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Suggest you include a reverse of the r:r so you include 2:1 or even 3:1. I find in all the testing I've done that a bigger stop than target is more profitable than the traditional smaller stop and bigger target. However, I've never studied this using a coin toss for entries. Would be interesting to see if the coin toss results show the same as what I've seen.
I ran the random entry with all-in/all-out at a 2:1 and 3:1 risk/reward ratio. The win percentages went up to 66%(2/(1+2)) and 75%(3/(1+3)) as suspected and the expectancy was basically 0 in both cases also.
So, basically taking your findings. Trade management does not matter from a expectancy point of view. Over a large enough sample size all methods converge to 0. So it becomes a function of personal preference vs any mathematical gain caused by the usage of such methods. Basically the edge comes down to the trader, how he manages that edge in a specific situation may increase or reduce profits. But in the long run, no trading management technique is superior to any other.
I think you have summarized it pretty succinctly whereby the trader must have an actual edge for the straight long/short method of trading in order to make a profit. Management would be used to fit the traders personality as well as control drawdown along with sizing during adverse periods.
Now I guess the next step would be to do trailing stops, or break even stops. I just came to think of it. I think these may have skewing effects because they adjust during the lifecycle of the trade as opposed to being fixed. I may try to run this myself. My hypothesis is that its going to be detrimental, because in essence these things only occur when you have gotten MFE, not when you have incurred MAE. So your always taking your full loser when it comes straight down. But you take smaller winners in general because of the trail or BE stops.
In my opinion an edge is knowledge that a trader has developed about market movement which leads to a positive expectancy when properly applied. So if you have a positive expectancy then you must have an edge, but an edge does not guarantee a positive expectancy without proper application.
That is the $64 question. In my opinion a stroke of good luck will eventually run out but a true edge will keep on going until the markets change which leaves you with another problem as to when to recognize that you no longer have an edge.
In my opinion a stroke of good luck will eventually run out but a true edge will keep on going until the markets change which leaves you with another problem as to when to recognize that you no longer have an edge.