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.
If it were so easy to direct your capital to a place where it doubles, then why risk losing money in a casino instead of investing your capital in such a business right away. And even if it is small now, it would be possible to regularly reinvest the profits earned.