Difficulty vs. Accessibility
A few months ago I wrote up a post on keeping in mind the assumed knowledge you have as both a designer and experienced player. It sparked a lot of great discussion, and I wanted to expand on a point raised. More than a few times it was suggested that if we try to make games for everyone, then our games will become easier.
However there is a big difference between accessibility and easiness. Making your game accessible could make your game easier, but accessibility does not preclude difficulty in the slightest. This is best explained by example.
Super Hexagon
Accessible, but Difficult.
Super Hexagon has two controls: move left and move right. It is clearly an accessible game — a new player could easily pick up the game and play it without any confusion.
However, it has just about one of the steepest difficulty curves of any recent game, especially on mobile. Lasting even a few seconds is extremely difficult until you get the hang of the controls and timing. Once you get into the flow and play for a while, you still get that brilliant feeling of mastery.
Super Hexagon is a great example of a game that is accessible, but difficult. The only needed skills to play are a fast reaction time and a bit of spatial orientation. Because of this, Super Hexagon is also a great example of a game with minimal assumed knowledge.
The Incredible Machine (Series)
Even with the complexity in the mechanics and level design, the game is very accessible to even a novice game player. Firstly, the mechanics are naturally intuitive (skeuomorphism): everything moves just as you would expect in real life. Bowling balls fall, mice run to cheese, and seesaws ... saw(?). These are naturally relatable mechanics that don't take more than a few seconds to 'get'.
Additionally, the controls make use of simple drag and drop — something that vast majority of users are already comfortable with.
For a slightly more modern take on this style of game, see the game The Fantastic Contraption.
Intriguingly, it is often the games we see as complex that are the most accessible. This is one of the reasons The Sims and Farmville became so huge— the only requirements to play are basic familiarity with a computer interface. Compare this to even a simple game such as Mario which requires learning initially unintuitive skills (which keys to press, jumping, side-perspective physics, correctly timing button presses, etc). More specifically, there is a distinct difference between the playable complexity and the underlying mechanical complexity in a game. Simulation games such as Sim City might be a complex knot of systems and mechanics, but the complexity of actually playing the game is quite low. While high playable complexity isn't always a huge barrier, it is useful as a game designer to be aware of these concepts. Otherwise you may find your intended audience has a tricky time adjusting to your "simple" mechanics.
This isn't to say that there isn't a reason to build complex, inaccessible games. However, as game designers, we should always have accessibility at the back of our minds, helping to mold design to adapt to ever-broadening numbers of players.
The last few years has seen a huge growth in the number of people picking up games for the first time. It's worth your time to take a moment to impress them.