I would like to introduce a game to the mix that you've probably never heard of. It's called "Corners" and it's played on a table (usually a 4-1/2 X 9) with only 2 pockets, located at the head of the table. The other rails were straight like those on a billiard table. There's a photo of a Corners table that I now own on the first post of this link. It's a 1923, or later, Brunswick Aviator. Unfortunately, it's been in storage since I bought it. Maybe one of these days I'll have a place to set it up. I keep hoping.
https://www.google.com/url?sa=i&rct=...49680307210967
Each player had a pocket and the winner was the first to get 8 balls in his pocket (the tables had deep pockets). There was no penalty for scratches and once a ball was in either pocket, it stayed there. Other than those unorthodox rules, the game was similar to one-pocket - except banks were much more prevalent, as you can probably see. Tons of 2 railers of various types, quite a few 3 railers, and occasionally a 4 or 5 railer. It was a much more aggressive game than one pocket. A bank example is that a ball frozen on a side rail could be shot down the rail into the corner and back up the rail into one's pocket.
It seems that Corners was played mainly (or, only) in that area where MO, KS, and OK come together. In my home town of 8,000, there were 3 pool halls, all within 2-1/2 blocks of the school (grades 7-12). In each, the front table, the one with spectator benches, was a Corner table. It was by far the most popular game, especially among the better players. Starting at age 12 (1952), I played mostly Corners - before school, during lunch break, after school, and all day Saturday. We usually played Snooker and Golf (on a Snooker table) on Sundays, for some reason. From ages 12 through 21, I estimate that I played about 40-50,000 games of Corners.
Corners lost its popularity and the last table I saw in a pool hall was about 30 years ago. I think most were converted to 6 pocket tables by re-cutting the slate. At present, I only know of 3 Corners tables. Mine, one in a bar in Joplin, MO, and I've heard there's one in someone's home in Hume, MO.
As far as my definition of "pure" goes, I would say that Rotation and Straight Pool are the "purest". Very simple straightforward rules. With one, you just shoot in numerical order and the other you shoot any ball in any pocket. Many other games seem more contrived to me, although I like some of them better.
My favorite games are, in order:
1 - Corners
2 - One-Pocket
3 - 3 Ball
4 - Golf on a Snooker table
5 - Eight Ball, if I had to pick another one.
In pool, like everything else in life, you like what you are good at and you are good at what you like.
I would love to try One-Pocket on a Corners table.