History Main / GamblersFallacy

* In the pilot of ''Series/{{NUMB3RS}}'', Don, watching a baseball game with his father, comments that a batter is "due" a big play after going four games without a hit, a concept which Charlie is quick to refute, only for the player to end up making a big hit. It turns out that Don is yanking Charlie's chain a bit; what they're watching is not a live game but a tape of a game from the day before, and Don, having read a recap in the paper, already knew what was going to happen.

Compare SunkCostFallacy.

* In ''Film/TheThinMan'', Dorothy Wynant breaks up with her fiancée out of fear that their children will grow up to be murderous psychopaths, as she believes her father to be. Her brother Gilbert assures her that he's been reading extensively on Mendelian genetics and that her children only have a one in four chance of being murderous psychopaths, so as long as she stops at three, she'll be fine... then he realises the first one might be the murderous psychopath. Setting aside the many things he gets wrong about Mendelian genetics in his speech, there's nothing that says ''exactly one'' child out of four would be a murderer.

A similar misinterpretation is that if an event has a probability of 1-in-n, then you are guaranteed a success if you make n attempts. As an exaggerated example, the probability of a "heads" on an unbiased coin is 1/2, therefore, flipping a coin twice is guaranteed to get at least one "heads." This is not true.

To explain the above in another way, flip a coin 10 times, and the chances that heads was flipped 4 times or more is 82.81%. Flip it 1000 times, and the chances heads was flipped 400 times or more is 99.99999999%. But even if it was less than 400, the next flip will still be 50/50: long-term odds predict the general trend of many results, not what will happen in a specific instance. This is also the reason why playing a high number of low-stakes games in Casinos increases the chances of the house making money; the house advantage only affects who wins a small percentage of the time, but this advantage "evens out" over the long haul. Unless you're a good card counter, taking advantage of free stuff, or just enjoy playing, you're more likely to be successful with a small number of high-stakes events.

Believing that dice/coins have memory, or that independent events will occur in "streaks". If a coin has just landed on heads four times in a row, surely it's much more likely to get tails this time, to even things out... or alternatively, heads is on a roll and will appear next time, too. See also RandomNumberGod and ArtisticLicenseStatistics.

* In the pilot of ''Series/{{NUMB3RS}}'', Don, watching a baseball game with his father, comments that a batter is "due" a big play after going four games without a hit. It turns out that Don is yanking Charlie's chain a bit; what they're watching is not a live game but a tape of a game from the day before, and Don, having read a recap in the paper, already knew how the play was going to end.

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* In a ''ComicStrip/{{Peanuts}}'' comic, Lucy uses this fallacy to [[http://www.gocomics.com/peanuts/1960/10/16 convince Charlie Brown to try to kick the football again]].

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* ''WebVideo/UltraFastPony'' has a doubly-fallacious example. First, Twilight is treating a not-remotely-random system (namely, hiding from a dangerous killer) as if it were random—and then, within that system, Twilight says a plan that's failed once is therefore due to succeed soon.
-->'''Twilight:''' Hmm. I've got it. We'll run away and hide! Because it didn't work ''this'' time, so according to the laws of heads and tails, it must work the next time!\\
'''Fluttershy:''' [[LampshadeHanging I don't think the laws of probability work like that.]]

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* ''Webcomic/DarthsAndDroids''. The {{Munchkin}} gamer Pete, facing a situation where a dice roll of 1 would be disastrous, encourages Annie to use one of his dice: [[http://www.darthsanddroids.net/episodes/0099.html "I've pre-rolled the ones out of it."]] TheRant explains that, beforehand, Pete had carefully prepared a number of 20-sided dice that had rolled two 1s in a row, and placed them in a special, roll-proof container. Since the chances of rolling three 1s in a row is only 1 in 8000, surely rolling another 1 from these pre-rolled dice is almost impossible, right? A bit later in the comic, [[http://www.darthsanddroids.net/episodes/0195.html one of those pre-rolled dice actually does come up as 1.]] Pete's reaction?
--> '''Pete:''' Awesome! That die will be even luckier next time!

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* Creator/AchievementHunter has had a long drawn out ''multiple video'' discussion on this. It started with Geoff asking Gavin an inane would you rather question that involved calling the outcome of three coin flips. They asked Ryan for the odds only to be confused by his unexpected complicated explanation. A video later it came down to Ryan correctly pointing out the fallacy and Gavin not getting it (though Gavin's... unique... phraseology was a contributing factor, at points he seemed to understand the fallacy but couldn't really say it or understand how Ryan was saying it). Humorously they decided to end it by actually doing to experiment... only for all the coins to land heads up, blowing Gavin's mind.

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* ''WebAnimation/ZeroPunctuation'' brings this up by name in Yahtzee's review of ''VideoGame/GrandTheftAutoV''. Yahtzee theorizes that the game constantly switches between three different protagonists in the belief that the player would ''have'' to find at least of one of them to be likable. Yahtzee, however, ends up equally disliking all three main characters.

* In the second Revival Round of ''Manga/LiarGame'', Nao falls into this, thinking that after her opponent had won a one-in-four chance gamble three times in a row, that it would be incredibly improbable for her to win a 4th time, meaning that she should bet all-in. [[spoiler: It's actually pretense for a trap. Nao had been fooling her opponent into think that she had a tell so that she can trick her into a massive loss. Nao was probably well aware of the actual odds but needed justification for her seemingly stupid bet.]]

* ''WebAnimation/ZeroPunctuation'' brings this up by name in Yahtzee's review of ''VideoGame/GrandTheftAutoV''. Yahtzee theorizes that game constantly switches between three different protagonists in the belief that the player would ''have'' to find at least of one of them to be likable. Yahtzee, however, ends up equally disliking all three main characters.

* ''WebAnimation/ZeroPunctuation'' brings this up by name in Yahtzee's review of ''VideoGame/GrandTheftAutoV''. Yahtzee believes that game constantly switches between three different protagonists in the hopes that the player would find at least of one of them to be likable, which Yahtzee says fails because he equally dislikes all three main characters for different reasons.

Believing that dice/coins have memory, or that independent events will occur in "streaks". If a coin has just landed on heads four times in a row, surely it's much more likely to get tails this time, to even things out... or alternatively, heads is on a roll and will appear next time, too. See also RandomNumberGod and ArtisticLicenceStatistics.

* When the events are not independent: If you draw 10 red cards from a shuffled deck without replacing them, then the next one really ''is'' more likely to be black than red because of the 42 cards remaining, 26 are black but only 16 are red. This sort of situation in the real world is, in fact, hypothesized to be how humans developed the intuitions that lead to this fallacy in the first place.

* Generally speaking, many video games have a mechanic that tweaks the RNG, so that long strings of excessively bad (or good) luck are less likely than they would be in a memoryless system. This is partly because players expect this, and partly because such strings are [[TropesAreNotBad really friggin annoying to deal with]] (at least, in games that aren't centered around being CrazyPrepared to deal with them).

* The [[LetsPlay/AchievementHunter Achievement Hunters]] had a long drawn out ''multiple video'' discussion on this. It started with Geoff asking Gavin an inane would you rather question that involved calling the outcome of three coin flips. They asked Ryan for the odds only to be confused by his unexpected complicated explanation. A video later it came down to Ryan correctly pointing out the fallacy and Gavin not getting it (though Gavin's... unique... phraseology was a contributing factor, at points he seemed to under stand the fallacy but couldn't really say it or understand how Ryan was saying it). Humorously they decided to end it by actually doing to experiment... only for all the coins to land heads up, blowing Gavin's mind.

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* The [[LetsPlay/AchievementHunter Achievement Hunters]] had a long drawn out ''multiple video'' discussion on this. It started with Geoff asking Gavin an inane would you rather question that involved calling the outcome of three coin flips. They asked Ryan for the odds only to be confused by his expected complicated explanation. A video later it came down to Ryan correctly pointing out the fallacy and Gavin not getting it (though Gavin's... unique... phraseology was a contributing factor, at points he seemed to under stand the fallacy but couldn't really say it or understand how Ryan was saying it). Humorously they decided to end it by actually doing to experiment... only for all the coins to land heads up, blowing Gavin's mind.

Note that Gambler's Fallacy applies only to systems that both ''have no memory'', and ''are explicitly known to be fair''. Drawing cards without replacement (read, deck now has "memory") does alter the probabilities of the next cards drawn, and if you do not explicitly know that the event being tested is fair, you can use things like n-heads-in-a-row to draw conclusions of bias in the system (see Non-examples and Theater sections below).

** However this fallacy doesn't apply to older purely mechanical slots. In theory these also use a random number generator, but the analog system can potentially wear down. This leads to a case where certain individual machines favor certain combinations above others because they are more likely to stop in certain places. This is why, despite their iconic nature, no sane casinos still use the old three reel slot machines. [[note]]That and classic three reel slots have an exponentially lower number of states than a modern digital slots since digital slots have more reels and each reel has more characters on it.[[/note]]

* {{Stephen King}}'s characters reason like this a couple of times, although one of the times [[AuthorAvatar the character is himself]].

Believing that dice/coins have memory, or that independent events will occur in "streaks". If a coin has just landed on heads four times in a row, surely it's much more likely to get tails this time, to even things out... or alternatively, heads is on a roll and will appear next time, too. See also RandomNumberGod and ArtisticLicenceStatistics. In fact, if you toss a previously untested coin and (say) heads come up, there's a larger chance to get heads on a second roll, because the coin might be biased, although not very much larger, unless the coin is so warped that the imperfection is clearly visible.

Psychologically, this fallacy tends to come from the fact that the odds to replicate a pattern ''do'' go up cumulatively. The probability of rolling 20 on a d20 twice is 1/400, the same as any expected sequence of two numbers. The probability of rolling the first is 1/20, and the probability of rolling the second is also 1/20. The fallacy occurs when someone assumes that once they've rolled two 20s in a row, it's less likely than usual (< 1/20) that they'll get another 20. In reality, once they've rolled two 20s in a row, it's just as likely as ever (1/20) that they'll roll a 20 again. This also, most notably, works the other way around - if they've lost many bets in a row, they aren't any more likely to win the next bet. Psychologically, what you're doing is inventing patterns that fit with the events you observe despite not really being there at all, combined with a big scoop of entitlement.

To explain the above in another way, flip a coin 10 times, and the chances that heads was flipped 4 times or more is 82.81%. Flip it 1000 times, and the chances heads was flipped 400 times or more is 99.99999999%. But even if it was less than 400, the next flip will still be 50/50. This is also the reason why playing a high number of low-stakes games in Casinos increases the chances of the house making money; the house advantage only affects who wins a small percentage of the time, but this advantage "evens out" over the long haul. Unless you're a good card counter, taking advantage of free stuff, or just enjoy playing, you're more likely to be successful with a small number of high-stakes events.

* If it has not been established that the trials are fair, then a significant deviation from the expected results could count as evidence that they are biased somehow. If a die rolls a 6 at least 10 times in a row, simple statistics say that the die is extremely likely to be weighted, which means that, [[IKnowYouKnowIKnow your adversary trying to manipulate you notwithstanding]], you'd better bet on another 6.