FUNDAMENTALS OF GAME DESIGN, SECOND EDITION
Logic and Mathematical Challenges
Logical and mathematical reasoning has been part of gameplay since the dawn of human history. Logic provides the basis for strategic thinking in any turn-based game of perfect information and many other games in which the player can make precise deductions from reliable data. This section is confined to logic puzzles. The "Strategy" section, later in the chapter, deals with strategic thinking.
Mathematics underlies all games in which chance plays a role or the player does not have reliable data and so must reason from probabilities. Such games present explicit mathematical challenges to the player: If he doesn't compute the odds when playing poker, or at least know the odds and reason correctly given what he knows, he's much more likely to lose.
In the broadest sense, any game that includes numeric relationships offers a mathematical challenge, because the player must learn how those relationships work. Much of the time, games present mathematical challenges implicitly, couching numeric relationships in other terms: physics, strategy, or economics. (For an example about strategy, see the section "Production Rates, Unit Numbers, and Lanchester's Laws" in Chapter 14, "Strategy Games.") Other sections of this chapter deal with implicit mathematical challenges.
A puzzle is a mental challenge with at least one specific solution. Formal logic means classic deductive logic in which the definition of the puzzle contains, or explains, everything the player needs to know to solve the puzzle. A formal logic puzzle can be solved by reasoning power alone. It shouldn't require any outside knowledge. Many other types of puzzles require logic too, but they also expect the player to supply some additional information.
A logic puzzle typically presents the player with a collection of objects related in ways that are consistent but not directly obvious. To solve the puzzle, the player must put the objects into a specified configuration. The player manipulates the objects and receives feedback about their relationships, which he eventually comes to understand by observation and deduction. Rubik's Cube, a classic logic puzzle with a simple mechanism, consists of so many cubes that move in ways so intricately interrelated that it is quite difficult to solve.
Adventure games often present logic puzzles as combination locks or other machinery that the player must learn to manipulate because those devices make sense in the fantasy world in which the game exists. Other puzzle-based games don't try to be realistic but concentrate on offering an interesting variety of challenges.
To adjust the difficulty of a logic challenge, raise or lower the number of objects to be manipulated and the number of possible ways in which the player can manipulate them. A Rubik's Cube with four tiles per side (a 2 x 2 x 2 cube) instead of nine (3 x 3 x 3) would be far easier to solve.
Players normally get all the time they need to solve puzzles. Because different people bring differing amounts of brainpower to the task, requiring players to solve a puzzle within a time limit might make the game impossible for some. Exceptions to this rule can sometimes succeed; ChuChu Rocket! offers both a time-limited multiplayer mode and an untimed mode.
A few games do not make the correct solution clear at the outset of the puzzle. The player not only has to understand how the puzzle works but she also has to guess at the solution she must try to achieve. This is bad game design: It forces the player to solve the puzzle by trial and error alone because there's no way to tell when she's on the right track. In order to open the stone sarcophagus at the end of Infidel, the player had to find the one correct combination of objects out of 24 possible combinations. The game gave no hints about which combination opened the box; the player simply had to try them all.
Solving most logic puzzles requires a certain amount of experimentation, but the player must be able to make deductions from his experiments. Do not make puzzles that can only be solved by trial and error.
 |
 |
Games don't usually test the player's mathematical abilities explicitly but often do require the player to reason about probabilities. Many games include an element of chance or require the player to make educated guesses about situations of which he has only an imperfect knowledge. Consider Microsoft Hearts (see Figure 9.4) as an example of a game giving imperfect information. Initially, the player does not know what cards the other players hold, but a skilled player can work out to a reasonable degree of certainty what those cards must be by using the information revealed as cards are passed and played during the game.
