Statistically if you had enough hashing power to more or less assure yourself a solved block before difficulty change then you could potentially come out even or ahead. Otherwise in an accelerating difficulty frame solo mining will fall behind pooled mining for most people. Luck is, of course, luck.
This is a bogus argument.
Consider: You give me a dollar. I roll a six-sided die. If it comes up '1', I give you $1,000. You only get to play once.
Is this a good deal? By your reasoning, it's not. Most people who take the deal will come out behind $1.
That's a stupid comparison as it is completely unrelated and has nothing to do with my reasoning.
The two cases are precisely the same, it's just more obvious in my example. With solo mining, just like in my deal, most people will come out behind. However, with solo mining, just like in my deal, the expected return is greater.
The difficulty change is irrelevant noise. It's based on the mistaken notion that you need time to allow the law of averages to even things out. That is not true. Playing a slot machine one time has precisely 1/100th the expected loss of playing the slot machine 100 times. If playing once is a bad deal, playing 100 times is 100 times worse. If playing once is a good deal, playing 100 times is 100 times better.
I think you have the "Law of Averages" backwards.
The law of averages is a lay term used to express a belief that outcomes of a random event will "even out" within a small sample.
Quite the opposite of what you are suggesting.
Anywho, the cases are not precisely the same. There is a difference in valuing what you already possess against what you can potentially gain, against what you can potentially gain vs. what you can definitely gain.
Furthermore going back to the original point, all statistical probability requires a large sample, in the case of mining bitcoins, this sampling is time. If I flip a coin one time I have a 50/50 chance of either result. If I flip it twice, same thing. By your logic no matter how many times I flip it, betting on heads will yield the same results, which is completely untrue. Given a large enough pool of flipping it will come out 50/50. But on a small scale betting heads every time can yield profit, or loss. Large numbers and small numbers are not equivalent.
I don't really want to get into the mathematics because while I have a decent handle on it, it's not a current enough aspect of my life that I can whip out equations off the top of my head. But rest assured that while statistically independent events are not the same as mutually exclusive events. Events that are independent can in theory either never or always occur, so why does this not actually happen given Big samples? Something to think about.