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I think that there's compelling counter-examples to the author's title, at least. The rest (about how trials shouldn't always be assumed to be independent etc)

I think that there's compelling counter-examples to the author's title, at least. The rest (about how trials shouldn't always be assumed to be independent etc) is interesting, but the title seems clickbaity and wrong. The bit where they present their main evidence against the gambler's fallacy: > So back to gamblers. What is the gambler's fallacy? Many have suggested to me that it's the tendency to think that a heads is more likely after a string of tails, despite knowing that the tosses are statistically independent. But this can't be right––for no one commits that fallacy. After all, knowing that the tosses are independent is just knowing that a heads is not more (or less) likely after a string of tails I think "no one commits that fallacy" is plainly untrue. There are various games (Gacha games, https://en.wikipedia.org/wiki/Gacha_game https://en.wikipedia.org/wiki/Gacha_game) where the outcome is random independent probability. In fact, due to gambling laws, these games have to publish exact probabilities. Despite there being clear evidence, people will commit a combination of the sunk cost fallacy and gambler's fallacy and convince themselves to spend more money on more independent random trials because surely they're almost there. We've seen similar things with lootboxes with published odds. We see similar things with casinos that contain various games of true independent random probability. They key difference here is between people rationally knowing that those odds are independent, and them being able to bridge that to their irrational belief that they're special, or lucky, or that they're "owed" luck. People are not rational, people can hold conflicting things in their head, and the gambler's fallacy is one of the common irrationalities a lot of people act on.

rahimnathwani 5y ago
"convince themselves to spend more money on more independent random trials because surely they're almost there" Interestingly, the Wikipedia page you linked says that in some games, the player's chance does go up with each roll. (Ctrl+F for 'pity')
flukus 5y ago
The author must have smarter friends than me because I've definitely witnessed mine fall for this fallacy. I've even had them ague that's it's a good strategy away from the casino where there are no sunk costs. > They key difference here is between people rationally knowing that those odds are independent, and them being able to bridge that to their irrational belief that they're special, or lucky, or that they're "owed" luck. I think in part it's just greed as well, they think they can have that money that all those unlucky people have lost. This greed then gets rationalized as luck/skill/smarts in a way that's not dissimilar to how people rationalize joining pyramid schemes.
- bombcar 5y ago
  Lots of people fall for it. Why do you think casinos show the last ten or so roulette numbers? They know when a streak appears passersby are more likely to jump in “because it can’t be red again”.
gretch 5y ago
> In fact, due to gambling laws, these games have to publish exact probabilities. These pre-determined fixed odds make it such that the games support the opposite of your argument. If outcomes were independent probability then it would be possible to for example win 100 games in a row (with astronomical probability, but it's still possible). In fact the machine owner neuters it so that the house won't lose in such a streak. Similarly, the machines have a fixed payout %. If each outcome were truly independent, it would be possible for the machine to never pay out, just like it's possible to flip Heads any arbitrary number of times in a row. Anyone sucked into these games thinking 'the next one will hit' is not committing to gambler's fallacy because these outcomes are not independent.
- morgante 5y ago
  The fixed odds do not guarantee that a certain payout will happen. You seem to have misunderstood how it works. The odds determine the likelihood on any individual roll, not some theoretical "payout per hour." Slot machines are based on RNGs. > If each outcome were truly independent, it would be possible for the machine to never pay out It is possible for a machine to never pay out. That would probably trigger an audit to see if there's a bug, but there is no guarantee that th
  - SimonPStevens 5y ago
    This may be jurisdiction dependant, but in the UK, the small prize fruit machine style games you find in pubs are required by law to payout a fixed percentage of their income over time. I believe it's 70%, but I think there are variations and exceptions to the rule. So if £1000 is paid in during the day, the machine by law must pay out at least £700 in prizes. This is not allowed to be fully random, the odds of each game are not independent because they must by law ensure the minimum payout. It's semi-common knowledge that the way to win at these machines is to watch them until you have seen someone else have a long losing streak, then take your turn when they leave as the machine is now 'behind' and overdue a payout.
    - morgante 5y ago
theptip 5y ago
A classic case of a smart person overthinking it; the answer really is that the average person is much worse at statistics than the smart person can believe.
fenomas 5y ago
I think you're being too kind - TFA strikes me as basically a long confused "if we assume X then we find X". I mean, in the introduction the author gives a standard definition of the Gambler's Fallacy, but then he immediately says "but it can't really mean that, because that's clearly irrational". It's not very hard to prove something is rational if you start by rejecting definitions that are irrational!

rahimnathwani 5y ago

"convince themselves to spend more money on more independent random trials because surely they're almost there" Interestingly, the Wikipedia page you linked says that in some games, the player's chance does go up with each roll. (Ctrl+F for 'pity')

flukus 5y ago

The author must have smarter friends than me because I've definitely witnessed mine fall for this fallacy. I've even had them ague that's it's a good strategy away from the casino where there are no sunk costs. > They key difference here is between people rationally knowing that those odds are independent, and them being able to bridge that to their irrational belief that they're special, or lucky, or that they're "owed" luck. I think in part it's just greed as well, they think they can have that money that all those unlucky people have lost. This greed then gets rationalized as luck/skill/smarts in a way that's not dissimilar to how people rationalize joining pyramid schemes.

bombcar 5y ago
Lots of people fall for it. Why do you think casinos show the last ten or so roulette numbers? They know when a streak appears passersby are more likely to jump in “because it can’t be red again”.

gretch 5y ago

> In fact, due to gambling laws, these games have to publish exact probabilities. These pre-determined fixed odds make it such that the games support the opposite of your argument. If outcomes were independent probability then it would be possible to for example win 100 games in a row (with astronomical probability, but it's still possible). In fact the machine owner neuters it so that the house won't lose in such a streak. Similarly, the machines have a fixed payout %. If each outcome were truly independent, it would be possible for the machine to never pay out, just like it's possible to flip Heads any arbitrary number of times in a row. Anyone sucked into these games thinking 'the next one will hit' is not committing to gambler's fallacy because these outcomes are not independent.

morgante 5y ago
The fixed odds do not guarantee that a certain payout will happen. You seem to have misunderstood how it works. The odds determine the likelihood on any individual roll, not some theoretical "payout per hour." Slot machines are based on RNGs. > If each outcome were truly independent, it would be possible for the machine to never pay out It is possible for a machine to never pay out. That would probably trigger an audit to see if there's a bug, but there is no guarantee that th
- SimonPStevens 5y ago
  This may be jurisdiction dependant, but in the UK, the small prize fruit machine style games you find in pubs are required by law to payout a fixed percentage of their income over time. I believe it's 70%, but I think there are variations and exceptions to the rule. So if £1000 is paid in during the day, the machine by law must pay out at least £700 in prizes. This is not allowed to be fully random, the odds of each game are not independent because they must by law ensure the minimum payout. It's semi-common knowledge that the way to win at these machines is to watch them until you have seen someone else have a long losing streak, then take your turn when they leave as the machine is now 'behind' and overdue a payout.
  - morgante 5y ago

theptip 5y ago

A classic case of a smart person overthinking it; the answer really is that the average person is much worse at statistics than the smart person can believe.

fenomas 5y ago

I think you're being too kind - TFA strikes me as basically a long confused "if we assume X then we find X". I mean, in the introduction the author gives a standard definition of the Gambler's Fallacy, but then he immediately says "but it can't really mean that, because that's clearly irrational". It's not very hard to prove something is rational if you start by rejecting definitions that are irrational!