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Introduction To A Simple Game Having Many Prospects Md. Asfak Mahamud [email_address] KAZ Software Ltd. Dhaka, Bangladesh Dated: March 09, 2010 ,[object Object],[object Object]
Index ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Index ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],http://richardwiseman.files.wordpress.com/2009/05/question-mark3a.jpg
What it is (1/4). ,[object Object],[object Object],[object Object],Chess  ---  Arimaa ------------------------------- King  Elephant Queen  Camel Rook  Horse Bishop  Dog Knight  Cat Pawn  Rabbit
 
What it is (3/4). Rules:  http://arimaa.com/arimaa/rules/   Online Gameroom:  http:// www.arimaa.com/arimaa/gameroom /   Puzzles:  http://arimaa.com/arimaa/puzzles/list.cgi   Match Rules:  http://arimaa.com/arimaa/rules/matchRules.html   Bot ladders:  http://www.arimaa.com/arimaa/gameroom/botLadder.cgi   Arimaa Notation:  http:// arimaa.com/arimaa/rules/notation.htm
What it is (4/4). ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],David A. Wheeler   Linux Security Consultant http://www.dwheeler.com/blog/2004/ “ Its rules are very simple, much simpler than chess -- kids can learn the rules in a few minutes. Yet with those simple rules you end up with a very strategic and interesting game."
Index ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],http://www.chess-theory.com/images_links/image_002.jpg
History (1/10) The Turk  was a fake chess-playing machine constructed in the late 18th century invented by  Wolfgang von Kempelen .  From 1770 until its destruction by fire in 1854,it was exhibited by various owners as  an automaton, though it was explained in the early 1820s as an elaborate hoax. The Turk was in fact a mechanical illusion that allowed a human chess master hiding inside to operate  the machine. With a skilled operator, the Turk won most of the games played during its demonstrations around  Europe and the Americas for nearly 84 years, playing and defeating many challengers including statesmen  such as Napoleon Bonaparte and Benjamin Franklin.   Arimaa history is rooted at that of Chess
History (2/10) “ Chess is generally considered to require ‘thinking’ for skilful play; a solution of this problem will force us either to admit the possibility of a mechanized thinking or to further restrict our concept of ‘thinking’.” “ Shannon noted  the  theoretical existence of a perfect solution to Chess  and the  practical  impossibility  of  finding  it.” Source: “ANALYSIS AND IMPLEMENTATION  OF THE GAME ARIMAA”  by  Christ-Jan Cox Universiteit Maastricht  Maastricht ICT Competence Centre  Institute for Knowledge and Agent Technology  Maastricht, The Netherlands  March 2006 Claude Shannon Link: http://portal.acm.org/citation.cfm?id=67002
History (3/10) Alan Turing The "Turing" machine was  described by  Alan Turing  in 1937. Turing Machine = Algorithm Universal Turing Machine = Computer 1951,  Alan Turing  develops on paper the first program capable of playing a full game of chess.  Its play  is best described as “aimless”; it loses to weak players.
History (4/10) Given enough time and memory, any computer can run any algorithm. Image source: http://www.credenda.net/efit/ So all that is left of computer science is building a faster computer, right? ,[object Object],[object Object]
History (5/10) Game Algorithm #1: Tree Chess game-tree complexity: (2^5)^80 = 2^400 ≈ 10^120 Tic-tac-toe game-tree complexity:  10^5 ,[object Object],[object Object],Game Algorithm #2: Dictionary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Tic-tac-toe state-space complexity:  10^3 Chess state-space complexity: More than 64!/(32!8!226) ≈ 10^43 Actually ≈ 10^50 Game Algorithm #3: Tree + Evaluation Shannon speculates: Algorithm #3 is too slow Improved evaluation not enough Must not search worthless branches Must extend critical branches
History (6/10) You can visit the IBM page :  http:// www.research.ibm.com/deepblue/home/html/b.shtml The creation of Arimaa was inspired by the  Deep Blue  vs  Gary Kasparov match  in which the computer defeated the world chess champion.  Arimaa was created to show that  humans can still outplay computers  using a chess set and provide  the  next challenge  to the AI community.   Computer Chess Time - Level 60s  – beginner 70s  – intermediate 80s  – grand master Finally in 1997 …
History (7/10) “ When will computer hardware match the human brain?”   - 1997   http://www.transhumanist.com/volume1/moravec.htm Hans Moravec Robotics Institute  Carnegie Mellon University   “ At the present rate, computers suitable for humanlike robots will appear  in the 2020s”
History (8/10) Marvin Minsky  - Father of AI 2000  -  " No one has tried to make a thinking machine …  The bottom line is that we really haven't progressed  too far toward a truly intelligent machine.  We have collections of dumb specialists in small  domains; the true majesty of general intelligence  still awaits our attack.  We have got to get back to the deepest questions  of AI and general intelligence and quit wasting time  on little projects that don't contribute to the main  goal. “ [as interviewed in "Hal's Legacy", Edited by David Stork]  Source:  http://mitpress.mit.edu/e-books/Hal/chap2/two4.html http:// www.agiri.org/forum/index.php?showtopic =45
History (9/10) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Omar Syed Link: http://arimaa.com/arimaa/papers/030801ICGA/ Aamir Syed Aamir Syed  is a student at Birchwood Elementary School.  He hopes to be a NASA Engineer someday so he can build robots that explore other planets.
History (10/10) Bill Gates  - Founder, Microsoft 2004  - " If you invent a breakthrough in  artificial intelligence, so machines can  learn, that is worth 10 Microsofts. "  http:// www.agiri.org/forum/index.php?showtopic =45
Index ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],http://michaelhyatt.com/wp-content/uploads/2009/02/goal-setting-the-90-day-challenge.jpg
Challenge The first  person ,  company  or  organization  that develops a  program  which  can defeat the top human Arimaa players in an official Arimaa  challenge match before the year 2020 will win the Arimaa challenge prize.  The prize is currently $16,250   USD.  The official challenge match will be between the current best program and three selected human players.  To know more about the current challenge:   http://arimaa.com/arimaa/challenge/2010/ Challenge Match:   Apr 4, 2010 to Apr 24, 2010
Index ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],http://farm1.static.flickr.com/120/299078131_507febc71a_m.jpg
Why this is hard (1/6) “ Human intelligence, refusing to be put on the back foot,  is taking refuge in creative ingenuity, inventing games like  Arimaa ,  which are specifically designed to be easy for humans but hard for artificial intelligence. “ BBC 28 August 2007   State of Play: Man versus machine By Margaret Robertson  Video game consultant and writer  Margaret Robertson  She has written extensively about games for Wired and the BBC,  and has edited Edge, the world's most respected videogame magazine.  Now as a game designer and consultant, she works on videogame projects of all sizes,  for mainstream (EA, Sony, DICE) and indie(Kuju, Zoonami) developers,  as well as for educational organisations, broadcasters and major studios.   Bram Cohen  is an American computer programmer,  best known as the author of the  peer-to-peer  (P2P)  BitTorrent  protocol ,  as well as the first file sharing program to use the protocol, also known as  BitTorrent .   Arimaa's  a better game than I thought. It follows a fairly sound approach to making the game difficult for computers.
Why this is hard (2/6) ,[object Object],Tic-tac-toe – Game tree complexity. A simple upper bound for the size of the game tree is 9! = 362,880.  (There are nine positions for the first move, eight for the second, and so on.)  This includes illegal games that continue after one side has won.  A more careful count gives 255,168 possible games.  When rotations and reflections of positions are considered the same, there are only  26,830  possible games.  Game-tree complexity  is the size of the game tree: that is,  the total number of possible games that can be played.  Game tree size of various games as powers of 10 Tic-tac-toe :  5  (10^5 or 100,000) Chess  :  123 Arimaa  :  296 http://www.codescope.com/docs/tictac.aspx
Why this is hard (2/6) Complexity Analysis The  complexity  of  a  game  is  measured  by  two  different  factors,  the  state-space complexity   and  the  game-tree  complexity .  The  state-space  complexity   roughly indicates the number of different board positions that are possible in principle. In Arimaa it is almost  1.66x10 43 . The  game–tree  complexity   is  an  indication  of  how  many  nodes  there  are  in  the  solution  tree.  The  number depends on  the specific search  techniques used. In Arimaa it is almost 3.1x10 300 . “ Analysis and Implementation of the game ARIMAA “ by  Christ-Jan Cox Universiteit Maastricht  Maastricht ICT Competence Centre, Institute for Knowledge and Agent Technology  Maastricht, The Netherlands, March 2006 http://arimaa.com/arimaa/papers/CoxThesis/Cox_thesis1.pdf
Why this is hard (3/6) Source:  “ Methods of MCTS and the game Arimaa”   by  Tom´aˇs Kozelek  ( Dec 2009 ) Department of Theoretical Computer Science and Mathematical Logic, Faculty of Mathematics and Physics,  Charles University in Prague Huge branching factor Arimaa was intentionally created as a game with an enormous branching factor. The number of moves in an average position: In Chess is around 35  (2 5 =32) ,  In Go it is around 200,  In Arimaa this number rockets to 17,000  (2 14 =16384)  unique moves on average and in complicated middle game situations up to 50,000 unique moves. http://static.panoramio.com/photos/original/11952977.jpg Assume one million positions per second Chess five-move search:  (2 5 ) (10/2)  = 2 25  = 34 million = 34 seconds Arimaa five-move search:  (2 14 ) (10/2)  = 2 70  ≈ 10 21 million ≈  31 688 764.6 years >  30 million years * * More accurately 37.44 million years ,[object Object],[object Object],[object Object]
Why this is hard (4/6) Source:  “ Methods of MCTS and the game Arimaa”   by  Tom´aˇs Kozelek  (Dec 2009) Department of Theoretical Computer Science and Mathematical Logic Faculty of Mathematics and Physics Charles University in Prague Stability Tactical combinations are much less common than in chess. There are mainly two reasons for this:  1. the fact that a move consists of 4 steps and  2. the absence of “long shooting” pieces.  This  longterm planning is a huge weapon in the hands of the humans  who can beat computers with systematic cumulation of little strategic advantages. http://media.photobucket.com/image/human%20thinking/VedaSun/Mind-1.jpg
Why this is hard (5/6) Source:  “ Methods of MCTS and the game Arimaa”   by  Tom´aˇs Kozelek  (Dec 2009) Department of Theoretical Computer Science and Mathematical Logic Faculty of Mathematics and Physics Charles University in Prague Opening Initial positioning of pieces is not prescribed which virtually makes opening books obsolete.  It has not been agreed on yet which opening setup is the best (or if there exists such a concept at all).
Why this is hard (6/6) Source:  “ Methods of MCTS and the game Arimaa”   by  Tom´aˇs Kozelek  (Dec 2009) Department of Theoretical Computer Science and Mathematical Logic Faculty of Mathematics and Physics Charles University in Prague No endgame While in chess or Go the position usually gets simpler when approaching the end of the game, this might well not be the case in Arimaa where most of the games are decided in the late middle game.
Index ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Current Status(1/) Challenge history:  To see more you can visit:  http:// en.wikipedia.org/wiki/Arimaa   Current Status
Current Status (2/2) ,[object Object],Karl Juhnke (Fritzlein) Karl Juhnke (Fritzlein) discovered Arimaa in 2004 and within one year became one of the  top Arimaa  players in the world winning the annual Arimaa World Championship in 2005 and 2008 . He is also  writer of  the book “Beginning Arimaa”.  With a  background in applied mathametics  he is currently employed as a  quantitative analyst at  Yahoo Inc .  ,[object Object]
Index ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],http://www.marinmagazine.com/images/cache/c37f186e5b6fd4d04d87e3e88b02db32.jpeg
How I can participate (1/4) ,[object Object],[object Object],[object Object],2. As a developer you can 1. build your own bot to play games. 2. participate in Arimaa Computer World Championship. 3. take a chance to win the challenge 2020. 3. As a predictor you can  1. predict the world championship matches and win prize.
How I can participate (2/4) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
How I can participate (3/4) 9. Go to  http://www.activestate.com/activeperl/  , download and install Perl. 10. Write click on the ‘bot’ file and run with Perl Interpreter (You can also run it from  command Panel by “perl bot”. 11. The bot will then log into the  www.arimaa.com/arimaa/gameroom  and will wait for  somebody to play with. 12. Now log in at  www.arimaa.com/arimaa/gameroom  with your own account and you will find your bot is waiting to play a game. 13. Click on the “sit” and start to play a game with this bot.
How I can participate (2/)
Index ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],KAZ
How We can participate (1/2) If few of us feel to do something we can 1. build a bot to play games. 2. participate in Arimaa Computer World Championship. 3. take a chance to win the challenge 2020. bot_kazarimaa??
How We can participate  (2/2) (In future)
Index ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],http://lifeboat.com/images/conclusion.jpg
Conclusion Intent of the challenge:   The main intent of the Arimaa challenge is to promote  research in AI , which can help to advance the  field and potentially have applications in other areas.  Some areas of AI that would be involved depending on the approach taken include  pattern recognition, machine learning, neural networks, evolutionary algorithms, and expert systems .  It is hoped that in the processes of achieving the Arimaa challenge some new techniques are developed  in one or more of these areas that can also be applied to other problems.  The Arimaa challenge is designed to be met if  significant progress is made in software and not from the  advances in hardware , which are almost guaranteed.  As such the challenge will define the hardware and OS to be used and participants need only to develop the  software.  Advancing the state of the art:   It is recommended that the participants (especially those with programs in the computer tournament)  submit  articles to the ICGA technical journal describing their research and results .  If a program wins the Arimaa challenge, it  must be described in a paper submitted to the ICGA technical  journal  after winning the challenge in order to receive any prize.  http://arimaa.com/arimaa/challenge/2010/
References ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Thank You. Arimaa World League 2010 http://arimaa.com/arimaa/mwiki/index.php/2010_Arimaa_World_League   Image source: http://www.boardgamegeek.com/image/614887/arimaa

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Arimaa

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  • 6. What it is (3/4). Rules: http://arimaa.com/arimaa/rules/ Online Gameroom: http:// www.arimaa.com/arimaa/gameroom / Puzzles: http://arimaa.com/arimaa/puzzles/list.cgi Match Rules: http://arimaa.com/arimaa/rules/matchRules.html Bot ladders: http://www.arimaa.com/arimaa/gameroom/botLadder.cgi Arimaa Notation: http:// arimaa.com/arimaa/rules/notation.htm
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  • 9. History (1/10) The Turk was a fake chess-playing machine constructed in the late 18th century invented by Wolfgang von Kempelen . From 1770 until its destruction by fire in 1854,it was exhibited by various owners as an automaton, though it was explained in the early 1820s as an elaborate hoax. The Turk was in fact a mechanical illusion that allowed a human chess master hiding inside to operate the machine. With a skilled operator, the Turk won most of the games played during its demonstrations around Europe and the Americas for nearly 84 years, playing and defeating many challengers including statesmen such as Napoleon Bonaparte and Benjamin Franklin. Arimaa history is rooted at that of Chess
  • 10. History (2/10) “ Chess is generally considered to require ‘thinking’ for skilful play; a solution of this problem will force us either to admit the possibility of a mechanized thinking or to further restrict our concept of ‘thinking’.” “ Shannon noted the theoretical existence of a perfect solution to Chess and the practical impossibility of finding it.” Source: “ANALYSIS AND IMPLEMENTATION OF THE GAME ARIMAA” by Christ-Jan Cox Universiteit Maastricht Maastricht ICT Competence Centre Institute for Knowledge and Agent Technology Maastricht, The Netherlands March 2006 Claude Shannon Link: http://portal.acm.org/citation.cfm?id=67002
  • 11. History (3/10) Alan Turing The "Turing" machine was described by Alan Turing in 1937. Turing Machine = Algorithm Universal Turing Machine = Computer 1951, Alan Turing develops on paper the first program capable of playing a full game of chess. Its play is best described as “aimless”; it loses to weak players.
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  • 14. History (6/10) You can visit the IBM page : http:// www.research.ibm.com/deepblue/home/html/b.shtml The creation of Arimaa was inspired by the Deep Blue vs Gary Kasparov match in which the computer defeated the world chess champion. Arimaa was created to show that humans can still outplay computers using a chess set and provide the next challenge to the AI community. Computer Chess Time - Level 60s – beginner 70s – intermediate 80s – grand master Finally in 1997 …
  • 15. History (7/10) “ When will computer hardware match the human brain?” - 1997 http://www.transhumanist.com/volume1/moravec.htm Hans Moravec Robotics Institute Carnegie Mellon University “ At the present rate, computers suitable for humanlike robots will appear in the 2020s”
  • 16. History (8/10) Marvin Minsky - Father of AI 2000 - " No one has tried to make a thinking machine … The bottom line is that we really haven't progressed too far toward a truly intelligent machine. We have collections of dumb specialists in small domains; the true majesty of general intelligence still awaits our attack. We have got to get back to the deepest questions of AI and general intelligence and quit wasting time on little projects that don't contribute to the main goal. “ [as interviewed in "Hal's Legacy", Edited by David Stork] Source: http://mitpress.mit.edu/e-books/Hal/chap2/two4.html http:// www.agiri.org/forum/index.php?showtopic =45
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  • 18. History (10/10) Bill Gates - Founder, Microsoft 2004 - " If you invent a breakthrough in artificial intelligence, so machines can learn, that is worth 10 Microsofts. " http:// www.agiri.org/forum/index.php?showtopic =45
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  • 20. Challenge The first person , company or organization that develops a program which can defeat the top human Arimaa players in an official Arimaa challenge match before the year 2020 will win the Arimaa challenge prize. The prize is currently $16,250 USD. The official challenge match will be between the current best program and three selected human players. To know more about the current challenge: http://arimaa.com/arimaa/challenge/2010/ Challenge Match: Apr 4, 2010 to Apr 24, 2010
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  • 22. Why this is hard (1/6) “ Human intelligence, refusing to be put on the back foot, is taking refuge in creative ingenuity, inventing games like Arimaa , which are specifically designed to be easy for humans but hard for artificial intelligence. “ BBC 28 August 2007 State of Play: Man versus machine By Margaret Robertson Video game consultant and writer Margaret Robertson She has written extensively about games for Wired and the BBC, and has edited Edge, the world's most respected videogame magazine. Now as a game designer and consultant, she works on videogame projects of all sizes, for mainstream (EA, Sony, DICE) and indie(Kuju, Zoonami) developers, as well as for educational organisations, broadcasters and major studios. Bram Cohen is an American computer programmer, best known as the author of the peer-to-peer (P2P) BitTorrent protocol , as well as the first file sharing program to use the protocol, also known as BitTorrent . Arimaa's a better game than I thought. It follows a fairly sound approach to making the game difficult for computers.
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  • 24. Why this is hard (2/6) Complexity Analysis The complexity of a game is measured by two different factors, the state-space complexity and the game-tree complexity . The state-space complexity roughly indicates the number of different board positions that are possible in principle. In Arimaa it is almost 1.66x10 43 . The game–tree complexity is an indication of how many nodes there are in the solution tree. The number depends on the specific search techniques used. In Arimaa it is almost 3.1x10 300 . “ Analysis and Implementation of the game ARIMAA “ by Christ-Jan Cox Universiteit Maastricht Maastricht ICT Competence Centre, Institute for Knowledge and Agent Technology Maastricht, The Netherlands, March 2006 http://arimaa.com/arimaa/papers/CoxThesis/Cox_thesis1.pdf
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  • 26. Why this is hard (4/6) Source: “ Methods of MCTS and the game Arimaa” by Tom´aˇs Kozelek (Dec 2009) Department of Theoretical Computer Science and Mathematical Logic Faculty of Mathematics and Physics Charles University in Prague Stability Tactical combinations are much less common than in chess. There are mainly two reasons for this: 1. the fact that a move consists of 4 steps and 2. the absence of “long shooting” pieces. This longterm planning is a huge weapon in the hands of the humans who can beat computers with systematic cumulation of little strategic advantages. http://media.photobucket.com/image/human%20thinking/VedaSun/Mind-1.jpg
  • 27. Why this is hard (5/6) Source: “ Methods of MCTS and the game Arimaa” by Tom´aˇs Kozelek (Dec 2009) Department of Theoretical Computer Science and Mathematical Logic Faculty of Mathematics and Physics Charles University in Prague Opening Initial positioning of pieces is not prescribed which virtually makes opening books obsolete. It has not been agreed on yet which opening setup is the best (or if there exists such a concept at all).
  • 28. Why this is hard (6/6) Source: “ Methods of MCTS and the game Arimaa” by Tom´aˇs Kozelek (Dec 2009) Department of Theoretical Computer Science and Mathematical Logic Faculty of Mathematics and Physics Charles University in Prague No endgame While in chess or Go the position usually gets simpler when approaching the end of the game, this might well not be the case in Arimaa where most of the games are decided in the late middle game.
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  • 30. Current Status(1/) Challenge history: To see more you can visit: http:// en.wikipedia.org/wiki/Arimaa Current Status
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  • 35. How I can participate (3/4) 9. Go to http://www.activestate.com/activeperl/ , download and install Perl. 10. Write click on the ‘bot’ file and run with Perl Interpreter (You can also run it from command Panel by “perl bot”. 11. The bot will then log into the www.arimaa.com/arimaa/gameroom and will wait for somebody to play with. 12. Now log in at www.arimaa.com/arimaa/gameroom with your own account and you will find your bot is waiting to play a game. 13. Click on the “sit” and start to play a game with this bot.
  • 36. How I can participate (2/)
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  • 38. How We can participate (1/2) If few of us feel to do something we can 1. build a bot to play games. 2. participate in Arimaa Computer World Championship. 3. take a chance to win the challenge 2020. bot_kazarimaa??
  • 39. How We can participate (2/2) (In future)
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  • 41. Conclusion Intent of the challenge: The main intent of the Arimaa challenge is to promote research in AI , which can help to advance the field and potentially have applications in other areas. Some areas of AI that would be involved depending on the approach taken include pattern recognition, machine learning, neural networks, evolutionary algorithms, and expert systems . It is hoped that in the processes of achieving the Arimaa challenge some new techniques are developed in one or more of these areas that can also be applied to other problems. The Arimaa challenge is designed to be met if significant progress is made in software and not from the advances in hardware , which are almost guaranteed. As such the challenge will define the hardware and OS to be used and participants need only to develop the software. Advancing the state of the art: It is recommended that the participants (especially those with programs in the computer tournament) submit articles to the ICGA technical journal describing their research and results . If a program wins the Arimaa challenge, it must be described in a paper submitted to the ICGA technical journal after winning the challenge in order to receive any prize. http://arimaa.com/arimaa/challenge/2010/
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  • 43. Thank You. Arimaa World League 2010 http://arimaa.com/arimaa/mwiki/index.php/2010_Arimaa_World_League Image source: http://www.boardgamegeek.com/image/614887/arimaa