Theory Behind Maths Games Boards

The television show "Numb3rs" has popularized game theory.

Game theory, as summed up by the World Almanac for Kids, is "mathematical analysis of any situation involving a conflict of interest with the intent of indicating the optimal choices that, under given conditions, will lead to a desired outcome." Although game theory is a way of analyzing real world situations involving conflict, the history of this strategic way of thinking is rooted in familiar games such as checkers and tick-tack-toe. Children who are introduced to game theory may find it useful in resolving playground problems as well as in playing board games.

Why Introduce Kids to Game Theory?

Game theory is all about "the strategies people use when making decisions," according to Leah, who lives in Israel and writes a blog, Ingathered, that concerns subjects such as parenting and multiculturalism. Activities such as board games that involve decision making can create "an opening for meaningful discussions about choices and relationships."

Getting Into Game Theory Mode

Players learn about when to cut their losses.

Before considering how game theory can be applied to board games, it's helpful to consider the "Dollar Auction" game proposed by Ingathered. The parent auctions off a Monopoly $100 bill. The child who bids the greatest amount wins the play money and must pay that sum even if it exceeds $100. The second-largest bidder pays whatever he bid and gets nothing for it. It's easy to foresee the confusion and interesting debate that will arise. If the winner has to pay $101, but the loser pays $79, the winner still loses less. As Ingathered notes, adults often find themselves in situations where they persist "even when we are clearly in for a loss."

Monopoly and Game Theory

Another multicultural site, Noogenesis, provides a number of game-theory related activities for kids, including the classic Rock, Paper, Scissors. Noogenesis also considers the question of whether there must always be only one winner in a game of Monopoly. That was the intention of the inventor. Situations in which only one person can win are considered "zero sum" games. But Noogenesis says that if Monopoly players decide to cooperate so that a win-win ending occurs, then it is a non-zero sum game.

Mancala From a Game Theory Perspective

What are the best moves in Mancala?

Fritz Dooley wrote an academic thesis concerning whether it is possible to create a computer program for discerning possible outcomes of the game Mancala. Parents can pick up some ideas from Dooley for discussing strategies. But it isn't necessary to read Dooley's research paper to help a child reflect on the choices he makes when playing games. Parents can initiate discussions about which moves are better than others and why. The trick is to listen well to what the kids say and to let them develop their own thinking.

How to Win at Dots and Boxes

Dots and Boxes is one of those simple pastimes where you create your own game board on the spot. It is perfect to play while waiting in restaurants. Draw a grid of five rows of eight dots apiece. Then two players take turns drawing lines between the dots. When a player finds a spot where there are three edges, he can draw a fourth line to complete a box. The gameboard looks like a maze until it fills up with boxes. The player who creates the most boxes is the winner. Mathematician Elwyn Berlekamp had so many strategies for winning this game that he wrote a book, "The Dots and Boxes Game: Sophisticated Child's Play."

References

• Ingathered: Game Theory Exercises for Children
• World Almanac for Kids: Game Theory
• Noogenesis: Games, Dilemmas, and Traps
• Fritz Dooley: How to Play Mancala-and Win!
• Mathematical Association of America: Dots and Boxes

Resources

• FinancialRounds: Using Game Theory on Kids