Poker probability math is incorrect

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I see it in books; they say e.g. that an ace on the flop will decrease the chance that the opponent has an ace. That's not true as it decreases only the chance that the opponent has that specific ace, the reason being that that ace on the flop was dealt AFTER players' hole cards.

That mistake comes from probability math that doesn't necessarily take the order of cards or whatever dealt into calculations and so calculates only a certain kind of an average like the rounded number of 0.5 that could be anything between 0.45 and 0.5499.

I think the cards dealt are similarly more or less non-random when it comes to online poker. One doesn't figure the averages to effect that much, and it's more likely it's less random offline. But having experienced it and knowing the probability math being somewhat incorrect, it's possible, and in parts it can effect more as if the next card coming is calculated from 4 cards rather than three card, it's a huge difference. The mistake in probability math and what one experiences online fits well together.

I am aware of studies about the probabilities of specific cards or numbers coming on specific streets, and it's even enough though some sites just barely. But considering the same mistake being on every street and number, it doesn't prove the deal is random.