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If strangely compelling coincidences are something you are looking for, you can look at different subjects of interest besides aliens to widen your chances of hitting the lottery. With a pool of 500 subjects involving holy text chapter wordcounts, wikipedia historical event dates, and landmark coordinates among other possibilities, you are more likely to hit the lottery in one subject so that when you narrow down the scope it seems profound and impossible. From there you can create a narrative about why something like that happened because it seems too unlikely to happen by random chance.

I think ultimately if you are looking at info at face value without also digging deeply into how people found out about it in the first place, you are more likely to get tripped up into making strange conclusions even with perfect understanding of probability.

In a world with imperfect information, or where people are willing to lie about their methods, there's not much that can be done but accept that you will be fooled on occasion.