I know it’s true, it’s just something that seems hard to wrap my head around. How is this not a logical paradox?
In: Mathematics
Considering both gambler’s fallacy and logical paradox are outside the understanding of most 5 year-olds, I’ll use similar level terms to what were in the question. The gambler’s fallacy (and indeed most fallacies) exist because they seem like they should be sound based off of what society assumes. Or, based off of what society assumes to be true. The fact that you think it is a logical paradox shows that you are susceptible to this fallacy yourself and should probably avoid gambling. Not meant as an insult, everyone has some logical fallacy they believe in, it’s human nature.
The coinflip one you brought up only makes sense if the outcome of previous coin flips somehow change its balance. But in this case, you would have to know what it landed on every time it was dropped, flipped, or jangled in its life. This is a false scenario though so doesn’t matter, other than to show the absurdity of past flips altering the probability of the next one.
If, before a single flip, you were to bet on 25 flips in a row being heads, yes, those are some long odds. If, after 24 heads you stop and ask what the odds are the next one is heads, its still 50/50 because, well, past flips physically don’t change the coin so individual flips are still 50/50. It would be the same as saying “I’m going to flip this coin 25 times. What are the odds the last one is heads?” It’s 50% chance, from the first flip, that the coin will land on heads at number 25.
TL;DR Individual flips are always 50/50 and past events and perceived future events don’t change that. The fact that this seems illogical to some people is exactly why the fallacy exists in the first place.
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