Quote from neke:
There are ways and ways to trade the markets. Some profitable traders fade moves, some others go with the trend, yet others are direction-neutral, and of course some mix all of the above. It is naive to think all profitable traders see the same thing the same way at the same time. As for question about an "edge", that is better left to individual interpretation, but since I read somewhere you won a mathematical championship, I would pose this to you:
If you had $10,000 to start with, and staked 50% of your balance on the toss of a fair coin. Heads, you win as much as you staked; tails you lose your stake. (So if first toss is a win, you have $15,000 for the next play, and can stake 7,500). There is some chance that after 2 tosses you could be ahead. What is the probability of having more than $10,000 balance after 100 tosses? I pose this to you because you should easily be able to compute this from your background, and my own statistics tells me without an edge, leverage diminishes your chance of being ahead in the long-run and not the reverse.
Part of my drawdowns come from rule violations, and I seek to get better in avoiding those. Others are a natural part of my trading, and there is nothing to do than bear them. Drawdowns are inevitable part of my trading, and it would be silly to get worked up after every such. I have traded long enough to be able to put one week's result in the longer-term perspective.
Neke:
I think I see your point, and I am impressed by your clear thinking. What you are saying at the core of your post is that your own positive performance is proof that you have an edge with a high probability, because otherwise , and because you use leverage, you would have already blown out or at least have a negative performance by now.
So you prove by contradiction that you must have an edge (which is what people in probability would call almost-certain as the prob of the existence of an edge tends towards one. It should, the more you play and stay positive).
If I am allowed a friendly comment, I would say that "You are not as dumb, as the gyration in your equity may make you look". You have a very sharp mind. You understand deeply the probs.
Now back to your question about probability, which I will adjust a bit. In the game you offered, the arithmetic return for a large number of trials/coin is zero. So the probability of the arithmetic return to be higher than 10K is 50%. Now the answer to your question.
In the case the game should tend towards the geometric average, which is always less than the arithmetic average.
Therefore the probability that the balance will greater than 10k is LESS than 50%, because the arithmetic mean is always higher than the geometric and the former is already at 50% prob.
The more leverage one uses, the more one should be able to detect whether there is an edge or not.
Since you have used leverage, and your balance is positive in its return, I declare you have with an edge with a high probability (almost certain, but practically certain), even if I am not sure now what it is, although I think I have an idea why you have an edge.
Thanks my friend. All of you please give a hand to Neke. We just proved that he has an edge. The case is closed.