I had a little flash some days ago, when I realized that we're dealing more often than we think with the mathematical value of infinity, when we try to 'create'. Take someone who wants to make a game - you start with the unlimited power of spawning, for example, creature after creature so that it can be farmed endlessly. Or you can write a little code in which from your apple tree each and every player can pick apple after apple. People even dreamed of stuff like this - the cornucopia. But that wouldn't be sports, and in an attempt to create a game of skill, you reduce the infinity to fractions. I think this is the wrong way to make a game, because when trying to split the infinite, we, being limited, lack a sense of proportion, and that will cause mistakes in the game. So instead of reducing infinity, you should create it (well, it's more about creating an image of it).
For example, if you think of a plan of square tiles of the same size, then you decide to reduce it to a limited space - say, 9 by 10, and then you split it in two and add pieces on the last two rows - that would be reducing the infinite. If you start by placing pieces on a space, in accordance to your purposes and the principles of interaction that you want to showcase, then you might end up with a boardgame on a board of 9 by 10, but it would be obtained by creating the infinite. How so: according to the mind of the players, the space obtained can be further expanded to limitless spaces, or a pawn can be seen as a squad of 10 people, or 100, or 1000. There is a sense of proportion to the game and in fact, what you might have created is a small replica of the universe.
All that may not matter when the end game looks the same, but I don't think you can get as good a result when you try to reduce the infinite. And that's an essential trait to cultivate if you're trying to create something: resist the temptation of believing in things such as 'godly powers'...