In my own opinion, the best way to reduce gambling addiction is by educating the masses about the problems associated with gambling addiction. Letting people know gambling addiction can affect their daily activities and also financial status negatively will go a long way. Placing a ban like you mentioned is a no no, it would rather escalate the situation.
This is actually a pretty good suggestion. I also believe that enough knowledge about something can make a difference which will allow people to make better decisions and sound judgement.
Banning gambling won't do much change in reducing the addiction in one country. Gambling is also a business for those who own casinos, and the like. And they will surely disagree with it (ban). Another is that, being an addict is a choice. It's a matter of self-control. People are somehow blinded by the benefits alone without considering the risks it possess. So giving them insights may be able to change their perspectives.
Educating the mass may not change those who are already addicted but for others who are prone to become a victim, they must know better so they will not be trapped in the pitfalls of gambling and other forms of addiction, in general.