1. Gambling in fact has many negative externalities. If someone gets addicted, the likelihood is much higher to be depressed. Depression is factor, which leads to high costs for the society.
2. Gambling addiction leads to economic costs because of crime actions. Other market actors have to increase their security standards, which means higher costs.
3. Many gambling addicts go as a consequence to jail. Jail means EXTREMELY high costs to society.
What are your thoughts on this topic?
While I do mostly agree with the points you raised, the claims that you made are all fallacious, being a slippery slope.
Any addiction caused to a person has always its negative externalities, not just gambling. While gambling may be considered one of those addictions that are common, you must also consider those other addictions as they contribute to the costs in society.
In addition, while those negative externalities in gambling are present, you cannot escape the fact that gambling brings revenue to the government. The revenue garnered from these gambling establishments enable to government to construct infrastructures which bring positive externalities as a result.
It is thus, imperative to know where to draw the line on how to balance these negative and positive externalities. While the result of gambling addiction is detrimental to the society, we also cannot disregard the financial aspect on how it brings revenue to the government.
Short answer: OP is right and there is absolutely no way the tax raised from gambling could cover the costs society incurs due to gambling/addicts.
Long answer: it requires extensive and fundamental research to actually come up with concrete numbers.
Especially online gambling socially isolates the players. One could argue that the five friends playing poker in the garden having a barbecue is even a net positive to society because of the recreational effect. How recreational the effect still is to someone sitting alone in front of his screen, I don't know.
Anyway, the topic is certainly interesting and a very good idea to look at it from the angle OP brought up!
Since it takes extensive research to come up concrete numbers I think we can't say gambling taxes collected by the government aren't enough to cover costs with problem gamblers. This industry profits a lot of money. Most people will never see such amounts of money during their life, so it's even harder to have some notion about this huge income application.
It's also hard to have notion regards the number of gamblers who will create such issues for the society. There are many people involved on this market and only a minority of them will present negative behaviors. Moreover, many addicted gamblers are rich people who can't control themselves. I think it's unlikely they will start robbing people or stores around to keep gambling.
I just saw I forgot to add that it does of course depend on the country and the tax laws. In some countries there is no tax whatsoever on gambling while in others there might be a pretty high tax. What is even more important is from what angle are you looking at the problem? Nationally? Globally? Here is why it is important:
First of all I would say that intuitively an activity where your loss is my gain and your gain is my pain doesn't sound like it could ever be a net positive in terms of social cost. But apart from that, if we look at a country with a gambling industry (take Nevada, Vegas), of course the statistics will show that Vegas is in an awesome position in terms of social cost. That is the national perspective. But what about the countries that the players came from and spend their money in Vegas? If they win money in Vegas they bring it home, spend it at home and reduce social cost. But no matter how you look at it, it is obvious that that had to come from somewhere in the first place.
So moneys balance can't be the basic measure for social costs here, I think we agree on that.
One of the questions that remains is does the winner spread so much positive energy that his surrounding society becomes more productive, and does that net out or even exceed the serious cost (maybe he lost it all) incurred by the loser? While the marginal effect of joy is strongly decreasing (that is scientifically proven), the loser could literally lose the ground under his feet, become an alcoholic, lose the job and destroy the family, cause the kids to get off track, maybe is forced to attend psychotherapists and what not.
I don't know, just some thoughts on the issue. I wouldn't look at isolated geographical areas. It is like: hey I got some statistics from Monaco, let's see if gambling their supports or undermines the socioeconomic system...