If someone was gambling for the sake of profits alone and they later became extremely rich with infinite money, they might not stop gambling unless they don't have time to do so, if they have the time, they might even start gambling with a huge amount so that they can also win big and continue to double their finance. Both some people that even gamble for fun, when they become very rich, they could stop gambling.
You know that it's impossible for anyone to make profits in the long run, which makes it a bad idea for you to think that you can continue gambling for profits after having infinite money. If I am gambling for profits and I become wealthy, I wouldn't gamble anymore. I will channel the money into setting up an investment to double my wealth.
Yea, it's not that that person won't set up investments to create more sources of income for theirself, they will but depending on how attached the person is to gambling and how unsatisfied they are with the money they already have, they will still continue gambling with a huge amount of money so that they can keep multiplying their income. People are different and there are obviously many people like that.