# What is the name of this logical fallacy involving probabilities of two unrelated events?

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?

• 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
• 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
• @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

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.