I would describe this situation in 2 types.: -
If you are playing for entertainment then you can play with profits earned if any.
If you only play for profit then, you should not play with profits. You should take away profit and leave the game. Because longer you play more you while end up losing.
I don't think there's a big difference in what you are telling because it's almost the same, it's just that the goal is different. I think no one is going to think of just playing for entertainment when you start winning, you would feel you would have a lot of chance to win more and in the long run, you'll end up losing again.