The point is you don't know who will win until the match is over. Before the match it's purely a gamble with the odds determined by those betting. The odds will change as the match progresses. Any kind of trading that is not gambling is illegal.
It's a "little" bit more complicated then that. LOL. This is a controlled experiment you offered. You have the coin, you know it's fair and you know exactly the outcome possibilities. In the real world, you have thousands of coins you are flipping. You don't know if they are fair and you don't even know their distributions. So when this trader has a lucky run, we won't know if it's him or the coins. The coins in this example is analogous to the example I gave earlier regarding trading environment.
You have completely missed the point, oh well ... May I suggest a K12 course on the Probabilities Theory?
If you were to play Andy Murray at Wimbledon for 200 grand... would that result be random just because you do not know the winner ahead of time. Would it matter to you if you were to play one point or if you were to play 3 out of 5 sets.
Ok lets plug it in. I think I need help. Ok.... help me plug this in... when I was daytrading stocks. Which at times had one cent ticks. Not looking at commissions a representative year back then was.. 2000 round trip trades of stocks with an average of 700 shares and profit of $350,000 dollars.
Ok, here are the rough calculations. Assuming that your average take was $1 a share per trade, your Drift should be as big as = sqrroot(2 * 2000 * 1 /pi) * 700 = $24,984. The fact that you have made 14 times more than the drift tells me that your trading has an undisputable edge compared to the normal random walk. Is that the answer were you looking for?
Perhaps for the next run you do with jem you could ask him to fill you in on the facts. Say forinstance, what was his intial capital. Or something like: did you ever compound profits? Let jem fill in some facts. Here is an example: 27K is position traded. profits are compounded and no withdrawals. 62 trades are done 60 wins 2 losses. In 3 months the annualized ROI is 159K In four months the annulized ROI is 250K We all know the formula you are using. you add missing data to provide and example. Jem cannot follow. He tells you he cannot understand. At least explain to Jem how the formula you used would help him. He wants to know why he had to quit trading for a while. he wants to know why he has to repeat learning this or that lesson and yet not be able to learn to not freeze up anymore. Jem cannot analyze his problems because he has no knowledge or skills to problem solve. He cannot follow methods of any trader. He does not know how his gambles are working.
Often people say they are lucky when they get capital extracted from Wall Street. (it is given to their cause). I never really think about who gave me the money. It just keeps being made available.
I could probably do with re-doing High School stats/maths myself, but is the above correct? For a 1-D random walk on the integer line, of integer steps (i.e. +1, or -1), the expected translation distance after n steps (in lim n -> very large) is sqrroot(2/pi). I can more or less see how you would get from that to D = sqrroot(2G/pi) ... but the additional sqrroot(N) factor doesn't look correct ... is it?