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Again, nobody's having issues with meaningful decisions in multiplayer games -- it's single player games that are proving to be the issue here, so that's what I'll be addressing. Firstly, for any single-player game, you simply have to have random elements.
If your game doesn't have randomness, then it has a correct answer, and if it has a correct answer, then there really aren't meaningful decisions for a player to make (it more closely resembles a puzzle as described above). Further, if you care about having any meaningful decisions, then "losing" has to exist in some form, and having several flavors of winning doesn't count!
Many of you who know about the dungeon-crawling genre known as "roguelikes" might know that they are one of the last defenders of this sort of play in a single-player game. The internet podcast Roguelike Radio recently had a show topic called "Roguelike Features in Other Genres" (listen to this episode here).
I was a guest on this episode, and I predicted that we were going to start seeing more and more quote-unquote "roguelike" features in all genres of single-player games. Not because of how great roguelikes are, but because roguelikes don't actually own concepts like "permadeath" (which really just means, losing) and randomization at all -- up until the 1990s, all games had these qualities.
Here's a few examples of single-player games that do, in my view, have meaningful decisions.
Klondike (the solitaire card game that came with Windows, which we often just refer to as "solitaire") is a solid example of a single-player game that has real meaningful decisions. I've been playing the game a long time myself, and while it might not be clear to some who've only played a handful of games, I notice these moments where I have a real choice that changes the future challenges and even the outcome of the game.
More recently, Derek Yu's Spelunky ran with this concept, literally, and became one of the first well-known platformers to do what I've always thought platformers should be doing: randomizing the levels. Because the levels are random each time you play, becoming good at Spelunky has absolutely nothing to do with memorization or any kind of "process of elimination". It has to do with your skill at making decisions in Spelunky.
Desktop Dungeons is not only a game with meaningful decisions, but it does so in a brilliantly innovative way. In the game, you gain bonus experience for defeating a monster that's higher level than yourself. So, you can choose to use potions early-game (usually reserved for the end-game boss) in order to defeat some mid-level monsters to get that extra experience.
It's a great example of an "ambiguous decision" -- you don't know for certain if the spent potion will be worth the extra experience or not. No level of experience playing other games will have really helped you make this decision, either. This is what's so exciting about games: the idea that when someone comes up with a game that's really new, it actually exercises your brain in new ways. It forces you to make new kinds of decisions that work in a way that your brain never had to work before.
If we can agree that meaningful decisions are important, then we can hone in, focus our games down on offering as many interesting, meaningful decisions as possible per moment spent playing the game. I call this "efficiency in game design".
While Klondike does have some meaningful decisions, it has many no-brainers, or false decisions -- so I'd say it has a rather low level of efficiency in this way. Spelunky's a bit higher, since it's real time and you're actually threatened most of the time, but there are still some situations that are no-brainers. Desktop Dungeons is highly efficient, and while it may seem to newcomers that there are no-brainers, better players realize that the most obvious moves are rarely the best ones.
And here's another way to look at the whole "ambiguous decision" thing -- this is what makes games special and interesting: even when you won, there was always room for you to have won by more, and you're not sure how. In contests, you always know how -- hit the moles even faster when they appear next time. There's no ambiguity about what you should be doing. In puzzles, if it's solved, it's solved. There may be different ways to solve the puzzle, but all solutions are equal. This feeling of "I wonder how I could improve" is what's so magical and amazing about games. In a way, games ask us to rise to our unknown theoretical highest level of ability, and this is really valuable.
I propose this philosophy about games not to be pedantic or controlling about how we look at games. It is my sincere belief that the only way we can really improve our games is by looking closely at what makes a game a game. I don't see many people really doing this; instead I see a lot of people simply echoing safe but conversationally useless ideas like "games are different things to different people".
Again, I propose that we remember that there is a thing called game, and even if you don't agree with my ideas, I hope that you do pursue your own truth about what games are, so that you can focus your games into the most efficient, fun games they can possibly be. To quote the author Robert McKee in his book Story, "We need a rediscovery of the underlying tenets of our art, the guiding principles that liberate talent."