I think you are thinking about this the wrong way.
Profitability is not about your per-transaction profitability "batting average" as much as it is your total profit relative to the mean over time.
If you make one transaction, and you make a profit, by your metric, your strategy is "truly profitable" because you have made a profit 100% of the time. Not a good metric.
Instead, what you really want to be thinking about first is what is your overall profit, and second, how it looks relative to the average.
In other words, if I make ten transaction that cost me each $1, but I make one transaction that makes me $100, I would say that my strategy would be profitable, since I'm now up $90. However, if an index fund would have made me $1000, I would say that my strategy was probably a poor one, because of the opportunity cost of other investments (even though my strategy was, by definition, profitable).
Now, look at how your strategy performs over time. Which is how you often look at funds: if I invested $X in MyStrategy vs IndexFund, and after a few time periods I would have $Y in MyStrategy and $Z in IndexFund, the measure of my performance is $Y-$Z.
Lastly, and most importantly, remember that past performance is no guarantee of future performance. A couple of good transactions does not mean your next couple will be good.