I believe that if we're playing a game with a house edge, where winning depends purely on luck, then bankroll management doesn’t really matter.
What you deposit is already intended for gambling, so whether you go all-in or divide it into smaller bets, the reality is that bankroll management won’t change the odds. It just adds an extra layer of stress in making decisions that, in the end, won’t really affect the outcome of a luck-based game.
But I guess the bigger the bankroll, the higher your chances of winning?
So it might slightly go in your favor let's say for a slot machine, your budget is $100.00 and maybe with lower stake, your bankroll will last that long and maybe you can hit a bonus and win big. So as let's say your capital is just $50.00 or less, only couple of spins for you and you will be unlucky and not hit anything.