> be wary that the subconscious is constantly generating narratives to explain statistical anomalies
This comes up all the time in sports. Let's take pool for example. There are various guesstimates floating around, and I do not have access to detailed tournament statistics, but I have heard that in games where sinking a ball on the break is an advantage, for decent players there's maybe a 75% chance that a ball will go down.
So once in every four breaks, you won't sink a ball. How often do you fail twice in a row? Once in every sixteen breaks. Failing three times in a row? Once in every 64 breaks. Four times in a row? Once in every 256 breaks.
What about five straight breaks without sinking a ball? Once in every 1,024 breaks. That's a lot of breaks. But wait up a moment.
Let's ask, "If you miss a break, what're the odds of it becoming a streak of five misses in a row?" The answer is, "One in every 256 streaks of misses will be a streak of five or more misses." 1/256 is not particularly rare, if you play often enough to sink a ball on the break 75% of the time.
What is the point of knowing that a streak of five misses in a row is rare but not that rare? Well, if you miss five in a row, do you chalk your cue for break number six as usual? Or do you tell yourself that your break isn't working, and start adjusting your stance, aim, spin, &c?
If you start adjusting everything when you get a streak of five misses in a row, you may just make things worse. You have to pay enough attention to your distribution of misses to work out whether a streak of five misses in a row is just the normal 1/256 streaks, or if there really is something amiss.
The brain is a great pattern matcher, but it sucks at understanding statistics.
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The flip side of this, of course, is that if you upgrade your brain well enough to understand statistics, you can win a lot of money.
If a pro misses five in a row, feel free to wager money that they'll sink a ball on their next break. Your friends may actually give you odds, even though the expectation of winning is 75-25 in your favour.