The Gambler’s fallacy, also known as the Monte Carlo fallacy (because its most famous example happened in a Monte Carlo Casino in 1913) or the fallacy of the maturity of chances, is the belief that if deviations from expected behaviour are observed in repeated independent trials of some random process, future deviations in the opposite direction are then more likely. (Wikipedia)
The reversal is also a fallacy, in which a gambler may instead decide that tails are more likely out of some mystical preconception that fate has thus far allowed for consistent results of tails; the false conclusion being: Why change if odds favor tails? Again, the fallacy is the belief that the “universe” somehow carries a memory of past results which tend to favor or disfavor future outcomes.
We assume nothing. This concretism is based on the fact that we cannot differentiate heads and tails (coin tossing), therefore both appear with the same probability and the coin tossing does not influence future coin tosses (independence).
Still, in order not to assume anything, we need to think a bit about Heisenberg’s rule. In an ideal world, where “nobody” tosses a coin in time that does not matter, under “no special circumstances”, it is true. But in real-world tossing requires assumptions, which leads to- I will leave you alone here.
Therefore, reifications may be true in closed mathematical environments, which I love, but in the same time mathematics needs to evolve due to, for instance, the goemetry is nearly for sure untrue and unrealistic in terms of objective existence. The same applies to set theory. And, here we see a problem related to Gambler’s fallacy. (see: paragraph 1; see: Poincare and movement from geometry to topology; see: Cardan’s attempts)
Cardan believ’d great states depend
Upon the tip o’th’ Bear’s tail’s end;
That, as she wisk’d it t’wards the Sun,
Strew’d mighty empires up and down;
Which others say must needs be false,
Because your true bears have no tails. (Richard Hinckley Allen)
Remembering states (second quotation) may be untrue but the problem remains, because reification involves the use of rigid contraints described earlier in the post. Still, based on the experimentally obtained know-how (muscle memory, transistor construction implying its memory etc.), I’d be careful with so-called fallacies. Of course, in the described closed environment everything’s okay.
See entrepreneurs that squeeze others to seek their nonexistent (and contradictory) dreams. They do understand Pytagorean triangle. Would the world allow them understand how it works? Partially paraphrazing Einstein and Goedel in this paragraph.