This is true, what I believe before was the more losing I am the more I am near in the winning part which was not really true. I tried different strategies in dice game and what I realize is that you would only be profitable in long term if you have huge amount of bankroll, a strict strategy and at the same time a very low starting bet which was impossible and if you are going to win the profit will be way too small. They only way you can only win in provably fair games is by being lucky.
Though honestly, I find some players in crash game become profitable with their strategy I'm not just sure how much is their bankroll and I think it might be a combination of strategy and luck.
In the long run, it doesn't matter whether you have a huge bankroll or a very small one. The result will be the same because sooner or later, the casino will take your deposit anyway due to the house edge. The only way to avoid this in the long run is to stop in time, especially if you win a big prize.
But we cannot really deny that having huge bankroll give us huge advantage especially if we have good discipline towards our bets. Since having low funds will somehow make the gambler easily got drained especially if they are having a bad day.
Also you can do lot of things especially if some certain games or strategy you applied didn't work. And there are times that good situation happen and instead we are having a bad day there's lucky streak occur then we recover those supposed to be losses we gotten earlier.
For winning we can provably agree that both have same great chances it will matter on the discipline done by gambler if they can take out their winning or just totally got broke after their gambling session ends.