Due September 12, 2002 at 3pm. Send problem sets to orwant@media.mit.edu.
1. Write two game proposals. Each proposal should include the title of the game, a description of the genre and gameplay, the intended audience, what skills the player will need to succeed, what beginning players will be thinking as he or she plays, and how that thinking will change as they become more experienced. At least one of the proposals should draw on material from an MIT class, and at least one of the proposals should have a gameplay wholly unlike any game currently in existence.
The games you propose needn’t have any chance of success in today’s market, but they should be games that you personally would find fun to play. The goal is simply to practice expressing the distinct features of two interesting games concisely. Each proposal should be a page or less.
2. Very approximately, how many possible games are there for: a) 3x3x3 tic tac toe, b) checkers, c) Champagne (which has 56 pieces), d) Othello (also called Reversi), and e) Go? (For all of these games, assume that a board state can never be repeated.) Show how you came up with the numbers. If a computer can evaluate a million moves a second, how much time is needed to “solve” (evaluate all moves) each of these games? Explain how a simple static evaluator would work for each of these games.
3. Choose a problem that can be represented with a game tree and describe the rules of a deterministic game for “playing” it. For instance, a cop trying to catch a robber in a grid of city streets, or a negotiation between labor and management over several issues (salaries, working hours, benefits).
4. Chess is ostensibly about war, but no one really thinks warlike thoughts while playing. The game can easily be "recontextualized" to have a different theme. For instance, if the two sides were corporations, the CEO might be the queen (the most powerful employee) and president of the corporation might be the king (the most important position, but not as active as the CEO). Come up with a new theme for chess, with new names for all the pieces and rough justifications for why they move the way they do.
5. Extra credit. Imagine a three-player version of Go, where three players alternate placing black, white, and red stones on the board. How would player strategies change? Why is it hard to generalize the minimax procedure to more than two players?