Please go and read what the gambler's fallacy actually is, since it's not what you posted. What you posted is an entirely different fallacy (which I don't know if it has an official name), but I would call something like the "odds fallacy".
Here's a helpful
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, if you don't want to google it.Yes, as you roll more attempts, the chances of getting at least one success approach 100% no matter how unlikely that event is, which is NOT what the gambler's fallacy is. It is only about the lack of memory between one random event and another, but humans tend to assume that a small number of samples hold true for a larger sample. Roulette colors landing is where this was first codified, thus why I used that in my example. Coin flips, child genders, and other similar random events with a low number are easiest to see this with, but low probability things in games often lead to the assumption as well. Like thinking the boss has a 5% chance of dropping item X, so the more times I run the boss fight the more likely it is to drop X.
Regardless, this is going to be the last I post on this, since it'll get progressively more off topic (and possibly start a flamewar) if I continue.
