It would be necessary to see in which studies you can do your thesis on gambling. Mathematics or sociology come to mind, maybe economics too. And you have to find a thesis supervisor who is interested in directing you in that subject.
In my case I wouldn't do it, but I understand that there may be lines of research in these disciplines that could be interesting for a doctoral thesis.
I think gambling will be connected with the study of sociology, economics, and law because each study will explore the discussion of the thesis. But it all depends on what topic the thesis writer will use and if you use too many topics, the problem of discussing the thesis can become more and more.
Not many people want to be thesis supervisors, especially if gambling is prohibited in that country. It will take some time to find the thesis supervisor and I think collecting data for the thesis can take too long.
Gambling can be interpreted from so many perspectives that a thesis would probably only be able to focus on one aspect. If maths and statistics are going to be the focus, I can already tell you that it would require a very original perspective to create something new. Probabilities, statistics and other are well studied fields because these influence many industries already.