Nic,
If you can find and enter trades with a 3 to 1 risk/reward ratio, you cannot lose over the long run.
Unfortunately not true, as my example clearly showed. The problem is the 3:1 reward/risk ratio is determined before you are in the trade where you set your profit target and your stop loss and divide to get the ratio. And therefore it's very arbitrary i.e., should 1.50 be my target or maybe 1.00 (lower ratio), but I see resistance up there in the high of yesterday, or was it the close of yesterday, oops the trendline shows resistance at another point, oops the moving average shows resistance at another point, oops the bollinger bands show resistance at still another point, etc. etc.
Since reward/risk is determined before you enter the trade you could easily select a multitude of trades that appear to you (depending on what you base your targets and stops on) to have excellent R/R ratios. Yet the trades fail a good portion of the time because your targets aren't hit before your stops are hit.
In contrast, positive expectancy isn't determined before the trade, it's determined after reviewing a large sampling of your trades. So it doesn't care what indicators you use, how you determine your targets or stops, etc. It only shows whether, over a period of time, with ample opportunities, your system is profitable. Just like the casinos.