l don't think it's all about trading big or big risks. It's not just risk, but calculated risks. And yes, having the capital is a necessary starting point for big investments and prosperity. The operational word is 'calculated' risk.
Having big capitals and the mindset to select a good asset were you can buy at the right time is what makes one prosper in trading. Risk is part of our life and what the poor see as risk is what the rich see as opportunity.