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I mentioned the role that variants could take in replacing achievements, and I'd like to talk a bit more about that here.
Go through a list of achievements for one of your favorite games. Try to isolate the top five or 10 achievements or so. Let's say one says "win a fight without using grenades" or something. Now, instead of this being an always-on thing that gets triggered once you beat the game without using grenades, there's now a new Challenges Menu from the title screen.
On this hypothetical challenges menu, there are a number of, well, basically "achievements" that must be chosen from the start. It doesn't really make sense to have 150 different goals active at once. Beyond being noisy, the player will certainly end up getting some of these unwittingly, by accident, while trying to achieve some other goal.
So, the player can choose the "No Grenades Challenge", and then the game begins. Only once he's told the system that he's going for this challenge can be awarded that "medal" or, if you prefer, "achievement," for having won the game. If he achieves this without having told the system that he's trying to achieve it, it's not worth anything.
This might seem strange, but it's again important to remember that this is how games work! When we start a game, we must know precisely what the goals are, and are not. A player in chess can't capture a your rook, and then declare victory. "I was going for your rook! That was my goal!" The goal must be clear and agreed on by all participants up front, and no, single-player games are no exception to this.
Variants, unlike in-game content, are a great way to expand your game. There is literally absolutely no harm that can come to your game by selling players another game mode.
Puzzle modes of non-puzzle games are really great, not just for players, but even for designers. Creating a puzzle mode variant, where it's a non-random, pre-built puzzle out of your game system, can be a great way to analyze the kinds of depths that your game actions have. If you can't figure out how to make a clever puzzle using your gameplay's actions, then that's a pretty good sign that your system doesn't have enough depth, because the way that puzzles become hard is through non-obvious use of those actions.
I did this with 100 Rogues in a mode we called Challenge Mode. I found this mode, a puzzle-room mode, to be extremely useful in testing out the player abilities of the different classes. Many of the abilities got leveled-up -- or in at least one case, completely changed -- because of this phase of testing.
Other great modes to have are more story-based campaigns and episodes. It's a great, non-destructive way for people to experience the world you've created in a new way.
These are only a couple of examples, of many, many possibilities. With so much pressure to have good, fair DLC for our games, we really need to start focusing on different kinds of game modes we can add.
At the end of the day, variants simply represent new ways to experience your gameplay concept. Most variants won't be as good as the base game, but most variants also cost far less to "make", being that they are simply a modification of something that already exists, so overall, they're often worth the trouble. As long as we never allow ourselves to get carried away, or to lose the original game concept, exploring the possibilities of variants is only a positive thing.