History Main / GamblersFallacy

10th Apr '16 2:16:40 PM Josef5678
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* Similar to the roulette example above, gamblers apply this logic to slot machines, which is pointed out in the book ''[[http://www.amazon.com/Smart-Slot-Strategies-mathematical-strategies/dp/1453609261/ref=sr_1_1?ie=UTF8&qid=1351266797&sr=8-1&keywords=smart+slot+strategies Smart Slot Strategies]]''. The author points out how gamblers will ignore the fact that a machine is controlled by a random number generator and will assume a machine is "hot" or "cold" based on how it's performing. It's further explained that many players believe they can tell how a machine is programmed by playing the machine around 20 times, despite the random number generator having millions of possibilities. A sample size of 20 plays is far too small to determine any trend in a population that size. With that said, individual machines really can be set with different payout tables. Still, 20 plays is too small for trends.

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* Similar to the roulette example above, gamblers Gamblers apply this logic to slot machines, which is pointed out in the book ''[[http://www.amazon.com/Smart-Slot-Strategies-mathematical-strategies/dp/1453609261/ref=sr_1_1?ie=UTF8&qid=1351266797&sr=8-1&keywords=smart+slot+strategies Smart Slot Strategies]]''. The author points out how gamblers will ignore the fact that a machine is controlled by a random number generator and will assume a machine is "hot" or "cold" based on how it's performing. It's further explained that many players believe they can tell how a machine is programmed by playing the machine around 20 times, despite the random number generator having millions of possibilities. A sample size of 20 plays is far too small to determine any trend in a population that size. With that said, individual machines really can be set with different payout tables. Still, 20 plays is too small for trends.
7th Apr '16 6:22:18 PM Nakuyabi
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* During each of the World Wars, a variant of this appeared as the Shell Hole Fallacy: when enemy artillery were randomly blazing away at the field, some troops (and some commanders!) believed that jumping into a crater a bursting shell had just made would increase their chances of survival, since the odds of a place being hit ''twice'' during any giving shelling were relatively low. While the artillery gunners weren't ''entirely'' unbiased (since they were trying to distribute their shots so as to hit as many parts of the field as possible in hopes of maximizing the number of targets hit), they really didn't have much control over any of the randomizing factors, so the actual odds that any given shell would strike where one had already struck were pretty much the same as the odds of that place being struck the first time. In any event, jumping into those craters did not perceptibly improve the soldiers' survival rate.
24th Dec '15 2:37:55 PM billybobfred
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* ''VideoGame/CityOfHeroes'' utilises a system called [[http://paragonwiki.com/wiki/Streakbreaker#The_Streak_Breaker the Streak Breaker]]. This mechanic in the attack calculations sometimes ''forces'' attacks that would normally be misses to instead hit, based on the current number of misses in a row versus your chance to hit. In short, it breaks streaks of misses.
* This one also shows up among players of ''VideoGame/WorldOfWarcraft'', in particular with the rare dragon whelp pets that drop out in the world, with many players assuming the more you kill the whelps, the higher your chance grows of finally getting a drop, while in reality the chance is independent of each past or future kill.
** Because people refuse to accept that improbable does not mean impossible or certain (or simply because the large variation in time required was ''annoying''), ''World of Warcraft'' developers actually modified this detail to conform to players' expectations. [[http://www.sirlin.net/blog/2010/3/11/gdc-2010-day-1.html Your chances for a drop do gradually increase the more you kill.]] This was also implemented because of some "kill this mob and loot this item off them" quests, where the drop rate was not 100%. Some of these quests had unusually low drop rates, and you could spend an hour or more trying to finish a quest. With this change, the chance goes up and up with each "loot", and then resets itself to the default rate with every success.
** In fact, many video games play around with the RNG like this, both because players expect it, and because it's really, really annoying to be on the receiving end of a string of bad luck, unless it's the kind of game where being CrazyPrepared for bad luck is expected of the player.



* 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 such strings are friggin annoying to deal with in games that aren't centered around being CrazyPrepared to deal with them.




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* ''VideoGame/CityOfHeroes'' utilises a system called [[http://paragonwiki.com/wiki/Streakbreaker#The_Streak_Breaker the Streak Breaker]]. This mechanic in the attack calculations sometimes ''forces'' attacks that would normally be misses to instead hit, based on the current number of misses in a row versus your chance to hit. In short, it breaks streaks of misses.
* This one also shows up among players of ''VideoGame/WorldOfWarcraft'', in particular with the rare dragon whelp pets that drop out in the world, with many players assuming the more you kill the whelps, the higher your chance grows of finally getting a drop, while in reality the chance was initially independent of each past or future kill... but because people refuse to accept that improbable does not mean impossible or certain (or simply because the large variation in time required was ''annoying''), ''World of Warcraft'' developers actually modified this detail to conform to players' expectations. [[http://www.sirlin.net/blog/2010/3/11/gdc-2010-day-1.html Your chances for a drop do gradually increase the more you kill.]] This was also implemented because of some "kill this mob and loot this item off them" quests, where the drop rate was not 100%. Some of these quests had unusually low drop rates, and you could spend an hour or more trying to finish a quest. With this change, the chance goes up and up with each "loot", and then resets itself to the default rate with every success.
* ''VideoGame/KingdomOfLoathing'''s "adventure queue" remembers the last 5 combat and non-combat encounters you've had in each area, and if the normal selection method picks one of them, it'll reject it 75% of the time and pick a new one.
2nd Nov '15 3:34:42 PM Berrenta
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A similar misinterpretation is that if an event has the odds 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." [[CaptainObvious This is not true]].

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A similar misinterpretation is that if an event has the odds 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." [[CaptainObvious This is not true]].
true.
24th Oct '15 9:05:52 AM eroock
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-->--'''Engie-tan''', ''Webcomic/NerfNow''

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-->--'''Engie-tan''', -->-- '''Engie-tan''', ''Webcomic/NerfNow''
20th Sep '15 4:59:05 PM CaptainCrawdad
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** It's also how counting cards in Blackjack works, but seriously, between the 6 to 8 deck sabots, constant reshufflings, Rainman-like mental math needed and pit bosses kicking out players for doing it? Not worth the hassle. Stick to mastering the basic game principles and play a perfect game, it's far easier.
** Casinos have no problem with perfect play. It still awards the house a small advantage, and off that tiny statistical edge casino owners build financial empires. Some casinos give out cards with "perfect play" (called [[http://en.wikipedia.org/wiki/Blackjack#Basic_strategy Basic Strategy]]) on them. The gamblers often then lose even more because they buy into this trope and then don't believe the casino would tell you how to play Blackjack correctly.
13th Sep '15 12:10:49 PM ElodieHiras
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Added DiffLines:


[[AC: VideoGames]]
* In Normal or lower difficulties ''VideoGame/XCOMEnemyUnknown'', a shot fired by a soldier after another soldier missing a 50%+ shot is more likely to hit... Because the game cheats in your favor and secretly adds an additional 10% chance to the next shot, and does so until a shot hits. It also reduces alien shots accuracy by 10% after a shot hits, until a shot misses. The game stops cheating in Classic or Impossible difficulty, throwing off veteran Normal players.
7th Sep '15 3:35:04 PM SilverDragon
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* When we finally meet Nico's father in season two of ''Series/TheWire'', he's sitting in a bar betting on the horses according to his "system", and is currently losing. But he boasts that he's still up $7,000... if you aggregate the last ''25 years'' [[TheGamblingAddict he's been playing]].
7th Sep '15 3:13:59 PM Premonition45
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** In one episode, billionaire 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.
** In another, Krusty loses a lot of money betting against the Harlem Globetrotters, because he figured that "the Generals were due".

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** In one episode, billionaire "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.
** In another, "Homie the Clown", Krusty loses a lot of money betting against the Harlem Globetrotters, because he figured that "the Generals were due".
26th Jun '15 8:48:18 AM mlsmithca
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---> "And Chuck, 9 out of 10 people who have this operation die on the table. But don't you worry 'bout it, 'cause we've already done 9 people this year, and they're all dead. So you're in the clear, you know what I mean?"

to:

---> --> "And Chuck, 9 out of 10 people who have this operation die on the table. But don't you worry 'bout it, 'cause we've already done 9 people this year, and they're all dead. So you're in the clear, you know what I mean?"



** Because people refuse to accept that improbable does not mean impossible or certain (or simply because the large variation in time required was ''annoying''), ''World of Warcraft'' developers actually modified this detail to conform to players' expectations. [[http://www.sirlin.net/blog/2010/3/11/gdc-2010-day-1.html Your chances for a drop do gradually increase the more you kill.]]
*** This was also implemented because of some "kill this mob and loot this item off them" quests, where the drop rate was not 100%. Some of these quests had unusually low drop rates, and you could spend an hour or more trying to finish a quest. With this change, the chance goes up and up with each "loot", and then resets itself to the default rate with every success.

to:

** Because people refuse to accept that improbable does not mean impossible or certain (or simply because the large variation in time required was ''annoying''), ''World of Warcraft'' developers actually modified this detail to conform to players' expectations. [[http://www.sirlin.net/blog/2010/3/11/gdc-2010-day-1.html Your chances for a drop do gradually increase the more you kill.]]
***
]] This was also implemented because of some "kill this mob and loot this item off them" quests, where the drop rate was not 100%. Some of these quests had unusually low drop rates, and you could spend an hour or more trying to finish a quest. With this change, the chance goes up and up with each "loot", and then resets itself to the default rate with every success.



* In one episode of ''WesternAnimation/TheSimpsons'', billionaire 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.

to:

* ''WesternAnimation/TheSimpsons'':
**
In one episode of ''WesternAnimation/TheSimpsons'', episode, billionaire 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.



* The Martingale system works if three conditions are met: the player must have access to infinite reserves of capital, the player must be willing to endure a losing streak of any length, and the house must tolerate a table bet of infinite size. [[CaptainObvious So it doesn't work.]] Casinos can hire mathematicians too; they'd never ''allow'' any system which can beat them, but what they will do is design it to look beatable.
** Now, losing ten times in a row is pretty rare right? Well, it's a 1 in 1024 chance, which means it's likely to happen before you win 1024 times, and almost certain to happen before you win much more than that. And that's assuming 50/50 odds. Basically, it's like the house is buying under-priced lottery tickets from you and you're hoping they don't win. Also, since you're playing so many games to do this, the "evening out" effect of the house advantage makes your chances worse than some other strategies (more information on that near the end of the trope description).

to:

* The Martingale system works if three conditions are met: the player must have access to infinite reserves of capital, the player must be willing to endure a losing streak of any length, and the house must tolerate a table bet of infinite size. [[CaptainObvious So it doesn't work.]] work. Casinos can hire mathematicians too; they'd never ''allow'' any system which can beat them, but what they will do is design it to look beatable.
**
beatable. Now, losing ten times in a row is pretty rare right? Well, it's a 1 in 1024 chance, which means it's likely to happen before you win 1024 times, and almost certain to happen before you win much more than that. And that's assuming 50/50 odds. Basically, it's like the house is buying under-priced lottery tickets from you and you're hoping they don't win. Also, since you're playing so many games to do this, the "evening out" effect of the house advantage makes your chances worse than some other strategies (more information on that near the end of the trope description).



* Similar to the roulette example above, gamblers apply this logic to slot machines, which is pointed out in the book ''[[http://www.amazon.com/Smart-Slot-Strategies-mathematical-strategies/dp/1453609261/ref=sr_1_1?ie=UTF8&qid=1351266797&sr=8-1&keywords=smart+slot+strategies Smart Slot Strategies]]''. The author points out how gamblers will ignore the fact that a machine is controlled by a random number generator and will assume a machine is "hot" or "cold" based on how it's performing. It's further explained that many players believe they can tell how a machine is programmed by playing the machine around 20 times, despite the random number generator having millions of possibilities. A sample size of 20 plays is far too small to determine any trend in a population that size.
** With that said, individual machines really can be set with different payout tables. Still, 20 plays is too small for trends.

to:

* Similar to the roulette example above, gamblers apply this logic to slot machines, which is pointed out in the book ''[[http://www.amazon.com/Smart-Slot-Strategies-mathematical-strategies/dp/1453609261/ref=sr_1_1?ie=UTF8&qid=1351266797&sr=8-1&keywords=smart+slot+strategies Smart Slot Strategies]]''. The author points out how gamblers will ignore the fact that a machine is controlled by a random number generator and will assume a machine is "hot" or "cold" based on how it's performing. It's further explained that many players believe they can tell how a machine is programmed by playing the machine around 20 times, despite the random number generator having millions of possibilities. A sample size of 20 plays is far too small to determine any trend in a population that size.
**
size. With that said, individual machines really can be set with different payout tables. Still, 20 plays is too small for trends.



*** Casinos have no problem with perfect play. It still awards the house a small advantage, and off that tiny statistical edge casino owners build financial empires. Some casinos give out cards with "perfect play" (called [[http://en.wikipedia.org/wiki/Blackjack#Basic_strategy Basic Strategy]]) on them. The gamblers often then lose even more because they buy into this trope and then don't believe the casino would tell you how to play Blackjack correctly.

to:

*** ** Casinos have no problem with perfect play. It still awards the house a small advantage, and off that tiny statistical edge casino owners build financial empires. Some casinos give out cards with "perfect play" (called [[http://en.wikipedia.org/wiki/Blackjack#Basic_strategy Basic Strategy]]) on them. The gamblers often then lose even more because they buy into this trope and then don't believe the casino would tell you how to play Blackjack correctly.



* Recognizing a [[http://en.wikipedia.org/wiki/Poisson_process Poisson Process]] at work. A simple question: if 21 just came up on a roulette wheel, which spin is most likely to produce the ''next'' 21? Most will naively conclude it is most likely in about thirty-eight spins or that all spins have the same odds of producing the next 21. In fact, the correct answer is the ''very next spin.'' After a 21 comes up, the odds of a 21 on the very next spin is one in thirty-eight. However, for the ''very next'' 21 to occur two spins later, first a 21 cannot occur on the first spin. In other words, the odds of a spin turning up the very next 21 is equal to (1/38)*(37/38)^(N-1), where N is the number of spins after that first 21. Consequently, this sort of process produces an exponential distribution of results. This applies in any such case where the process is truly random, from the flips of a coin to a gamer's dice. This accounts for the counter-intuitive "clumpiness" of real randomness.
** To clarify, the next roll is the ''mode'' of the distribution (the outcome with the highest probability) while 38 is the ''expected value'' (the outcome with the least variance). If you want to guess ''exactly'' when a 21 will be rolled, pick the next roll, but if you want to get ''as close as possible'' to when the next 21 is rolled, guess 38. Also, since Poisson is memory-less, you can start counting whenever you want--no matter if you just rolled a 21 or not, the next roll will always be the most like one to yield a 21, and the expected number of rolls before the next 21 will always be 38, regardless of history.

to:

* Recognizing a [[http://en.wikipedia.org/wiki/Poisson_process Poisson Process]] at work. A simple question: if 21 just came up on a roulette wheel, which spin is most likely to produce the ''next'' 21? Most will naively conclude it is most likely in about thirty-eight spins or that all spins have the same odds of producing the next 21. In fact, the correct answer is the ''very next spin.'' After a 21 comes up, the odds of a 21 on the very next spin is one in thirty-eight. However, for the ''very next'' 21 to occur two spins later, first a 21 cannot occur on the first spin. In other words, the odds of a spin turning up the very next 21 is equal to (1/38)*(37/38)^(N-1), where N is the number of spins after that first 21. Consequently, this sort of process produces an exponential distribution of results. This applies in any such case where the process is truly random, from the flips of a coin to a gamer's dice. This accounts for the counter-intuitive "clumpiness" of real randomness.
** To clarify, the
randomness. The next roll is the ''mode'' of the distribution (the outcome with the highest probability) while 38 is the ''expected value'' (the outcome with the least variance). If you want to guess ''exactly'' when a 21 will be rolled, pick the next roll, but if you want to get ''as close as possible'' to when the next 21 is rolled, guess 38. Also, since Poisson is memory-less, you can start counting whenever you want--no matter if you just rolled a 21 or not, the next roll will always be the most like one to yield a 21, and the expected number of rolls before the next 21 will always be 38, regardless of history.



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