Consider a game to be a system, S. You can think of S as the rules of the game. S is a system of rules that can be modeled as a black box having input I and output O.

In the classic control system model you would then have :

IS = O

This basically means that the output of a system can be described as the product of input to the system and the inner workings (rules) of the system. Therefore the system model (rules) can be thought of as:

S = O/I

This simply means that the complexity of a system (the system model itself) is equal to the ratio of output complexity to input complexity. So as input complexity goes to zero, system complexity goes to infinity which is the definition of chaos and this works out well in our model. This would be equivalent to pulling the controller from the game console which means you have no control over the outcome of the system. However, it is safe to assume that this system can not exist perpetually. A system whose output is non-zero and has input of zero is also known as a perpetual motion device and via conservation of energy cannot exist in nature.

On the other hand, as output complexity goes to zero, complexity also drops to zero. Imagine the system is a vacuum or an open circuit (an infinitely long suspension of an OS that does nothing no matter what the input). In this case, no matter what you put in, you get nothing out.

Another way of stating the above analysis is to say that complexity is directly related to predictability. If the outcome of a system is predictable then it is safe to say that the complexity of the system is low. However, if outcome is less predictable the system is more complex.

Chess is hardcore and checkers is casual. In chess, the outcome of the game is very hard to predict and many players have tried to figure out the formula for winning but it tends to be a lost cause. Checkers on the other hand is a much more predictable system.

I think that hard core games tend to have complex input and of course, much more complex output. But there are are exceptions to this and there truly can’t be a formula that resolves a game to be hard core or casual because they are not divided by a clear border. However, I do think it is safe to say that a game with low input complexity will tend to be casual. For instance, the input in checkers is far less complex than that of chess since all of the pieces are created equal. You don’t have many options on your turn in checkers. In chess, there is complexity in movement of each type of piece. Just because the input in a checkers game is simple does not mean that the output is simple. In fact there are infinite ways to win a game of checkers. However, the simplicity of input makes it easy to learn to play and therefore more accessible to everyone. The complexity of the outcome in checkers is what makes it such a good casual game.

Now to finally answer your question:

So can you make a complicated rule-set accessible by limiting the interface? Can you reduce the rules of the game to a handful and make an otherwise complex game easier to grok?

I think the questions are answered by example. Take a look at Geometry Wars. The input is fairly simple. However the outcomes are wildly unpredictable. The rules of Geometry Wars are pretty complex and many interactions take place that change the outcome of the system. Very high output complexity and low input complexity make this a very popular casual game. I don’t think that making a game casual means you have to make the game system less complex. In fact, it may be better to make the game system as complex as possible while keeping input complexity to a minimum in order to maximize complexity and meaningful play when making a casual game.