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I've often heard that you have better chances of winning the lottery than you do where X is some unhappy event.

Occasionally, I hear people who have actually experienced X say they should buy a lottery ticket, implying that because they have experienced X, they are more likely to win the lottery.

Is there a formal name for this fallacy?

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    I'm not confident enough of this to actually write an answer, but it could be a variation of the Hot Hand Fallacy, where previous experience of a rare event makes you think that additional rare events are more likely for you. The reason I'm not sure that quite fits is that it isn't usually applied to two separate types of events – Kevin Jun 1 '17 at 20:35
  • @KevinWells Additional rare events can be more (or less) likely depending on whether or not they comprise a Markov chain/process, e.g., randomservices.org/stat/markov/General.html For example, if you're diagnosed with and cured of a very rare cancer, recurrence of that same cancer is typically much more likely. Contrariwise, for much less (in this case zero) likely, if you're in a rare accident where,say, both your legs are amputated, it's "much less" likely that will happen again. Future outcome probabilities of Markov processes, on the other hand, are independent of past outcomes – user19423 Jun 2 '17 at 0:27
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    There is also affinity to the Gambler's fallacy, but I think the Hot Hand is closer. Erroneous probabilistic reasoning is a particular case of cognitive bias caused by heuristic inference patterns likely hard-wired into the brain. – Conifold Jun 2 '17 at 1:21
  • maybe synchronicity? Two unrelated events that occur that appear to be related, but are not. Or maybe syllogism? – Swami Vishwananda Jun 2 '17 at 6:56
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    @JohnForkosh Of course there are events that really are correlated or causative of one another, but the general idea behind that fallacy is that it applies to rare and unrelated events (e.g. being on a "hot streak" while playing craps, which isn't a real thing) – Kevin Jun 2 '17 at 15:33
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According to Wikipedia, this is an informal fallacy known as the "Post hoc ergo propter hoc"

Latin for "after this, therefore because of this" (faulty cause/effect, coincidental correlation, correlation without causation) – X happened, then Y happened; therefore X caused Y.

This fallacy becomes the foundation of the anecdote described in the OP. Thus it creates a "regression fallacy"

Ascribing cause where none exists... failing to account for natural fluctuations.

Or perhaps you can apply the informal fallacy known as the "Gambler's fallacy"

the incorrect belief that separate, independent events can affect the likelihood of another random event. If a fair coin lands on heads 10 times in a row, the belief that it is "due to the number of times it had previously landed on tails" is incorrect.

This can be paired with the "hot hand fallacy" which uses the same flawed reasoning to say that the pattern of a series increases the likelihood of it continuing. In this case, "If a fair coin lands on heads 10 times in a row", the belief is that it will continue to land on heads again. Or the fact that a person has guessed correctly what face would be up 10 times, means that they are more likely to be correct the 11th time.

LINK

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  • I think it's just the latter. They're trying to figure out what will happen next, not what caused something to happen. – Canyon Jun 2 '17 at 1:13
  • I actually think the Gambler's fallacy is exactly the opposite. The gambler's fallacy generally states that you expect small sets of results to follow the probabilities too closely. Meaning if you flip a coin and it lands heads, the next one is more likely to be tails (which isn't accurate). In this case the assumption is that one rare event makes another rare event more likely, which would be more like flipping a coin 10 times, getting all heads, and assuming that that makes it more likely that you could get 10 heads in a row again (also inaccurate, but in the other direction) – Kevin Jun 2 '17 at 15:36
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    I also don't think "Pos hoc ergo propter hoc" applies here because that would take a form more like "I got struck by lightning, then a won the lottery, therefore I won the lottery because I got struck by lightning", which isn't the OP's scenario – Kevin Jun 2 '17 at 15:38
  • @KevinWells If a person was struck by lightning and then won the lottery, and then was struck by lightning again, wouldn't that be the exact scenario the OP describes? Perhaps it only describes the situation that establishes the presidency that leads to the scenario the OP describes. – PV22 Jun 2 '17 at 17:41
  • Yeah, in that case that would make sense, but the OP describes someone who has been effected by one, but not the other yet, so there isn't a precedent from which to establish a pattern – Kevin Jun 2 '17 at 18:56
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I have seen such comparisons between unrelated and rare events, but only to illustrate a point, not to argue for some kind of cause and effect. Typically the event is something catastrophic that gets a lot of public attention. Pointing out that the chances that the event will happen to any given person are lower than the chances of being struck by lightning is to put things in perspective.

If the proponent is saying that the one unrelated event is affecting the other, then the ordinary pitfalls of such arguments appear.

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