Yeah, if a player doesn't worry about bankroll management and doesn't control his emotions, the chance of winning will be close to zero in the long run. It seems to me that the optimal bankroll for slot games should be 500 or even 1000 times more than the initial bet per one spin. In other words, the principle is the same as in poker, except that the dispersion in slots is clearly many times greater than in poker.
Your chance of winning doesn't directly correspond to your bankroll management as you could win from your first bet or not with whole budget.But yes you should be utilising your funds in a very effective manner on slots or any game you prefer but aggressively going above your budget is bad for yourself and should be managed well.
This is true. Bank roll management just lengthened your survivability rate since you can avoid improper increases of bet due to spur of the moment emotion. I usually set a huge bank roll when playing table games and stay on my normal base bet until I hit my lucky streak then leave. I usually stick to this strategy even if I’m losing at the start since there always a time that I can recover all my losses by continuing playing using same bet as long as I still have money to continue playing.