To go back to the original point I was disputing, I will try and make myself clearer - I am not for a second saying it is not possible to have a profitable trade, nor am I saying stops are a bad thing or shouldn't be used. My point is that in order to make a profit, you have to predict the market direction more often than not - regardless of how you skew the payoff in terms of stop vs take profit.
Assume the following:
A liquid asset trades at S
Your stop is at S - n
Your profit is S +xn where x is bigger than 1
If you have many more losing trades than winning trades, fine, you have a big value for x required. But that is only a very simplistic model. Assume you have a standard stochastic process obeying Brownian characteristics, which is reasonable in this example. That means you have a 50/50 of the price going up or down. However, the end result is path dependent. It is the fact it is path dependent that makes the difference.
In essence your stop is a knock out level. So, your upside optionality is reduced, because you can knock out your profitability. Smaller the stop, larger the probability of knocking out, larger the x you need.
It doesn't need to be complex in any way - in order to profit, you have to beat the market. Your returns have to be better than the statistical average. Given than any independent trader has limited information, limited access to liquidity, limited reaction time, and is a price taker only, it is highly unlikely that you will make money without having an edge. In turn, its very unlikely you will have an edge on the market.