I once found an algorithm named "gambling ruin" which means that when a player competes with an opponent richer than him he'll end up losing all his funds.
Well in that sense it makes a lot of sense, because it's true that the more money a Person has the more opportunity they have to play and win, but you have to understand something, a person who has more money can do a lot more than a person who has little money , and if that person who has a lot of money plays with small amounts then they will have a much greater chance of playing and even winning, but a person who has a lot of money can Play with such High Amounts that it Doesn't matter if they lose the first few times , if they win with a bet they are Capable of winning back Everything they have lost, that's the Difference.
It's a huge difference, but I was referring to the house in that algorithm. The house has more money than all the players. There's no possible means of defeating the house.
From a unique perspective, considering your idea, a low-income player competing with a rich player in a game is only wasting his money. Because the low-income player would lose all his funds, and his wealthy adversary would still have lots of money left on him.