I'd count myself as moderately successful, and would quite happily admit that I've lost many times previously. That wasn't quite what I was referring to.
In the system we have wealth begets more wealth, and as much as you say you admire the American system for opportunities it creates, the great majority of wealthy people in America (truly wealthy, not merely upper middle), are not wealthy because of their own abilities alone - they are wealthy because their families were before them, and so on.
Privilege exists, quite clearly to anyone who looks, and privilege is what creates an unequal market.
Monopolies, slave labour and similar are all an artifact of privilege. I'm referring to the idealistic free market. I don't believe it can exist in any form larger than involving a few hundred people (at most) who exchange goods directly with one another.
I don't think freedom automatically means equality at all. Americans may espouse that all men are created equally, but I think anyone who so much as glances at America will be able to see little there to back these high concepts.
The greater starting wealth should be quite obvious. Whether people are entitled to their inheritance or not is not something I'm willing to argue over (I believe that they are, to a point). I'm simply pointing out that an imbalance in starting wealth when entering the market, will automatically cause the market to be unbalanced.
For illustration, please see how supermarkets pay farmers pittances for their produce. I'm not trying to argue morals here, simply illustrate that the market is not free and equal.