An important factor in game knowledge is the relationship between games which, although having various levels of complexity, are very similar in terms of logic and/or approach. For example, checkers is vastly different and simpler than chess, yet there are similarities due to the fact that both games are played on an 8x8 grid. In fact, a subset of these similarities can be applied to all "grid" games. Finding these similarities and capitalizing upon them gives a person a great advantage in playing a given game.

Two simple examples demonstrate the power of game relationships, or scalability between games. The first returns us to a classic problem in computer science. Freecell is a popular form of solitaire. But, when viewed from a slightly different perspective, it's also a form of the Towers of Hanoi problem. The common thread is the use of recursion and temporary space (piles or cells) to solve the problem. While Freecell is obviously a bit more complex than Towers, the concept is the same. What's really interesting in this case is how it relates back to the discussion of how people solve problems vs. how computers solve them. A human generally plays this game by making what he/she considers to be useful moves, i.e. they are specifically thought out and planned to reach the goal. A computer could much more quickly use a brute force method in which it tries all legal moves. This may result in a need to restart the game and requires a huge number of moves. Real AI comes into play in a program that attempts to finish a game using the same methods as a human. But a human is using instinct, experience, and pattern matching. How solvable is the problem for a computer when it can no longer rely on computational superiority?

The second example is everyone's favorite game of Tic Tac Toe (as available elsewhere on this site) but with a twist. Imagine a game for more than two players. For each additional player, another row and another column must be added to the grid. The object of the game is still to get three in a row. The game is interesting because it often results in a player having to choose between two other players to block. But it is also interesting because it scales well with original Tic Tac Toe. The gameboard for the expanded version can be thought of as a series of (sometimes overlapping) regular gameboards. The strategies (if they can be called that) for playing the game remain the same. The AI doesn't need to change much either. We can take this a step further, though. Instead of playing on a two dimensional board, let's try 3 dimensions. This is the true test of scalability. Again, much of what we know about Tic Tac Toe is directly applicable. But, can a computer adapt?