What do the systems of games amount to?

The goal here is not to list what the objective or victory condition is in a game, but to say “what the game amounts to” or “what is actually happening”, “what is the player actually trying to do?”

The biggest problem with this list is whether to include the psychological or just the “physical”.  Poker is about bluffing, about reading the other player, yet what the game amounts to in each hand is a form of pattern-matching plus collection (of money).  I think I’ll leave the psychological out of this list, and stick to the systems.

At some point another problem is, what is a game?  For example, I’d say most single-player video games are actually interactive puzzles, not games, but we call them games.  Fortunately, the list below also applies to many if not all puzzles.

“Achieve a particular state” is the generalized version.  Victory points are a generalized way of doing several different things at once.  Sometimes the “state” is very simple, as in rock-paper-scissors where you want to make a pattern, such as paper to the opponent’s rock.

The list includes the general activity, then some of the common variations.
When we come down to it, most games are about just a few things–in no particular order:

1.  Get to a particular place
    Get there fastest (a race) [player interaction may be missing]
    Get your any of your pieces there (Axis&Allies enemy capital)
    Get a special piece there (football, hockey, many other team sports)
    Get to end of the story (console RPGs)

2.  Collect something (many card games, many video games)(sometimes economic)
    Find something (exploration) (Easter egg hunt)
    It drops in your lap (draw a card)
    Take it from someone else (Monopoly, some card games especially trick-taking)
    Don’t collect something (Old Maid, Hearts, etc.)

3.  Wipe someone or something out (Risk, shooters, checkers, bowling!)
    Wipe out one thing—chess

4.  Achieve patterns in something (getting to a place could be seen as part of this!)
    Patterns in piece location (this includes rock-paper-scissors, Tetris, many puzzle games)
        Only your pieces (Tic-Tac-Toe), or yours plus opponent’s (rock-paper-scissors)
    Patterns in relation to the “board” (Scrabble, Carcassonne)
    Patterns of cards (related to sets–e.g. Canasta)

5.  Improve your capabilities. This is often subsidiary, a way to achieve something else.  Common in RPGs, vehicle simulations, construction/management simulation, collectible card games)

6.  Survive, Especially common in arcade games (which are generally unwinnable).
I’m not sure about “engine” games, where you’re trying to make the right moves to take full advantage of an often economically-based system.  In the end, you’re likely doing one of the six things above when you make a “right move”.

So what have I missed? I’m sure other people have made such lists, but I need references to such.