Many card games involve an aspect of strategy in determining what cards other players have, thereby allowing a player to make a more mathematically safe maneuver. The difficulty arises with representing in a computer what we know about other players and ourselves. Classic approaches have relied on probability theory to represent the possibility of a certain outcome, however this can only represent possibilities and does not distinguish which players know this knowledge. The problem we examined was how to describe the knowledge possessed by a player and the importance of that knowledge in game playing within the confines of classic Minimax search.

Our approach to this problem was to determine a card game that relied on probability and conceptually use a Minimax search to play the game. We initially selected Rummy, but after exploring the numerous nuances of the game we deemed it too difficult and cumbersome to deal with. The game of War was also thrown out because it was overly simplistic and not interesting enough to analyze. Ultimately we ended up selecting Go Fish because it's limited number of actions made it a simple and very thought provoking game.

After repeated attempts to draw a simple state tree for Minimax we soon determined that the number of states would be enormous. We also determined that Minimax becomes N layered, where N is the number of players. Because of this we had to re-evaluate how we described the state of the game. Instead of looking at the tangibles of a state we focused on the knowledge struggle that is present in games with hidden information.

In games of perfect information (Othello, Chess, etc…) hidden knowledge is unimportant because all information is readily available to the player. Knowledge becomes more critical in games of imperfect information (such as Rummy and Spades) where more information will allow more accurate decision making. Our first realization was the division of knowledge into separate categories that allowed us to distinguish between the many different "levels" of knowledge. Below is a diagram representing the set of all information and the knowledge possessed by the game player.

Information can fall into four distinct categories:

Games such as Checkers only contain information known to all players, whereas Rummy contains all categories except shared knowledge (hand, played cards, and the deck respectively). For our study of card games we focused on the issues associated with public and private knowledge, and their role in playing card games.

We were then able to conclude that card games included a knowledge struggle between players; with a player’s goal being to uncover the opponents’ private knowledge while revealing little of its own. We determined this to be a considerable factor that needed to be handled when programming an intelligent game player in situations where complete knowledge of the game is unknown.

The application of this knowledge struggle could be applied to many situations and games. Future development would be to determine if distinguishing public and private knowledge would contribute to the decision making process. Does discerning who knows information help an agent play better? Is a knowledge struggle worth examining in games in which information is revealed? Can the information gained in analyzing this knowledge conflict be applied to the struggle between companies requesting knowledge about their consumers? These are all areas that could be derived from the study of knowledge privacy in game playing.

Russell, Stuart and Norvig, Peter, Artificial Intelligence: A Modern Approach. Prentice-Hall, 1995