I'm recovering from a lot of activity over the weekend, so I'm not going to be saying much for a few days. However, I thought I'd direct people to Jason Vey's blog, where his recent article on reading the DMG cover to cover comments on how Gygax's design philosophy is the inverse of modern design philosophy: instead of starting from a core mechanic and trying to fit probabilities for success in different actions into that framework, Gygax starts with a couple probabilities and finds a mechanic that fits that specific range.
I'm not sure he's completely correct. Note, for example, that the 2 in 8 probability in Jason's example is also = 1 in 4. This is why I paraphrased his idea as "fits a probability range." If Gygax had an idea that he wanted probabilities from 1 in 8 to 3 or 4 in 8, he would have picked d8 as his base unless he knew he would need other probabilities that couldn't fit a d8 well.
I may gave more to say on this later.