A fork is usually caused by very low hash rate - whether or not it is more likely when solo mining, I would guess, is dependent on exactly how low that hash rate is. (sort of guessing here) 
I have got to learn more about blockchain construction, what's in it, how to interpret it. For instance, I just had a quick look through the block explorer in the wallet. Noticed that there's very erratic hashrates shown there from block to block. However, when I jump back to say block 200,000 or so I see the same thing. This scene and it's sparse tool-set has definitely brought out the old coder geek in me but let's just say that the last compiler I used was Borland C++ ... on my 386 (first one was Apple ][ Pascal!) Not really looking forwards to it but I'm also not looking forwards to being put out on the ice-floe this winter. S'true, they still do that up here.
Guessing by your local time - you in Alaska, or that region, in general?
My first "compiler" (lol!) was this "space age" doo-dad, er.. computer, that I got in 1978 for my 16th birthday. Wow - I feel olllllllldddd!
Wow! You got birthday presents? Awesome!
Ah, I never bother to set the time-zones on these forums. I'm from Mantoba where we've had to import our own (look up Red-River floodway). Great place to do some serous overclocking.