Mathematicians Explore Board Game's Real-World Applications

Photo: Enthusiasts and newcomers focus intently on a game of Go at Berkeley Games on Shattuck.
Anne Marie Schuler/Photo
Enthusiasts and newcomers focus intently on a game of Go at Berkeley Games on Shattuck.

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Photo: Enthusiasts and newcomers focus intently on a game of Go at Berkeley Games on Shattuck.   Photo: Herb Doughty, who founded Berkeley's original Go Club in 1967, plays at Berkeley Games on Shattuck.   

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In the ancient game of Go, two players face off to gain control of the board by moving stones strategically. When UC Berkeley mathematicians looked at the game, they found that the complexity behind the moves brought fresh insight into how to engineer separate parts of a complex system.

Elwyn Berlekamp gave a talk on Coupon Go, a version of the game he and former UC Berkeley students devised to measure how favorable one move is over the other, at this month's American Association for the Advancement of Science meeting.

A unique aspect of Go is that after the game has continued for some time, moves on separate regions of the board do not have much impact on other regions, allowing scientists to analyze different parts of the system separately.

Concepts of the game may be applicable to real-world systems, in which a large database could potentially be easier to organize if divided into separate components.

Berlekamp, a UC Berkeley professor emeritus in mathematics, electrical engineering and computer science, said he hopes his research can help people develop computer programs to deal with complex systems.

Due to the complexity of the game, computers are not yet able to play as well as professionals.

"Go is sort of the current game of choice for advancing artificial intelligence because to solve chess, all you have to do is look at lots of possibilities without sophisticated A.I., and it doesn't seem to be possible to attack Go in the same way," said David Wolfe, who received his computer science doctorate at UC Berkeley while working on the project with Berlekamp.

Significant progress has already been made. At the conference, a professional Go player lost marginally to a computer, which had a seven-turn head start. This was an impressive feat compared to two years ago, when the computer would have required a greater handicap.

"There was a major step forward in computers in the last year and a half, but there's still hundreds of thousands who can beat computers," Berlekamp said.

In Coupon Go, players can either take a coupon from the stack, which is arranged in order of decreasing point value, or make a move. If the player feels a move is more valuable than the coupon, they will make the move.

The addition of coupons to the game helped researchers assess how much experienced players value moves.

"Most players are trained to solve the whole board," Berlekamp said. "We try to learn about different parts of the board as simply as we can. Near the end of the game, it works well."

Scientists said they found the game useful as a simple, understandable model of more complex scenarios.

"Humans play the game and it's fun, but by looking at a simplified model of the world, you can get insight into the real world," Wolfe said. "One of the things in engineering that's hard to understand is the inter-relationship of different components of the system which affect the whole thing."


Christine Chen covers research and ideas. Contact her at [email protected]

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