Your thinking of the gamblers falacy. https://en.wikipedia.org/wiki/Gambler%27s_fallacy
That’s not what I was referring to. I am specifically saying, if you have suffered a string of loses that were truly cause by RNG and not misplays, then the only way to have a CHANCE to recover is to play at least twice as many games (typically, assuming a WR around 50%.)
I didn’t say anywhere that because you suffered an unlucky set of events your future is looking more likely to have fortunate events. I simply said you have a chance to average out the losses in your future games.
LUCK by definition is only important in short-time processes. That is, if you plan to play 12 games and win 12, LUCK plays a massive role, because sample size is 12. So whatever you roll in that small number of samples will have an outsized effect on the outcome. These short-timed processes are well known and documented (for example read the effects on skill vs luck in Major League Baseball https://sabr.org/journal/article/calculating-skill-and-luck-in-major-league-baseball/) to be extremely high in variance (see standard error description below.)
What I’m referring to in my post is actually a very simple property:
The standard error, which is defined to be an error on your estimate of a statistic (such as win-rate or skill of a player), decreases with the number of samples you take, but grows quadratically with standard deviation (RNG). See https://en.wikipedia.org/wiki/Standard_error
If you want a good understanding of games that have both LUCK and SKILL, I highly recommend reading topics on baseball. It is a really well studied game and really breaks this down.
For example, because final series in MLB have a small number of games (I think 7?) between two teams for the world title, even if one team is twice as likely to beat the other team due to being higher skill, because of the small number of games, the percent chance they will win the title is only ~60%, which is shocking. That’s how powerful RNG can be if you don’t give enough samples to average out the variance.
So when you watch competitive sports or e-sports keep this in mind. Because the sample size is typically very small, LUCK plays an outsized role in short events like tournaments.