But the money can also go from the wealthy to the poor. If the tax from casinos gets collected by the government and is used effectively, it can help a lot of those in need. The money can be used to improve infrastructure, education, healthcare and etc.
This is what's happening in our country, there is so much tax in the gambling sector but we don't know if they are actually budgeted into infrastructures and the other sectors that you've mentioned. While there is a good purpose for it. If we speak about the effects that it gives individually, the wealth distribution in gambling isn't really going to the poor but to the casinos because the house always wins. But if it's in general way of gambling impacts the entire economy, that's one way of them giving back but it's through taxation.
In fact, I will say gambling taxes are widely discriminatory, you know low earners spending a large proportion of their income on wagering, flipside benefiting far less from tax funded scheme. For example I could mention clubs in Victoria, which spend just 1.5% of pokie revenue on seniors welfare, most of which is consumed on venue costs. If you look over USA, states accumulate billions from gambling tax revenues, where a few dust amount are going to addiction services, maybe less than 1%. Other hand mental health burdens remain unaddressed, though they consider these as larger social costs.