History Main / GamblersFallacy

* Frieren of ''Anime/FrierenBeyondJourneysEnd'' often falls prey to ChestMonster treasure traps despite having a spell that can detect them with 99% accuracy. If anything, using that spell makes her more reckless since she believes that because it's not 100% accurate, [[InsaneTrollLogic a "great mage" like her will "see through that one percent"]] to pull off "historic discoveries" with enough tries. So far, all this logic has gotten her is being chomped and slobbered over by these mimics.

* 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. Subverted as it turns out that Don ''knew'' what was going to happen because the game is a replay and he had read the recap in the paper, and was just taking the opportunity to yank Charlie's chain a bit.

See also RandomNumberGod and ArtisticLicenseStatistics. Compare SunkCostFallacy. Games which implement a BadLuckMitigationMechanic avert this trope.

* In [[Recap/TheTwilightZoneS1E17TheFever "The Fever"]], a gambling-themed episode of ''Series/TheTwilightZone1959'', the arrogant Franklin falls prey to the titular fever, a gambling addiction so horrendous that he doesn't get a wink of sleep for ''two straight days''. One of his professed reasons to keep at it is the gambler's fallacy -- in an effort to break even, he doesn't stop playing the slots until [[spoiler:the slot machine ''breaks'' from overuse with his dollar coin inside it, causing him to suffer a nervous breakdown.]]

** In "The Mansion Family", Mr. Burns needs to go to the hospital for a while and thinks he should get Homer to watch over his mansion while he's gone. When Mr. Smithers points out that this is a bad idea because Homer screwed up everything else Mr. Burns has ever asked him, Burns responds by saying that since Homer failed so many times, he's due for a good performance.

[[folder:Theatre]]
* Discussed at length in ''Theatre/RosencrantzAndGuildensternAreDead'', in which Rosencrantz flips a coin 85 times in a row and gets heads every time. Guildenstern suggests that it shouldn't be surprising since each coin has an equal chance of coming up heads or tails. Neither Rosencrantz nor Guildenstern is satisfied with this explanation. (Technically, Guildenstern is right in that given a fair coin, a series of 85 heads is exactly as probable as any other single series of that length [namely, 1 in 2^85]; however, if a coin should actually land the same 85 times, it's a good reason to believe that such a coin [or flip] is NOT fair.)
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The simplest explanation for why this fallacy can occur is that the human mind is trained by evolution to recognize patterns as a survival instinct.[[note]]If you get sick every time you eat a certain food, you learn the pattern of getting sick and eating the food; thus, you avoid eating the food so you stop getting sick. Alternatively, if you see five people cross a street when the street light is green, and all five people get hit by cars, you can recognize the pattern of the light's color, the traffic's movement, and the injuries on other people. Thus, you know not to cross the street when the light is green.[[/note]] The trouble is, the human mind can often find patterns in things where there simply isn't a pattern that can be replicated, such as in a game of chance. A coin might come up as heads ten times in a row if you flip it ten times, but that was entirely random chance; the coin has no more chance to come up heads on any flip than it does tails. (That is, of course, assuming you're not using a TwoHeadedCoin.)

The Gambler's Fallacy is believing that a random outcome is affected by previous outcomes, or believing that sequences of random events have memory (such as rolling dice, flipping coins, drawing cards, and pulling slot machines). Basically, it's the idea that events which are independent and random will occur in "streaks".

For instance, this fallacy occurs if you believe that a coin which has just landed on heads ten times in a row is now more likely to get tails next time to even things out. Or alternatively, heads is on a roll and will appear next time too. Both of those beliefs are fallacious, because every coin flip has a 50/50 chance of being heads or tails, no matter what came before it or how many times. A coin might come up as heads ten times in a row if you flip it ten times, but that was entirely random chance; the coin has no more chance to come up heads on any flip than it does tails. (That is, of course, assuming you're not using a TwoHeadedCoin.)

Believing that a random outcome is affected by previous outcomes, or believing that sequences of random events -- such as rolling dice, flipping coins, drawing cards, and pulling slot machines -- have memory. Basically, it's the idea 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.

Compare SunkCostFallacy. Games which implement a BadLuckMitigationMechanic avert this trope.

* Many ''TabletopGame/{{Warhammer}}'' gamers or tabletop roleplayers will tell you that [[RandomNumberGod this is absolutely true]]. Others will perform astounding feats of [[FanNickname Mathhammer]] in mid-game and tell you exactly how many units of each side should die in an assault, what is the expected variance, and whether or not the assault makes sense in terms of points of enemy units destroyed versus own losses.

* 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. Subverted as it turns out that the game is a replay and Don had read the recap in the paper; he had prior knowledge of how the play was going to turn out and was just taking the opportunity to yank Charlie's chain a bit.

* 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. Subverted as it turns out that the game is a replay and Don had read the recap in the paper; he ''knew'' how the play was going to turn out and was just taking the opportunity to yank Charlie's chain a bit.

* 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. Subverted as it turns out that Don is actually just 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.