Re-read my last post.
Risk:Reward ratio would be better named stop:target ratio.
If indeed you have a system that has 50% winners and 1:1.2 'risk reward ratio' then it is not random - it has a 20% edge. The edge is not necessarily present in the stop:target ratio, it could be present in the win %age.
You're trying so hard to prove your point, you're not listening or reading carefully.
either we're not talking about the same stuff, or your just stubborn.
if a system has 1:1.2 ratio (empirical, not pre-determined) and W% is 50% then the system is not a random entry one? are you OK?
a system is random entry, if the ENTRY IS RANDOM, time and direction.
about that +ve expectancy system blah blah. check out MA Xovers on a EOD data basis.
100 and 350 days MA. take that system and run it over high volume futures. it's a positive expectancy one.
basic money management. short stops vs large rewards (I'm not using the term targets, because in my systems I don't use targets - targets are boundaries for profit.)
pyramiding (martingale). position sizing of small percentage of equity. all those will turn a 50% W% to +ve expectancy one.
take a look at long term trend following systems.
they all have in common lower tan 50% W%, but much karger than 2:1 or even 3:1 risk reward ratios (empirical). and if it's empirical, it means that the chance of hitting the stop is in there.
so, there's absolutely no doubt, that you can turn a random entry to a long term trend following system.