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Roberto Lavieri wrote on Sat, Mar 29, 2008 12:44 AM UTC:

Originally published in Science Express on 19 July 2007
Science 14 September 2007:
Vol. 317. no. 5844, pp. 1518 - 1522
DOI: 10.1126/science.1144079
 Prev | Table of Contents | Next  

Research Articles
Checkers Is Solved
Jonathan Schaeffer,* Neil Burch, Yngvi Björnsson, Akihiro Kishimoto,
Martin Müller, Robert Lake, Paul Lu, Steve Sutphen 

The game of checkers has roughly 500 billion billion possible positions (5
x 1020). The task of solving the game, determining the final result in a
game with no mistakes made by either player, is daunting. Since 1989,
almost continuously, dozens of computers have been working on solving
checkers, applying state-of-the-art artificial intelligence techniques to
the proving process. This paper announces that checkers is now solved:
Perfect play by both sides leads to a draw. This is the most challenging
popular game to be solved to date, roughly one million times as complex as
Connect Four. Artificial intelligence technology has been used to generate
strong heuristic-based game-playing programs, such as Deep Blue for chess.
Solving a game takes this to the next level by replacing the heuristics
with perfection. 

Department of Computing Science, University of Alberta, Edmonton, Alberta
T6G 2E8, Canada. 

 Present address: Department of Computer Science, Reykjavik University,
Reykjavik, Kringlan 1, IS-103, Iceland. 

 Present address: Department of Media Architecture, Future University,
Hakodate, 116-2 Kamedanakano-cho Hakodate Hokkaido, 041-8655, Japan. 


* To whom correspondence should be addressed. E-mail:
[email protected]

Gary Gifford wrote on Sat, Mar 29, 2008 02:20 PM UTC:

Thanks Roberto for the very interesting comment. I was fairly big into checkers about 10 years ago and had read several books on it. Did you know that there are actually checker openings?

Anyway seeing that computers have solved a game (essentially a problem with 500 billion billion possible positions (5 x 1020); then I cannot help but wonder how many possible positions our various CVs have. With some of the very large games it must truly be a phenomenal number. Also, having large numbers of piece types... well, take Chess with Different Armies for example, the computers can have fun there. And Chu Shogi... wow!

In closing, the number for checkers is much higher than I would have expected.

Joe Joyce wrote on Sat, Mar 29, 2008 04:30 PM UTC:

Let me second that, Roberto. While I never played checkers past childhood,
I found it an interesting and often frustrating game then. That checkers
is so complex and took such time and effort to solve may well indicate
more complex games may resist complete analysis for a while, even with
better computers and algorithms. Thanks for the write-up [the article
summary, I believe]. Joe

Rich Hutnik wrote on Sat, Mar 29, 2008 07:18 PM UTC:

What they have done with checkers professionally is use a 3-Move randomized
opening.  They are also experimenting with randomly removing one of the
checkers at the start also, in addition to the 3-Move randomized opening. 
So, in a nutshell, they are going the Chess960 route with checkers to keep
it mixed up.  I believe another approach possible with checkers is gating
in different checkers from different version of checkers (aka,
IAGO/Seirawan Chess).  You could have a reserve of say Turkish or Polish
checkers, and then drop into a standard checker game.  Players decide when
to enter them.  By properly valuing the pieces, one could use the system as
a form of handicapping, but you also can do a random balanced shuffling of
which additional pieces enter the game.

This methodology will lead to the development of very sound principles
that can be taught, but not specific lines of play.

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