Each coin toss is independent toss, but there is a whole Mathematics invented on that subject called Probability and Statistics. While not 100% it gives you a pretty good estimate on what happens next.

I went down the rabbit hole and lost much more than I should have. Not catastrophic but p’d me off. If you are correctly bankrolled and the table limits are generous for your stake and bankroll one should not lose. The problem is betting at nosebleed levels to gain that first small stake and losses incurred in the progression. Loss of nerve is a real thing. You are correct about the gamblers fallacy but I do know that streaks have a life span. They may be more than one is willing to bet or beyond the table limits but sooner or later the streak will end. The longer the streak the less it occurs. But that occurrence could be catastrophic to one’s bankroll. Thank you for your wise insight.

There is only one mistake to avoid and it is playing to begin with!!!

Every roulette system I've seen on youtube is based on gambler's fallacy or chasing losses or both

House edge is the same on everything.. doesn’t matter where you bet..

WHY WOULD YOU TELL PLAYERS THAT THE OUTSIDE PAYOUT IS THE LOWEST OF ALL PLAYING ROULETTE WHEN ALL PAYOUTS ARE THE SAME. IF I BET EIGHTEEN DOLLARS ON RED IS THE SAME AS ONE DOLLAR ON EACH RED NUMBER AND THE PAYOUT IS 35 TO 1 18 DIVIDED BY 18 EQUALS 1 MULTIPLIED BY 36 EQUALS 36 ) GOT MY POINT .