Having that budget and prevent getting exceeded will keep you safe and will still be able to call yourself as responsible, though it's tough to compete against your ownself as sometimes you'll find yourself in a situation where you think that you have big potential to win but upset happen after, those are the times that you need to consider and always knows your bounderies so even you exist some you'll be able to catch up and pause to reassess, that will stop the bleeding and prevent you lose more.
You're very correct, gambling without setting a budget is another way of getting yourself into trouble as you will not know when you're supposed to stop and Walk away. This is the reason why people easily get addicted to gamble once you fail to set a budget be rest assured that you will be gambling without limitation and this is one the problem that all gamblers would like to avoid. and yes, avoiding this problem is very easy. As a gambler or someone who is about getting started do ensure that you make a budget for your gambling maybe you can have a fixed amount that you will be using to gamble every day or maybe during weekends this would help in minimizing some risk and also prevent you from getting addicted to gambling.