-snip-
I think not all of them but some just focus on their new task. This alone can already give them a good salary so why not look for more? It can only gave them a stress and they won't have enough free time anymore for their selves or their family. For those politicians who have a business, the public knows their business because they promote it at the same time when doing campaigns.
It also gives them a free exposure when they promote their business alone. There is no point of hiding the business as long as it was legal but some politicians are involved in a drug trading business but no matter how hard they hide it, it is still being discovered by the public.
I think you know for yourself the nature of humans, namely always feeling lacking and greedy so they have thoughts of getting even bigger results or salaries so they will do everything they can to make it happen, one of which is by doing the gambling business or other businesses that make a lot of money even though that is an illegal business.
There are lots of politicians like this and as an example some politicians in the country where I live they hold several businesses such as gambling and selling alcohol which is clearly prohibited in my country.
What is clear is that when politicians have a gambling business, no other party dares to mess with it because they have the power so that they are well utilized.
