I would trade with 1 billion. That will make the risk almost zero according to your logic. But if I have 1 billion why should I trade then? To lose it? With almost zero risk it will take years before I can lose it.... maybe it will even be impossible. It would make my life boring. So I am happy that I don't have money."Modest" is a relative term, but the simple fact remains, the more capital you start with, the longer you can survive, which has to equate to a higher success rate.
Starting with $10k and making a good living is probably squarely in lottery territory. Starting with $100k gives you better odds. $1mm even better, and so on.