How about "Could sports betting be banned?" People are strongly motivated to do this and often spontaneously form networks to share bets. How exactly would the state put a stop to this? Even with really thorough access to all financial transactions it would be hard to prove what went on without direct testimony which is unlikely to be available.
Legalized gambling with big enterprises running it and ads visible to most people, many of whom wouldn't usually gamble, should be orders of magnitude worse than informal networks. One may not get rid of the latter, but stopping the former has a very great value.
Interesting question! Depends on how strong is your desire to ban it. The humanity has a long history of banning things, including certain plants, certain thoughts (for example, religious beliefs), certain ideas, certain symbols, certain pictures, and even certain numbers.
I have a few ideas. Criminal groups are often broken by having a police infiltrate the group and collect the evidence. We could have police officers joining the gambling groups (the groups need to accept some people, so they have someone they can make bets with) and catching the perpetrators. I also don't think that - at least right now - gamblers use tor or sufficiently anonymous proxies, so it would be easy to get most of them by just observing network traffic. Also, significant money transfers between random private people are uncommon. You can find sets of people who often do transfers like this, and find the "gambler networks".
