning combination. Three days later only 24
706:
By losing one toss, the player's probability of winning drops by two percentage points. With 5 losses and 11 rolls remaining, the probability of winning drops to around 0.5 (50%). The probability of at least one win does not increase after a series of losses; indeed, the probability of success
1147:
and becomes pregnant on a given night, and concluding that she has been engaging in unprotected sex for longer than if we hear she had unprotected sex but did not become pregnant, when the probability of becoming pregnant as a result of each intercourse is independent of the amount of prior
859:
implications" but may also have "important theoretical implications" that need investigation and research, saying " thorough understanding of such reasoning processes requires that we not only examine how they influence our predictions of the future, but also our perceptions of the past."
915:
or around 1 in 66.6 million, assuming the mechanism is unbiased. Gamblers lost millions of francs betting against black, reasoning incorrectly that the streak was causing an imbalance in the randomness of the wheel, and that it had to be followed by a long streak of red.
1296:
In a study aimed at discovering if the negative autocorrelation that exists with the gambler's fallacy existed in the decision made by U.S. asylum judges, results showed that after two successive asylum grants, a judge would be 5.5% less likely to approve a third grant.
817:
is a situation where a gambler entering a room and seeing a person rolling a double six on a pair of dice may erroneously conclude that the person must have been rolling the dice for quite a while, as they would be unlikely to get a double six on their first attempt.
453:
283:
941:
is drawn from a deck and not reinserted, the next card drawn is less likely to be an ace and more likely to be of another rank. The probability of drawing another ace, assuming that it was the first card drawn and that there are no
1287:
Within a real-world setting, numerous studies have uncovered that for various decision makers placed in high stakes scenarios, it is likely they will reflect some degree of strong negative autocorrelation in their judgement.
1115:. Kahneman and Tversky interpret this to mean that people believe short sequences of random events should be representative of longer ones. The representativeness heuristic is also cited behind the related phenomenon of the
1571:
individuals selected 244, a 41.5% decrease. This is the gambler's fallacy in motion, as lottery players believe that the occurrence of a winning combination in previous days will decrease its likelihood of occurring today.
1317:. If outside of this zone, the ball does not count towards outing the batter. In a study of over 12,000 games, results showed that umpires are 1.3% less likely to call a strike if the previous two balls were also strikes.
1204:
with gambler's fallacy, so that the more activity exhibited in the amygdala, the less likely an individual is to fall prey to the gambler's fallacy. These results suggest that gambler's fallacy relies more on the
1130:. When a person believes that gambling outcomes are the result of their own skill, they may be more susceptible to the gambler's fallacy because they reject the idea that chance could overcome skill or talent.
543:
The fallacy leads to the incorrect notion that previous failures will create an increased probability of success on subsequent attempts. For a fair 16-sided die, the probability of each outcome occurring is
1052:
probability of a biased coin is say 1%, and assuming that such a biased coin would come down heads say 60% of the time, then after 21 heads the probability of a biased coin has increased to about 32%.
895:
on August 18, 1913, when the ball fell in black 26 times in a row. This was an extremely unlikely occurrence: the probability of a sequence of either red or black occurring 26 times in a row is
1091:, leading to the erroneous belief that small samples must be representative of the larger population. According to the fallacy, streaks must eventually even out in order to be representative.
1039:— 21 heads in a row — suggests that the coin is likely to be biased toward heads. Bayesian inference can be used to show that when the long-run proportion of different outcomes is unknown but
1313:
which is often subject to scrutiny is the 'strike zone' decision. Whenever a batter does not swing, the umpire must decide if the ball was within a fair region for the batter, known as the
1224:, which supports a choice-outcome contingency learning method. The striatum processes the errors in prediction and the behavior changes accordingly. After a win, the positive behavior is
1122:
The gambler's fallacy can also be attributed to the mistaken belief that gambling, or even chance itself, is a fair process that can correct itself in the event of streaks, known as the
289:
If after tossing four heads in a row, the next coin toss also came up heads, it would complete a run of five successive heads. Since the probability of a run of five successive heads is
1143:
observed as opposed to when there are only two sixes. This effect can be observed in isolated instances, or even sequentially. Another example would involve hearing that a teenager has
32:
701:
620:
327:
1245:
of participants was informed about the nature and existence of the gambler's fallacy, and were explicitly instructed not to rely on run dependency to make their guesses. The
1232:
to be avoided. In individuals exhibiting the gambler's fallacy, this choice-outcome contingency method is impaired, and they continue to make risks after a series of losses.
1119:, according to which people see streaks of random events as being non-random when such streaks are actually much more likely to occur in small samples than people expect.
164:
487:
If a fair coin is flipped 21 times, the probability of 21 heads is 1 in 2,097,152. The probability of flipping a head after having already flipped 20 heads in a row is
2857:
711:, because there are fewer trials left in which to win. The probability of winning will eventually be equal to the probability of winning a single toss, which is
2862:
641:(93.75%). According to the fallacy, the player should have a higher chance of winning after one loss has occurred. The probability of at least one win is now:
1104:
43:, where it may be believed, for example, that the next dice roll is more than usually likely to be six because there have recently been fewer than the
72:
1711:
Oppenheimer, D.M., & Monin, B. (2009). The retrospective gambler’s fallacy: Unlikely events, constructing the past, and multiple universes.
1804:
874:
2072:
1838:
1181:
1057:
762:
3240:
801:
After a consistent tendency towards tails, a gambler may also decide that tails has become a more likely outcome. This is a rational and
2897:
2739:
830:
exists for inferences about unknown past events based upon known subsequent events, calling this the "retrospective gambler's fallacy".
1031:
towards landing on heads, or that it is being controlled by hidden magnets, or similar. In this case, the smart bet is "heads" because
3051:
1738:
Hacking, I (1987). "The inverse gambler's fallacy: The argument from design. The anthropic principle applied to
Wheeler universes".
788:
1176:
and other cognitive biases are the most commonly cited cause of the gambler's fallacy, research suggests that there may also be a
850:
very different in their characters might be our best explanation for why at least one universe has a life-permitting character".
2349:
Huber, J.; Kirchler, M.; Stockl, T. (2010). "The hot hand belief and the gambler's fallacy in investment decisions under risk".
1241:
shuffled deck of index cards with shapes on them, and were instructed to guess which shape would come next in a sequence. The
3779:
1274:
losing, in the mistaken hope that their chances of winning are due to increase based on an interaction with previous events.
766:
3789:
3774:
3659:
2867:
1952:
1931:
1040:
933:. In such cases, the probability of future events can change based on the outcome of past events, such as the statistical
3794:
3695:
3671:
3260:
1617:
1255:
1242:
1173:
1112:
1108:
810:
2503:
Roney, C. J.; Trick, L. M. (2003). "Grouping and gambling: A gestalt approach to understanding the gambler's fallacy".
3764:
3272:
3016:
1632:
751:
3784:
3282:
1652:
1188:
of the brain is activated, resulting in more risk-taking behavior. In contrast, there is decreased activity in the
847:
35:) has occurred less frequently than expected, it is more likely to happen again in the future (or vice versa). The
770:
755:
3799:
3769:
3690:
3247:
3143:
2468:
Fischbein, E.; Schnarch, D. (1997). "The evolution with age of probabilistic, intuitively based misconceptions".
2433:
Beach, L. R.; Swensson, R. G. (1967). "Instructions about randomness and run dependency in two-choice learning".
1127:
1065:
discusses these issues as one man continually flips heads and the other considers various possible explanations.
1048:
92:
2543:"Decision-Making Under the Gambler's Fallacy: Evidence from Asylum Judges, Loan Officers, and Baseball Umpires*"
448:{\displaystyle \Pr \left(A_{5}|A_{1}\cap A_{2}\cap A_{3}\cap A_{4}\right)=\Pr \left(A_{5}\right)={\frac {1}{2}}}
3685:
3525:
2993:
2829:
2785:
2689:
1637:
1156:
Another psychological perspective states that gambler's fallacy can be seen as the counterpart to basketball's
930:
647:
566:
3705:
3520:
3036:
2732:
1588:
560:(6.25%). If a win is defined as rolling a 1, the probability of a 1 occurring at least once in 16 rolls is:
3627:
3617:
3567:
3541:
3317:
3191:
3158:
3059:
3041:
2941:
2790:
2772:
1913:
1657:
1602:
1185:
3665:
3653:
3633:
3622:
3537:
3350:
3326:
3148:
3104:
2956:
2882:
2795:
1348:
1123:
851:
1685:
1337:
2584:"Incentivizing Calculated Risk-Taking: Evidence from an Experiment with Commercial Bank Loan Officers"
3680:
3584:
3548:
3463:
3419:
3186:
2976:
2805:
2780:
2220:"The retrospective gambler's fallacy: Unlikely events, constructing the past, and multiple universes"
1964:
1607:
1229:
1201:
1088:
943:
869:
2685:"Gaming the System: Suboptimal Compliance with Loot Box Probability Disclosure Regulations in China"
1918:
1793:
1587:, a collection of in-game items awarded on opening with random contents set by rarity metrics, as a
1126:. Other researchers believe that belief in the fallacy may be the result of a mistaken belief in an
3558:
3457:
3404:
3380:
3303:
3206:
3138:
3064:
2877:
2872:
2849:
2824:
1365:
Table 1. Percentage change in numbers selected by lottery players based on Clotfelter, Cook (1991)
1214:
1210:
1116:
802:
278:{\displaystyle \Pr \left(\bigcap _{i=1}^{n}A_{i}\right)=\prod _{i=1}^{n}\Pr(A_{i})={1 \over 2^{n}}}
3743:
3676:
3490:
3375:
3360:
3307:
3267:
3216:
3153:
3112:
3089:
3069:
2972:
2816:
2800:
2725:
2704:
2485:
2366:
2241:
2165:
2121:
2064:
1988:
1357:
1266:
fallacy. When a person considers every event as independent, the fallacy can be greatly reduced.
1262:
1036:
1032:
892:
55:
2386:"An fMRI study of risk-taking following wins and losses: Implications for the gambler's fallacy"
475:= 0.03125 (a little over 3%), the misunderstanding lies in not realizing that this is the case
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3399:
3389:
3365:
3342:
3298:
3224:
3176:
3134:
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2936:
2931:
2753:
2647:
2564:
2520:
2450:
2415:
2331:
2323:
2282:
2200:
2113:
2105:
2068:
2034:
1980:
1874:
1834:
1612:
1206:
1028:
516:
321:. Since the first four tosses turn up heads, the probability that the next toss is a head is:
1830:
3712:
3553:
3452:
3394:
3332:
3127:
3006:
3001:
2986:
2951:
2911:
2839:
2834:
2694:
2639:
2603:
2595:
2554:
2512:
2477:
2442:
2405:
2397:
2358:
2313:
2272:
2231:
2192:
2155:
2097:
2026:
1972:
1923:
1774:
1747:
1662:
1647:
1622:
1197:
1157:
71:
2183:
Keren, Gideon; Lewis, Charles (1994). "The Two Fallacies of Gamblers: Type I and Type II".
2088:
Rogers, Paul (1998). "The cognitive psychology of lottery gambling: A theoretical review".
50:
The term "Monte Carlo fallacy" originates from an example of the phenomenon, in which the
3433:
3409:
3229:
3201:
3181:
3029:
2997:
2981:
2052:
1627:
1193:
1144:
1096:
3469:
2946:
2057:
16:
Mistaken belief that more frequent chance events will lead to less frequent chance events
1968:
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3277:
3196:
3122:
2762:
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1642:
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1100:
843:
44:
1074:
teams learn about and play against their weaknesses. This is another example of bias.
3758:
3495:
3385:
3117:
3080:
3024:
2892:
2887:
2708:
2668:
Clotfelter, Charles; Cook, Philip (1991). "The "Gambler's Fallacy" in lottery play".
2643:
2583:
2370:
2261:"The hot-hand fallacy and the gambler's fallacy: Two faces of subjective randomness?"
1992:
1823:
1246:
1225:
1011:
937:
of events. An example is when cards are drawn from a deck without replacement. If an
929:
The gambler's fallacy does not apply when the probability of different events is not
2245:
2125:
3507:
2926:
2169:
1326:
1092:
1062:
2627:
2017:
Tune, G. S. (1964). "Response preferences: A review of some relevant literature".
1976:
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3414:
1751:
1314:
1027:
probability is so small, if it happens, it may well be that the coin is somehow
934:
856:
814:
740:
519:, the likely outcome of each flip is the probability of the fair coin, which is
80:
2302:"Randomness and inductions from streaks: "Gambler's fallacy" versus "hot hand""
1996:
87:
The gambler's fallacy can be illustrated by considering the repeated toss of a
3610:
3604:
3531:
3443:
2683:
Xiao, Leon Y.; Henderson, Laura L.; Yang, Yuhan; Newall, Philip W. S. (2021).
2362:
2236:
2219:
2160:
2143:
2101:
1865:
O'Neill, B.; Puza, B.D. (2005). "In defence of the reverse gambler's belief".
1580:
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2109:
1898:
1878:
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3501:
3485:
3168:
1861:"Dice have no memories but I do: A defence of the reverse gambler's belief".
1778:
1347:
significant drop in selections in the following lottery. A popular study by
1177:
1015:
155:
127:(one in four) and the probability of getting three heads in three tosses is
88:
3647:
2524:
2419:
2335:
2286:
2196:
2117:
2038:
1984:
2717:
2454:
3595:
2559:
2542:
1584:
1306:
1221:
1189:
888:
835:
51:
40:
2699:
2684:
2749:
2608:
2599:
2318:
2301:
2277:
2260:
36:
2489:
2401:
978:(5.88%), while the probability for each other rank has increased from
2516:
2446:
2030:
1927:
1310:
1213:, goal-directed processes, and less on the brain areas that control
1184:
has shown that after losing a bet or gamble, known as riskloss, the
111:(one in two). The probability of getting two heads in two tosses is
2481:
1860:
1309:, decisions are made every minute. One particular decision made by
2628:"A test of the gambler's fallacy: evidence from pari-mutuel games"
2144:"Biases in casino betting: The hot hand and the gambler's fallacy"
1336:
76:
70:
1220:
The desire to continue gambling or betting is controlled by the
827:
2721:
2541:
Chen, Daniel; Moskowitz, Tobias J.; Shue, Kelly (2016-03-24).
938:
734:
510:
The probability of 20 heads, then 1 head is 0.5 × 0.5 = 0.5
507:
The probability of 20 heads, then 1 tail is 0.5 × 0.5 = 0.5
887:
An example of the gambler's fallacy occurred in a game of
95:
and the probability of getting heads on a single toss is
31:, is the belief that, if an event (whose occurrences are
1765:
White, R (2000). "Fine-tuning and multiple universes".
1356:
key change in Terrell's study was the examination of a
1946:
1944:
1261:
Another possible solution comes from Roney and Trick,
1892:
1890:
1888:
1258:
and other cognitive biases can be overcome with age.
650:
569:
330:
167:
2185:
Organizational Behavior and Human Decision Processes
2137:
2135:
3594:
3582:
3441:
3432:
3341:
3316:
3291:
3215:
3167:
3103:
3078:
3050:
3015:
2965:
2919:
2910:
2848:
2814:
2770:
2761:
2384:Xue, G.; Lu, Z.; Levin, I. P.; Bechara, A. (2011).
1953:"Judgment under uncertainty: Heuristics and biases"
1549:Average percentage of players selecting previously
2056:
1822:
1087:The gambler's fallacy arises out of a belief in a
695:
614:
447:
277:
79:of red/blue coin tosses approaches 50-50, but the
2582:Cole, Shawn; Kanz, Martin; Kapper, Leora (2015).
1794:"The role of experience in the Gambler's Fallacy"
1792:Barron, Greg; Leider, Stephen (13 October 2009).
1200:after a riskloss. Activation in the amygdala is
411:
331:
236:
168:
1707:
1705:
1703:
1701:
1699:
1099:first proposed that the gambler's fallacy is a
727:(6.25%) and occurs when only one toss is left.
625:The probability of a loss on the first roll is
459:While a run of five heads has a probability of
54:wheel spun black 26 times in succession at the
2858:Affirmative conclusion from a negative premise
2863:Negative conclusion from affirmative premises
2733:
2470:Journal for Research in Mathematics Education
1680:
1678:
8:
1713:Judgment and Decision Making, vol. 4, no. 5,
826:Researchers have examined whether a similar
2505:Canadian Journal of Experimental Psychology
769:. Unsourced material may be challenged and
3591:
3438:
3313:
2916:
2767:
2740:
2726:
2718:
483:Why the probability is 1/2 for a fair coin
2698:
2607:
2558:
2409:
2317:
2276:
2235:
2159:
1917:
789:Learn how and when to remove this message
686:
682:
676:
662:
649:
605:
601:
595:
581:
568:
435:
422:
397:
384:
371:
358:
349:
343:
329:
267:
258:
246:
230:
219:
201:
191:
180:
166:
1551:winning numbers compared to day of draw
1363:
696:{\displaystyle 1-\left^{15}\,=\,62.02\%}
615:{\displaystyle 1-\left^{16}\,=\,64.39\%}
2300:Burns, Bruce D.; Corpus, Bryan (2004).
1951:Tversky, Amos; Daniel Kahneman (1974).
1897:Tversky, Amos; Daniel Kahneman (1971).
1829:. Courier Dover Publications. pp.
1674:
91:. The outcomes in different tosses are
33:independent and identically distributed
2218:Oppenheimer, D. M.; Monin, B. (2009).
875:A Philosophical Essay on Probabilities
2663:
2661:
2621:
2619:
2536:
2534:
2063:. New York: The Free Press. pp.
1801:Journal of Behavioral Decision Making
1182:Functional magnetic resonance imaging
1058:Rosencrantz and Guildenstern Are Dead
83:decreases to zero non-systematically.
7:
2670:National Bureau of Economic Research
2632:Insurance: Mathematics and Economics
1899:"Belief in the law of small numbers"
846:argues that "the presence of vastly
767:adding citations to reliable sources
477:only before the first coin is tossed
2547:The Quarterly Journal of Economics
2435:Journal of Experimental Psychology
1228:and after a loss, the behavior is
690:
609:
29:fallacy of the maturity of chances
14:
2306:Psychonomic Bulletin & Review
1825:Entertaining Mathematical Puzzles
1014:systems to work in games such as
3739:
3738:
2142:Sundali, J.; Croson, R. (2006).
1937:from the original on 2017-07-06.
1859:O'Neill, B.; Puza, B.D. (2004).
1810:from the original on 2011-03-22.
1152:Relationship to hot-hand fallacy
739:
2259:Ayton, P.; Fischer, I. (2004).
1863:Reprinted in abridged form as:
1372:Amount bet by lottery players
822:Retrospective gambler's fallacy
143:(one in eight). In general, if
3236:Correlation implies causation
1055:The opening scene of the play
350:
252:
239:
1:
2626:Terrell, Dek (October 1994).
1977:10.1126/science.185.4157.1124
2644:10.1016/0167-6687(94)90729-3
2224:Judgment and Decision Making
2148:Judgment and Decision Making
1686:"Why we gamble like monkeys"
1377:Numbers drawn 14 April 1988
1256:representativeness heuristic
1174:representativeness heuristic
1113:insensitivity to sample size
1109:representativeness heuristic
1010:(7.84%). This effect allows
39:is commonly associated with
2090:Journal of Gambling Studies
1633:Martingale (betting system)
1209:, which is responsible for
3816:
3660:I'm entitled to my opinion
1867:The Mathematical Scientist
1653:Regression toward the mean
1325:In the decision making of
3734:
3643:
3516:
2690:Behavioural Public Policy
2363:10.1007/s11238-008-9106-2
2237:10.1017/S1930297500001170
2161:10.1017/S1930297500000309
2059:How we know what isn't so
1752:10.1093/mind/xcvi.383.331
1618:Inverse gambler's fallacy
1548:
1382:
1376:
1371:
1369:
1128:internal locus of control
811:inverse gambler's fallacy
93:statistically independent
3686:Motte-and-bailey fallacy
2786:Affirming the consequent
1821:Gardner, Martin (1986).
1638:Mean reversion (finance)
503:. Assuming a fair coin:
150:is the event where toss
3706:Two wrongs make a right
3037:Denying the correlative
2102:10.1023/A:1023042708217
1779:10.1111/0029-4624.00210
1105:psychological heuristic
821:
3691:Psychologist's fallacy
3628:Argument to moderation
3618:Argument from anecdote
3568:Chronological snobbery
3192:Quoting out of context
3159:Overwhelming exception
3042:Suppressed correlative
2942:Quoting out of context
2817:quantificational logic
2791:Denying the antecedent
2197:10.1006/obhd.1994.1075
2019:Psychological Bulletin
1906:Psychological Bulletin
1658:Statistical regularity
1603:Availability heuristic
1343:
1186:frontoparietal network
1069:Changing probabilities
925:Non-independent events
697:
616:
449:
279:
235:
196:
158:comes up heads, then:
84:
3780:Statistical paradoxes
3654:The Four Great Errors
3634:Argumentum ad populum
3623:Argument from silence
3327:Argumentum ad baculum
3105:Faulty generalization
2796:Argument from fallacy
1340:
1202:negatively correlated
1124:just-world hypothesis
946:, has decreased from
852:Daniel M. Oppenheimer
698:
617:
450:
280:
215:
176:
74:
3790:Gambling mathematics
3775:Gambling terminology
3672:Invincible ignorance
3478:Reductio ad Stalinum
3464:Reductio ad Hitlerum
3420:Wisdom of repugnance
3187:Moving the goalposts
3052:Illicit transference
2977:Begging the question
2898:Undistributed middle
2806:Mathematical fallacy
2781:Affirming a disjunct
2265:Memory and Cognition
1728:. London: Routledge.
1089:law of small numbers
1046:For example, if the
870:Pierre-Simon Laplace
763:improve this section
648:
567:
328:
165:
23:, also known as the
3795:Relevance fallacies
3405:Parade of horribles
3381:In-group favoritism
3207:Syntactic ambiguity
2850:Syllogistic fallacy
2773:propositional logic
2700:10.1017/bpp.2021.23
2390:Human Brain Mapping
2351:Theory and Decision
1969:1974Sci...185.1124T
1963:(4157): 1124–1131.
1724:Leslie, J. (1989).
1583:feature the use of
1366:
1117:clustering illusion
25:Monte Carlo fallacy
3765:Behavioral finance
3491:Poisoning the well
3308:Proof by assertion
3283:Texas sharpshooter
3217:Questionable cause
3154:Slothful induction
3113:Anecdotal evidence
2973:Circular reasoning
2868:Exclusive premises
2830:Illicit conversion
2600:10.1111/jofi.12233
2588:Journal of Finance
2560:10.1093/qje/qjw017
2319:10.3758/BF03206480
2278:10.3758/bf03206327
1575:Video game players
1364:
1349:Charles Clotfelter
1344:
1243:experimental group
1236:Possible solutions
1037:empirical evidence
1033:Bayesian inference
893:Monte Carlo Casino
883:Monte Carlo Casino
709:actually decreases
693:
612:
445:
275:
85:
56:Monte Carlo Casino
3785:Cognitive inertia
3752:
3751:
3730:
3729:
3726:
3725:
3666:Ignoratio elenchi
3578:
3577:
3428:
3427:
3390:Not invented here
3095:Converse accident
3017:Correlative-based
2994:Compound question
2937:False attribution
2932:False equivalence
2906:
2905:
2402:10.1002/hbm.21015
2074:978-0-02-911706-4
1840:978-0-486-25211-7
1608:Gambler's conceit
1568:
1567:
1361:less influenced.
1217:decision-making.
1207:prefrontal cortex
799:
798:
791:
670:
589:
443:
273:
47:number of sixes.
21:gambler's fallacy
3807:
3800:Cognitive biases
3770:Causal fallacies
3742:
3741:
3713:Special pleading
3592:
3453:Appeal to motive
3439:
3415:Stirring symbols
3395:Island mentality
3333:Wishful thinking
3314:
3030:Perfect solution
3007:No true Scotsman
3002:Complex question
2987:Leading question
2966:Question-begging
2952:No true Scotsman
2917:
2840:Quantifier shift
2835:Proof by example
2768:
2742:
2735:
2728:
2719:
2713:
2712:
2702:
2680:
2674:
2673:
2665:
2656:
2655:
2623:
2614:
2613:
2611:
2579:
2573:
2572:
2562:
2553:(3): 1181–1242.
2538:
2529:
2528:
2517:10.1037/h0087414
2500:
2494:
2493:
2465:
2459:
2458:
2447:10.1037/h0024979
2430:
2424:
2423:
2413:
2381:
2375:
2374:
2346:
2340:
2339:
2321:
2297:
2291:
2290:
2280:
2271:(8): 1369–1378.
2256:
2250:
2249:
2239:
2215:
2209:
2208:
2180:
2174:
2173:
2163:
2139:
2130:
2129:
2085:
2079:
2078:
2062:
2053:Gilovich, Thomas
2049:
2043:
2042:
2031:10.1037/h0048618
2014:
2008:
2007:
2005:
2004:
1995:. Archived from
1948:
1939:
1938:
1936:
1928:10.1037/h0031322
1921:
1903:
1894:
1883:
1882:
1857:
1851:
1850:
1848:
1847:
1828:
1818:
1812:
1811:
1809:
1798:
1789:
1783:
1782:
1762:
1756:
1755:
1746:(383): 331–340.
1735:
1729:
1722:
1716:
1709:
1694:
1693:
1682:
1663:Problem gambling
1623:Hot hand fallacy
1383:Days after draw
1367:
1301:Baseball umpires
1198:ventral striatum
1158:hot-hand fallacy
1009:
1007:
1006:
1003:
1000:
993:
991:
990:
987:
984:
977:
975:
974:
971:
968:
961:
959:
958:
955:
952:
914:
912:
910:
909:
906:
903:
794:
787:
783:
780:
774:
743:
735:
731:Reverse position
726:
724:
723:
720:
717:
702:
700:
699:
694:
681:
680:
675:
671:
663:
640:
638:
637:
634:
631:
621:
619:
618:
613:
600:
599:
594:
590:
582:
559:
557:
556:
553:
550:
534:
532:
531:
528:
525:
502:
500:
499:
496:
493:
474:
472:
471:
468:
465:
454:
452:
451:
446:
444:
436:
431:
427:
426:
407:
403:
402:
401:
389:
388:
376:
375:
363:
362:
353:
348:
347:
320:
318:
317:
314:
311:
304:
302:
301:
298:
295:
284:
282:
281:
276:
274:
272:
271:
259:
251:
250:
234:
229:
211:
207:
206:
205:
195:
190:
142:
140:
139:
136:
133:
126:
124:
123:
120:
117:
110:
108:
107:
104:
101:
3815:
3814:
3810:
3809:
3808:
3806:
3805:
3804:
3755:
3754:
3753:
3748:
3722:
3696:Rationalization
3639:
3586:
3574:
3512:
3434:Genetic fallacy
3424:
3337:
3312:
3287:
3211:
3202:Sorites paradox
3182:False precision
3163:
3144:Double counting
3099:
3074:
3046:
3011:
2998:Loaded question
2982:Loaded language
2961:
2902:
2844:
2810:
2757:
2746:
2716:
2682:
2681:
2677:
2667:
2666:
2659:
2625:
2624:
2617:
2581:
2580:
2576:
2540:
2539:
2532:
2502:
2501:
2497:
2467:
2466:
2462:
2432:
2431:
2427:
2383:
2382:
2378:
2348:
2347:
2343:
2299:
2298:
2294:
2258:
2257:
2253:
2217:
2216:
2212:
2182:
2181:
2177:
2141:
2140:
2133:
2087:
2086:
2082:
2075:
2051:
2050:
2046:
2016:
2015:
2011:
2002:
2000:
1950:
1949:
1942:
1934:
1919:10.1.1.592.3838
1901:
1896:
1895:
1886:
1864:
1858:
1854:
1845:
1843:
1841:
1820:
1819:
1815:
1807:
1796:
1791:
1790:
1786:
1764:
1763:
1759:
1737:
1736:
1732:
1723:
1719:
1710:
1697:
1684:
1683:
1676:
1672:
1667:
1628:Law of averages
1598:
1577:
1391:Winner Numbers
1335:
1333:Lottery players
1323:
1305:In the game of
1303:
1294:
1285:
1280:
1238:
1170:
1168:Neurophysiology
1154:
1145:unprotected sex
1136:
1097:Daniel Kahneman
1085:
1080:
1071:
1024:
1004:
1001:
998:
997:
995:
988:
985:
982:
981:
979:
972:
969:
966:
965:
963:
956:
953:
950:
949:
947:
927:
922:
907:
904:
901:
900:
898:
896:
885:
866:
824:
795:
784:
778:
775:
760:
744:
733:
721:
718:
715:
714:
712:
658:
657:
646:
645:
635:
632:
629:
628:
626:
577:
576:
565:
564:
554:
551:
548:
547:
545:
541:
529:
526:
523:
522:
520:
497:
494:
491:
490:
488:
485:
469:
466:
463:
462:
460:
418:
414:
393:
380:
367:
354:
339:
338:
334:
326:
325:
315:
312:
309:
308:
306:
299:
296:
293:
292:
290:
263:
242:
197:
175:
171:
163:
162:
148:
137:
134:
131:
130:
128:
121:
118:
115:
114:
112:
105:
102:
99:
98:
96:
75:Over time, the
69:
64:
17:
12:
11:
5:
3813:
3811:
3803:
3802:
3797:
3792:
3787:
3782:
3777:
3772:
3767:
3757:
3756:
3750:
3749:
3747:
3746:
3735:
3732:
3731:
3728:
3727:
3724:
3723:
3721:
3720:
3715:
3710:
3709:
3708:
3698:
3693:
3688:
3683:
3674:
3669:
3662:
3657:
3650:
3644:
3641:
3640:
3638:
3637:
3630:
3625:
3620:
3615:
3614:
3613:
3600:
3598:
3589:
3580:
3579:
3576:
3575:
3573:
3572:
3571:
3570:
3556:
3551:
3546:
3545:
3544:
3535:
3528:
3526:Accomplishment
3517:
3514:
3513:
3511:
3510:
3505:
3498:
3493:
3488:
3483:
3482:
3481:
3474:
3473:
3472:
3455:
3449:
3447:
3436:
3430:
3429:
3426:
3425:
3423:
3422:
3417:
3412:
3407:
3402:
3397:
3392:
3383:
3378:
3373:
3368:
3363:
3358:
3353:
3347:
3345:
3339:
3338:
3336:
3335:
3330:
3322:
3320:
3311:
3310:
3301:
3295:
3293:
3289:
3288:
3286:
3285:
3280:
3278:Slippery slope
3275:
3270:
3265:
3264:
3263:
3253:
3252:
3251:
3244:
3234:
3233:
3232:
3221:
3219:
3213:
3212:
3210:
3209:
3204:
3199:
3197:Slippery slope
3194:
3189:
3184:
3179:
3173:
3171:
3165:
3164:
3162:
3161:
3156:
3151:
3146:
3141:
3132:
3131:
3130:
3125:
3123:Cherry picking
3115:
3109:
3107:
3101:
3100:
3098:
3097:
3092:
3086:
3084:
3076:
3075:
3073:
3072:
3067:
3062:
3056:
3054:
3048:
3047:
3045:
3044:
3039:
3034:
3033:
3032:
3021:
3019:
3013:
3012:
3010:
3009:
3004:
2991:
2990:
2989:
2979:
2969:
2967:
2963:
2962:
2960:
2959:
2954:
2949:
2944:
2939:
2934:
2929:
2923:
2921:
2914:
2908:
2907:
2904:
2903:
2901:
2900:
2895:
2890:
2885:
2880:
2875:
2870:
2865:
2860:
2854:
2852:
2846:
2845:
2843:
2842:
2837:
2832:
2827:
2821:
2819:
2812:
2811:
2809:
2808:
2803:
2798:
2793:
2788:
2783:
2777:
2775:
2765:
2759:
2758:
2747:
2745:
2744:
2737:
2730:
2722:
2715:
2714:
2675:
2657:
2615:
2594:(2): 537–575.
2574:
2530:
2495:
2482:10.2307/749665
2460:
2441:(2): 279–282.
2425:
2396:(2): 271–281.
2376:
2357:(4): 445–462.
2341:
2312:(1): 179–184.
2292:
2251:
2230:(5): 326–334.
2210:
2175:
2131:
2096:(2): 111–134.
2080:
2073:
2044:
2025:(4): 286–302.
2009:
1940:
1912:(2): 105–110.
1884:
1852:
1839:
1813:
1784:
1773:(2): 260–276.
1757:
1730:
1717:
1695:
1673:
1671:
1668:
1666:
1665:
1660:
1655:
1650:
1645:
1643:Memorylessness
1640:
1635:
1630:
1625:
1620:
1615:
1613:Gambler's ruin
1610:
1605:
1599:
1597:
1594:
1576:
1573:
1566:
1565:
1562:
1559:
1556:
1553:
1546:
1545:
1542:
1539:
1536:
1533:
1530:
1527:
1523:
1522:
1519:
1516:
1513:
1510:
1507:
1504:
1500:
1499:
1496:
1493:
1490:
1487:
1484:
1481:
1477:
1476:
1473:
1470:
1467:
1464:
1461:
1458:
1454:
1453:
1450:
1447:
1444:
1441:
1438:
1435:
1431:
1430:
1427:
1424:
1421:
1418:
1415:
1412:
1408:
1407:
1404:
1401:
1398:
1395:
1392:
1389:
1385:
1384:
1381:
1378:
1374:
1373:
1370:
1334:
1331:
1322:
1319:
1302:
1299:
1293:
1290:
1284:
1283:Types of users
1281:
1279:
1276:
1237:
1234:
1169:
1166:
1153:
1150:
1135:
1132:
1103:produced by a
1101:cognitive bias
1084:
1081:
1079:
1076:
1070:
1067:
1023:
1020:
926:
923:
921:
918:
884:
881:
865:
862:
857:methodological
848:many universes
838:. In his book
823:
820:
797:
796:
747:
745:
738:
732:
729:
704:
703:
692:
689:
685:
679:
674:
669:
666:
661:
656:
653:
623:
622:
611:
608:
604:
598:
593:
588:
585:
580:
575:
572:
540:
539:Other examples
537:
517:Bayes' theorem
512:
511:
508:
484:
481:
457:
456:
442:
439:
434:
430:
425:
421:
417:
413:
410:
406:
400:
396:
392:
387:
383:
379:
374:
370:
366:
361:
357:
352:
346:
342:
337:
333:
287:
286:
270:
266:
262:
257:
254:
249:
245:
241:
238:
233:
228:
225:
222:
218:
214:
210:
204:
200:
194:
189:
186:
183:
179:
174:
170:
146:
68:
65:
63:
60:
15:
13:
10:
9:
6:
4:
3:
2:
3812:
3801:
3798:
3796:
3793:
3791:
3788:
3786:
3783:
3781:
3778:
3776:
3773:
3771:
3768:
3766:
3763:
3762:
3760:
3745:
3737:
3736:
3733:
3719:
3716:
3714:
3711:
3707:
3704:
3703:
3702:
3699:
3697:
3694:
3692:
3689:
3687:
3684:
3682:
3678:
3675:
3673:
3670:
3668:
3667:
3663:
3661:
3658:
3656:
3655:
3651:
3649:
3646:
3645:
3642:
3636:
3635:
3631:
3629:
3626:
3624:
3621:
3619:
3616:
3612:
3609:
3608:
3607:
3606:
3602:
3601:
3599:
3597:
3593:
3590:
3588:
3581:
3569:
3566:
3565:
3564:
3560:
3557:
3555:
3552:
3550:
3547:
3543:
3539:
3536:
3534:
3533:
3529:
3527:
3524:
3523:
3522:
3519:
3518:
3515:
3509:
3506:
3504:
3503:
3499:
3497:
3494:
3492:
3489:
3487:
3484:
3480:
3479:
3475:
3471:
3468:
3467:
3466:
3465:
3461:
3460:
3459:
3456:
3454:
3451:
3450:
3448:
3446:
3445:
3440:
3437:
3435:
3431:
3421:
3418:
3416:
3413:
3411:
3408:
3406:
3403:
3401:
3398:
3396:
3393:
3391:
3387:
3386:Invented here
3384:
3382:
3379:
3377:
3374:
3372:
3369:
3367:
3364:
3362:
3359:
3357:
3354:
3352:
3349:
3348:
3346:
3344:
3340:
3334:
3331:
3329:
3328:
3324:
3323:
3321:
3319:
3315:
3309:
3305:
3302:
3300:
3297:
3296:
3294:
3290:
3284:
3281:
3279:
3276:
3274:
3271:
3269:
3266:
3262:
3259:
3258:
3257:
3254:
3250:
3249:
3245:
3243:
3242:
3238:
3237:
3235:
3231:
3228:
3227:
3226:
3223:
3222:
3220:
3218:
3214:
3208:
3205:
3203:
3200:
3198:
3195:
3193:
3190:
3188:
3185:
3183:
3180:
3178:
3175:
3174:
3172:
3170:
3166:
3160:
3157:
3155:
3152:
3150:
3149:False analogy
3147:
3145:
3142:
3140:
3136:
3133:
3129:
3126:
3124:
3121:
3120:
3119:
3118:Sampling bias
3116:
3114:
3111:
3110:
3108:
3106:
3102:
3096:
3093:
3091:
3088:
3087:
3085:
3083:
3082:
3081:Secundum quid
3077:
3071:
3068:
3066:
3063:
3061:
3058:
3057:
3055:
3053:
3049:
3043:
3040:
3038:
3035:
3031:
3028:
3027:
3026:
3025:False dilemma
3023:
3022:
3020:
3018:
3014:
3008:
3005:
3003:
2999:
2995:
2992:
2988:
2985:
2984:
2983:
2980:
2978:
2974:
2971:
2970:
2968:
2964:
2958:
2955:
2953:
2950:
2948:
2945:
2943:
2940:
2938:
2935:
2933:
2930:
2928:
2925:
2924:
2922:
2918:
2915:
2913:
2909:
2899:
2896:
2894:
2893:Illicit minor
2891:
2889:
2888:Illicit major
2886:
2884:
2881:
2879:
2876:
2874:
2871:
2869:
2866:
2864:
2861:
2859:
2856:
2855:
2853:
2851:
2847:
2841:
2838:
2836:
2833:
2831:
2828:
2826:
2823:
2822:
2820:
2818:
2813:
2807:
2804:
2802:
2799:
2797:
2794:
2792:
2789:
2787:
2784:
2782:
2779:
2778:
2776:
2774:
2769:
2766:
2764:
2760:
2755:
2751:
2743:
2738:
2736:
2731:
2729:
2724:
2723:
2720:
2710:
2706:
2701:
2696:
2692:
2691:
2686:
2679:
2676:
2671:
2664:
2662:
2658:
2653:
2649:
2645:
2641:
2637:
2633:
2629:
2622:
2620:
2616:
2610:
2605:
2601:
2597:
2593:
2589:
2585:
2578:
2575:
2570:
2566:
2561:
2556:
2552:
2548:
2544:
2537:
2535:
2531:
2526:
2522:
2518:
2514:
2510:
2506:
2499:
2496:
2491:
2487:
2483:
2479:
2476:(1): 96–105.
2475:
2471:
2464:
2461:
2456:
2452:
2448:
2444:
2440:
2436:
2429:
2426:
2421:
2417:
2412:
2407:
2403:
2399:
2395:
2391:
2387:
2380:
2377:
2372:
2368:
2364:
2360:
2356:
2352:
2345:
2342:
2337:
2333:
2329:
2325:
2320:
2315:
2311:
2307:
2303:
2296:
2293:
2288:
2284:
2279:
2274:
2270:
2266:
2262:
2255:
2252:
2247:
2243:
2238:
2233:
2229:
2225:
2221:
2214:
2211:
2206:
2202:
2198:
2194:
2190:
2186:
2179:
2176:
2171:
2167:
2162:
2157:
2153:
2149:
2145:
2138:
2136:
2132:
2127:
2123:
2119:
2115:
2111:
2107:
2103:
2099:
2095:
2091:
2084:
2081:
2076:
2070:
2066:
2061:
2060:
2054:
2048:
2045:
2040:
2036:
2032:
2028:
2024:
2020:
2013:
2010:
1999:on 2018-06-01
1998:
1994:
1990:
1986:
1982:
1978:
1974:
1970:
1966:
1962:
1958:
1954:
1947:
1945:
1941:
1933:
1929:
1925:
1920:
1915:
1911:
1907:
1900:
1893:
1891:
1889:
1885:
1880:
1876:
1872:
1868:
1862:
1856:
1853:
1842:
1836:
1832:
1827:
1826:
1817:
1814:
1806:
1802:
1795:
1788:
1785:
1780:
1776:
1772:
1768:
1761:
1758:
1753:
1749:
1745:
1741:
1734:
1731:
1727:
1721:
1718:
1714:
1708:
1706:
1704:
1702:
1700:
1696:
1692:. 2015-01-02.
1691:
1687:
1681:
1679:
1675:
1669:
1664:
1661:
1659:
1656:
1654:
1651:
1649:
1648:Oscar's grind
1646:
1644:
1641:
1639:
1636:
1634:
1631:
1629:
1626:
1624:
1621:
1619:
1616:
1614:
1611:
1609:
1606:
1604:
1601:
1600:
1595:
1593:
1590:
1586:
1582:
1574:
1572:
1563:
1560:
1557:
1554:
1552:
1547:
1543:
1540:
1537:
1534:
1531:
1528:
1525:
1524:
1520:
1517:
1514:
1511:
1508:
1505:
1502:
1501:
1497:
1494:
1491:
1488:
1485:
1482:
1479:
1478:
1474:
1471:
1468:
1465:
1462:
1459:
1456:
1455:
1451:
1448:
1445:
1442:
1439:
1436:
1433:
1432:
1428:
1425:
1422:
1419:
1416:
1413:
1410:
1409:
1405:
1402:
1399:
1396:
1393:
1390:
1387:
1386:
1379:
1375:
1368:
1362:
1359:
1354:
1350:
1339:
1332:
1330:
1328:
1327:loan officers
1321:Loan officers
1320:
1318:
1316:
1312:
1308:
1300:
1298:
1292:Asylum judges
1291:
1289:
1282:
1277:
1275:
1271:
1267:
1264:
1259:
1257:
1251:
1248:
1247:control group
1244:
1235:
1233:
1231:
1227:
1223:
1218:
1216:
1212:
1208:
1203:
1199:
1195:
1191:
1187:
1183:
1179:
1175:
1167:
1165:
1161:
1159:
1151:
1149:
1148:intercourse.
1146:
1140:
1133:
1131:
1129:
1125:
1120:
1118:
1114:
1110:
1106:
1102:
1098:
1094:
1090:
1082:
1077:
1075:
1068:
1066:
1064:
1060:
1059:
1053:
1051:
1050:
1044:
1042:
1038:
1034:
1030:
1021:
1019:
1017:
1013:
1012:card counting
945:
940:
936:
932:
924:
919:
917:
894:
890:
882:
880:
877:
876:
872:described in
871:
863:
861:
858:
853:
849:
845:
841:
837:
831:
829:
819:
816:
813:described by
812:
807:
804:
793:
790:
782:
772:
768:
764:
758:
757:
753:
748:This section
746:
742:
737:
736:
730:
728:
710:
687:
683:
677:
672:
667:
664:
659:
654:
651:
644:
643:
642:
606:
602:
596:
591:
586:
583:
578:
573:
570:
563:
562:
561:
538:
536:
518:
509:
506:
505:
504:
482:
480:
478:
440:
437:
432:
428:
423:
419:
415:
408:
404:
398:
394:
390:
385:
381:
377:
372:
368:
364:
359:
355:
344:
340:
335:
324:
323:
322:
268:
264:
260:
255:
247:
243:
231:
226:
223:
220:
216:
212:
208:
202:
198:
192:
187:
184:
181:
177:
172:
161:
160:
159:
157:
153:
149:
94:
90:
82:
78:
73:
66:
61:
59:
57:
53:
48:
46:
42:
38:
34:
30:
26:
22:
3681:Naturalistic
3664:
3652:
3632:
3603:
3587:of relevance
3530:
3508:Whataboutism
3500:
3476:
3470:Godwin's law
3462:
3442:
3325:
3318:Consequences
3299:Law/Legality
3273:Single cause
3255:
3246:
3239:
3079:
2947:Loki's Wager
2927:Equivocation
2920:Equivocation
2688:
2678:
2669:
2638:(1): 83–84.
2635:
2631:
2591:
2587:
2577:
2550:
2546:
2511:(2): 69–75.
2508:
2504:
2498:
2473:
2469:
2463:
2438:
2434:
2428:
2393:
2389:
2379:
2354:
2350:
2344:
2309:
2305:
2295:
2268:
2264:
2254:
2227:
2223:
2213:
2191:(1): 75–89.
2188:
2184:
2178:
2151:
2147:
2093:
2089:
2083:
2058:
2047:
2022:
2018:
2012:
2001:. Retrieved
1997:the original
1960:
1956:
1909:
1905:
1873:(1): 13–16.
1870:
1866:
1855:
1844:. Retrieved
1824:
1816:
1800:
1787:
1770:
1766:
1760:
1743:
1739:
1733:
1725:
1720:
1712:
1689:
1589:monetization
1578:
1569:
1550:
1345:
1324:
1304:
1295:
1286:
1272:
1268:
1260:
1252:
1239:
1219:
1178:neurological
1171:
1162:
1155:
1141:
1137:
1121:
1093:Amos Tversky
1086:
1072:
1063:Tom Stoppard
1056:
1054:
1047:
1045:
1041:exchangeable
1025:
928:
920:Non-examples
886:
873:
867:
839:
832:
825:
808:
800:
785:
779:January 2024
776:
761:Please help
749:
708:
705:
624:
542:
513:
486:
476:
458:
288:
151:
144:
86:
49:
28:
24:
20:
18:
3701:Red herring
3458:Association
3139:Conjunction
3060:Composition
2957:Reification
2873:Existential
2825:Existential
2609:10986/12002
1715:pp. 326-334
1581:video games
1358:pari-mutuel
1353:Philip Cook
1315:strike zone
1230:conditioned
1180:component.
1107:called the
994:(7.69%) to
962:(7.69%) to
935:permutation
931:independent
844:John Leslie
815:Ian Hacking
3759:Categories
3677:Moralistic
3611:Sealioning
3605:Ad nauseam
3532:Ipse dixit
3444:Ad hominem
3268:Regression
3070:Ecological
2883:Four terms
2801:Masked man
2003:2017-06-19
1846:2016-03-13
1670:References
1585:loot boxes
1226:reinforced
1172:While the
1134:Variations
1078:Psychology
864:Childbirth
806:outcomes.
81:difference
77:proportion
3718:Straw man
3596:Arguments
3585:fallacies
3559:Tradition
3549:Etymology
3521:Authority
3502:Tu quoque
3486:Bulverism
3256:Gambler's
3225:Animistic
3169:Ambiguity
3135:Base rate
2878:Necessity
2750:fallacies
2709:237672988
2652:0167-6687
2569:0033-5533
2371:154661530
2328:1069-9384
2205:0749-5978
2110:1050-5350
1993:143452957
1914:CiteSeerX
1879:0312-3685
1726:Universes
1380:Draw day
1250:fallacy.
1215:affective
1211:executive
1035:from the
1016:blackjack
868:In 1796,
840:Universes
750:does not
691:%
655:−
610:%
574:−
391:∩
378:∩
365:∩
217:∏
178:⋂
156:fair coin
89:fair coin
67:Coin toss
58:in 1913.
3744:Category
3376:Ridicule
3361:Flattery
3351:Children
3248:Post hoc
3128:McNamara
3090:Accident
3065:Division
2912:Informal
2693:: 1–27.
2525:12822837
2420:21229615
2336:15117006
2287:15900930
2246:18859806
2154:: 1–12.
2126:21141130
2118:12766438
2055:(1991).
2039:14140335
1985:17835457
1932:Archived
1805:Archived
1596:See also
1579:Several
1342:fallacy.
1307:baseball
1222:striatum
1190:amygdala
1049:a priori
889:roulette
836:Universe
803:Bayesian
62:Examples
52:roulette
45:expected
41:gambling
3563:Novelty
3538:Poverty
3400:Loyalty
3366:Novelty
3343:Emotion
3292:Appeals
3261:Inverse
3241:Cum hoc
3230:Furtive
2748:Common
2672:: 1–15.
2455:6062970
2411:3429350
2170:5019574
1965:Bibcode
1957:Science
1690:BBC.com
1311:umpires
1263:Gestalt
1194:caudate
1083:Origins
1008:
996:
992:
980:
976:
964:
960:
948:
911:
899:
891:at the
771:removed
756:sources
725:
713:
639:
627:
558:
546:
533:
521:
501:
489:
473:
461:
319:
307:
303:
291:
141:
129:
125:
113:
109:
97:
37:fallacy
27:or the
3648:Cliché
3583:Other
3554:Nature
3542:Wealth
3177:Accent
2763:Formal
2707:
2650:
2567:
2523:
2490:749665
2488:
2453:
2418:
2408:
2369:
2334:
2326:
2285:
2244:
2203:
2168:
2124:
2116:
2108:
2071:
2037:
1991:
1983:
1916:
1877:
1837:
1388:April
1196:, and
1029:biased
944:jokers
3410:Spite
3304:Stone
2705:S2CID
2486:JSTOR
2367:S2CID
2242:S2CID
2166:S2CID
2122:S2CID
2065:16–19
1989:S2CID
1935:(PDF)
1902:(PDF)
1833:–70.
1808:(PDF)
1797:(PDF)
1278:Users
688:62.02
607:64.39
154:of a
3496:Tone
3371:Pity
3356:Fear
2754:list
2648:ISSN
2565:ISSN
2521:PMID
2451:PMID
2416:PMID
2332:PMID
2324:ISSN
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