I was flipping through my copy of the 1e DMG today and realized that it's the only place I've ever seen a discussion of probability in a game book. (This may be because I haven't been reading the right RPGs.) This is how Gygax decided to open his Dungeon Master's Guide, and it makes a lot of sense: a thorough discussion of the tools of the trade. But as with a lot of what I've noticed about the DMG, there's a very specific attitude embedded here, and one that's really different from the one I associate with the later editions of the game that I got into the hobby with.
What I find interesting here is that Gygax assumes that you're going to be building your own random tables, or using the dice to adjudicate results on-the-fly. You've got to know how your dice work, so you can get them to give you the randomization or oracular input you need. Instead of a series of universal mechanics that, in theory, cover everything, you get some basic principles that help you make the decisions you need to make as they come up.
What opening the DMG with a discussion on probability says to me is: Sooner or later, you're going to need the dice to help you resolve something that the rules don't cover, or to give you some ideas to handle some wacky thing that your players just did. Which is just about exactly what I want the beginning of a guide to running a game to say.