Good OP talking about how to evaluate hands on the river.
But one question that's also interesting is, how can we use that grouping to guide us on the flop or turn?
For example, let's say that we have a flop of A
7
4
. How are we fitting different "made hands" and "draws" into the categories?
Personally I like to evaluate all my hands--both draws and made hands--by looking at the likelihood of what they will be by the river. For example, if I have AK with no clubs or diamonds, I think of that as, "very slim chance it will be the nuts or near nuts, some chance it will be a good hand, some chance it will be a hand of some value, some chance it will be a bluff catcher, no chance it will be trash". (Of course the actual percentages matter too.)
I think this is part of the point of the example that venice brought up about the KT vs. 87o (although I agree with BGP's analysis that the specific example is impossible). If we have AT on the A74 flop, there is a very small chance that by the river our hand will be better than a hand of some value or a bluff catcher, and those sorts of hands are always tricky to play. But if we have 65 with no clubs, then by the river we will either have the nuts, near nuts, a good hand, or trash, and virtually never will we have something in between. The chance we make a big mistake on the river is not as high as it is with the AT (we're less likely to miss bets we should make or call bets we should fold to). But, 65 is most likely to be trash on the river, while AT is somewhat likely to be a good hand, and almost all of the rest of the time will at least never be trash.
Also, this thought process--at least to me--gives more depth to how to evaluate draws. If I have a hand like 87 on a board of K73, there's an insignificant chance I'll make the nuts and a tiny chance I'll make the near nuts. So if I think I am behind, I'm almost never going to chase a longshot draw when I would only have "a good hand" even if it hits. It's not just about the odds of improving--it's also about how strong a hand I'm improving to.