The amount of money you start with does not matter,as long as you have a good bankroll management and you know your limits. Obviously a rich person can afford to play higher stakes, take more risks, and win more money but at the same time he has much more to lose on the long term because he's got so much money. A poor gambler can only lose the amount of money he has, which is little and even if he ends up losing everything it won't affect him that much. If a rich person ends up losing everything to gambling, that would be a disaster for them and their life. Therefore, both rich and poor gamblers should be careful to gamble and risk only the money they can afford to lose.
You are right as poor people can invest a lower amount the chance of winning is low and obviously the winning will be low as usual. But as the rich people can invest more the chance of winning is also more and at the same time the loss amount also be more than a poor people.